document_title: Orbit

question_text: what do you call the point farthest from a satellite's orbit to a planet

question_tokens: what do you call the point farthest from a satellite 's orbit to a planet

root

text: Orbit

text: History[edit]

text:
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tag: table

text: Historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached. It assumed the heavens were fixed apart from the motion of the spheres, and was developed without any understanding of gravity. After the planets' motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added. Although the model was capable of reasonably accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became increasingly unwieldy. Originally geocentric it was modified by Copernicus to place the sun at the centre to help simplify the model. The model was further challenged during the 16th century, as comets were observed traversing the spheres.[4][5]

tag: p

text: The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus.[6] Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits.

text: Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common center of mass. Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.

text: Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange (1736–1813) developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three body problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus.

text: Albert Einstein (1879-1955) in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes propagate instantaneously. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions (except where there are very strong gravity fields and very high speeds) but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate.

text: Planetary orbits[edit]

text: Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet.

text: Owing to mutual gravitational perturbations, the eccentricities of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune.

text: As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.)

text: In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and that energy is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.

text: Understanding orbits[edit]

text: There are a few common ways of understanding orbits:

text:
A force, such as gravity, pulls an object into a curved path as it attempts to fly off in a straight line.
As the object is pulled toward the massive body, it falls toward that body. However, if it has enough tangential velocity it will not fall into the body but will instead continue to follow the curved trajectory caused by that body indefinitely. The object is then said to be orbiting the body.

tag: ul

text: As an illustration of an orbit around a planet, the Newton's cannonball model may prove useful (see image below). This is a 'thought experiment', in which a cannon on top of a tall mountain is able to fire a cannonball horizontally at any chosen muzzle speed. The effects of air friction on the cannonball are ignored (or perhaps the mountain is high enough that the cannon will be above the Earth's atmosphere, which comes to the same thing).[7]

text: If the cannon fires its ball with a low initial speed, the trajectory of the ball curves downward and hits the ground (A). As the firing speed is increased, the cannonball hits the ground farther (B) away from the cannon, because while the ball is still falling towards the ground, the ground is increasingly curving away from it (see first point, above). All these motions are actually "orbits" in a technical sense – they are describing a portion of an elliptical path around the center of gravity – but the orbits are interrupted by striking the Earth.

text: If the cannonball is fired with sufficient speed, the ground curves away from the ball at least as much as the ball falls – so the ball never strikes the ground. It is now in what could be called a non-interrupted, or circumnavigating, orbit. For any specific combination of height above the center of gravity and mass of the planet, there is one specific firing speed (unaffected by the mass of the ball, which is assumed to be very small relative to the Earth's mass) that produces a circular orbit, as shown in (C).

text: As the firing speed is increased beyond this, non-interrupted elliptic orbits are produced; one is shown in (D). If the initial firing is above the surface of the Earth as shown, there will also be non-interrupted elliptical orbits at slower firing speed; these will come closest to the Earth at the point half an orbit beyond, and directly opposite the firing point, below the circular orbit.

text: At a specific horizontal firing speed called escape velocity, dependent on the mass of the planet, an open orbit (E) is achieved that has a parabolic path. At even greater speeds the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space" never to return.

text: The velocity relationship of two moving objects with mass can thus be considered in four practical classes, with subtypes:

text:
No orbit
Suborbital trajectories

Range of interrupted elliptical paths

Orbital trajectories (or simply "orbits")

Range of elliptical paths with closest point opposite firing point
Circular path
Range of elliptical paths with closest point at firing point

Open (or escape) trajectories

Parabolic paths
Hyperbolic paths

tag: ol

text: It is worth noting that orbital rockets are launched vertically at first to lift the rocket above the atmosphere (which causes frictional drag), and then slowly pitch over and finish firing the rocket engine parallel to the atmosphere to achieve orbit speed.

text: Once in orbit, their speed keeps them in orbit above the atmosphere. If e.g., an elliptical orbit dips into dense air, the object will lose speed and re-enter (i.e. fall). Occasionally a space craft will intentionally intercept the atmosphere, in an act commonly referred to as an aerobraking maneuver

text: Newton's laws of motion[edit]

text: Newton's law of gravitation and laws of motion for two-body problems[edit]

text: In most situations relativistic effects can be neglected, and Newton's laws give a sufficiently accurate description of motion. The acceleration of a body is equal to the sum of the forces acting on it, divided by its mass, and the gravitational force acting on a body is proportional to the product of the masses of the two attracting bodies and decreases inversely with the square of the distance between them. To this Newtonian approximation, for a system of two point masses or spherical bodies, only influenced by their mutual gravitation (called a two-body problem), their trajectories can be exactly calculated. If the heavier body is much more massive than the smaller, as in the case of a satellite or small moon orbiting a planet or for the Earth orbiting the Sun, it is accurate enough and convenient to describe the motion in terms of a coordinate system that is centered on the heavier body, and we say that the lighter body is in orbit around the heavier. For the case where the masses of two bodies are comparable, an exact Newtonian solution is still sufficient and can be had by placing the coordinate system at the center of mass of the system.

text: Defining gravitational potential energy[edit]

text: Energy is associated with gravitational fields. A stationary body far from another can do external work if it is pulled towards it, and therefore has gravitational potential energy. Since work is required to separate two bodies against the pull of gravity, their gravitational potential energy increases as they are separated, and decreases as they approach one another. For point masses the gravitational energy decreases to zero as they approach zero separation. It is convenient and conventional to assign the potential energy as having zero value when they are an infinite distance apart, and hence it has a negative value (since it decreases from zero) for smaller finite distances.

text: Orbital energies and orbit shapes[edit]

text: When only two gravitational bodies interact, their orbits follow a conic section. The orbit can be open (implying the object never returns) or closed (returning). Which it is depends on the total energy (kinetic + potential energy) of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, the speed is always less than the escape velocity. Since the kinetic energy is never negative, if the common convention is adopted of taking the potential energy as zero at infinite separation, the bound orbits will have negative total energy, the parabolic trajectories zero total energy, and hyperbolic orbits positive total energy.

text: An open orbit will have a parabolic shape if it has velocity of exactly the escape velocity at that point in its trajectory, and it will have the shape of a hyperbola when its velocity is greater than the escape velocity. When bodies with escape velocity or greater approach each other, they will briefly curve around each other at the time of their closest approach, and then separate, forever. This may be the case with most comets if they come from outside the solar system.

text: All closed orbits have the shape of an ellipse. A circular orbit is a special case, wherein the foci of the ellipse coincide. The point where the orbiting body is closest to Earth is called the perigee, and is called the periapsis (less properly, "perifocus" or "pericentron") when the orbit is about a body other than Earth. The point where the satellite is farthest from Earth is called the apogee, apoapsis, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part.

text: Kepler's laws[edit]

text: Bodies following closed orbits repeat their paths with a certain time called the period. This motion is described by the empirical laws of Kepler, which can be mathematically derived from Newton's laws. These can be formulated as follows:

text:
The orbit of a planet around the Sun is an ellipse, with the Sun in one of the focal points of that ellipse. [This focal point is actually the barycenter of the Sun-planet system; for simplicity this explanation assumes the Sun's mass is infinitely larger than that planet's.] The planet's orbit lies in a plane, called the orbital plane. The point on the orbit closest to the attracting body is the periapsis. The point farthest from the attracting body is called the apoapsis. There are also specific terms for orbits about particular bodies; things orbiting the Sun have a perihelion and aphelion, things orbiting the Earth have a perigee and apogee, and things orbiting the Moon have a perilune and apolune (or periselene and aposelene respectively). An orbit around any star, not just the Sun, has a periastron and an apastron.
As the planet moves in its orbit, the line from the Sun to planet sweeps a constant area of the orbital plane for a given period of time, regardless of which part of its orbit the planet traces during that period of time. This means that the planet moves faster near its perihelion than near its aphelion, because at the smaller distance it needs to trace a greater arc to cover the same area. This law is usually stated as "equal areas in equal time."
For a given orbit, the ratio of the cube of its semi-major axis to the square of its period is constant.

text: Limitations of Newton's law of gravitation[edit]

text: Note that while bound orbits of a point mass or a spherical body with a Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects (such as caused by the slight oblateness of the Earth, or by relativistic effects, thereby changing the gravitational field's behavior with distance) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion. The two-body solutions were published by Newton in Principia in 1687. In 1912, Karl Fritiof Sundman developed a converging infinite series that solves the three-body problem; however, it converges too slowly to be of much use. Except for special cases like the Lagrangian points, no method is known to solve the equations of motion for a system with four or more bodies.

text: Approaches to many-body problems[edit]

text: Rather than an exact closed form solution, orbits with many bodies can be approximated with arbitrarily high accuracy. These approximations take two forms:

text: Differential simulations with large numbers of objects perform the calculations in a hierarchical pairwise fashion between centers of mass. Using this scheme, galaxies, star clusters and other large assemblages of objects have been simulated.[citation needed]

text: Newtonian analysis of orbital motion[edit]

text: The Earth follows an ellipse round the sun. But unlike the ellipse followed by a pendulum or an object attached to a spring, the sun is at a focal point of the ellipse and not at its centre.

text: The following derivation applies to such an elliptical orbit. We start only with the Newtonian law of gravitation stating that the gravitational acceleration towards the central body is related to the inverse of the square of the distance between them, namely

text: Where F2 is the force acting on the mass m2 caused by the gravitational attraction mass m1 has for m2, G is the universal gravitational constant, and r is the distance between the two masses centers.

text: From Newton's Second Law, the summation of the forces acting on m2 related to that bodies acceleration:

text: Where A2 is the acceleration of m2 caused by the force of gravitational attraction F2 of m1 acting on m2.

text: Combining Eq 1 and 2:

text: Solving for the acceleration, A2:

text:
where

μ

{\displaystyle \mu \,}

 is the standard gravitational parameter, in this case

G

m

1

{\displaystyle Gm_{1}}

. It is understood that the system being described is m2, hence the subscripts can be dropped.

text: We assume that the central body is massive enough that it can be considered to be stationary and we ignore the more subtle effects of general relativity.

text:
When a pendulum or an object attached to a spring swings in an ellipse, the inward acceleration/force is proportional to the distance

A
=
F

/

m
=
−
k
r
.

{\displaystyle A=F/m=-kr.}

 Due to the way vectors add, the component of the force in the

x

^

{\displaystyle {\hat {\mathbf {x}}}}

 or in the

y

^

{\displaystyle {\hat {\mathbf {y}}}}

 directions are also proportionate to the respective components of the distances,

r

x

″

=

A

x

=
−
k

r

x

{\displaystyle r''_{x}=A_{x}=-kr_{x}}

. Hence, the entire analysis can be done separately in these dimensions. This results in the harmonic parabolic equations

x
=
A
cos

(
t
)

{\displaystyle x=A\cos(t)}

 and

y
=
B
sin

(
t
)

{\displaystyle y=B\sin(t)}

 of the ellipse. In contrast, with the decreasing relationship

A
=
μ

/

r

2

{\displaystyle A=\mu /r^{2}}

, the dimensions cannot be separated.[citation needed]

text:
The location of the orbiting object at the current time

t

{\displaystyle t}

 is located in the plane using Vector calculus in polar coordinates both with the standard Euclidean basis and with the polar basis with the origin coinciding with the center of force. Let

r

{\displaystyle r}

 be the distance between the object and the center and

θ

{\displaystyle \theta }

 be the angle it has rotated. Let

x

^

{\displaystyle {\hat {\mathbf {x}}}}

 and

y

^

{\displaystyle {\hat {\mathbf {y}}}}

 be the standard Euclidean bases and let

r

^

=
cos

(
θ
)

x

^

+
sin

(
θ
)

y

^

{\displaystyle {\hat {\mathbf {r}}}=\cos(\theta ){\hat {\mathbf {x}}}+\sin(\theta ){\hat {\mathbf {y}}}}

 and

θ
^

=
−
sin

(
θ
)

x

^

+
cos

(
θ
)

y

^

{\displaystyle {\hat {\boldsymbol {\theta }}}=-\sin(\theta ){\hat {\mathbf {x}}}+\cos(\theta ){\hat {\mathbf {y}}}}

 be the radial and transverse polar basis with the first being the unit vector pointing from the central body to the current location of the orbiting object and the second being the orthogonal unit vector pointing in the direction that the orbiting object would travel if orbiting in a counter clockwise circle. Then the vector to the orbiting object is

text:
We use

r
˙

{\displaystyle {\dot {r}}}

 and

θ
˙

{\displaystyle {\dot {\theta }}}

 to denote the standard derivatives of how this distance and angle change over time. We take the derivative of a vector to see how it changes over time by subtracting its location at time

t

{\displaystyle t}

 from that at time

t
+
δ
t

{\displaystyle t+\delta t}

 and dividing by

δ
t

{\displaystyle \delta t}

. The result is also a vector. Because our basis vector

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 moves as the object orbits, we start by differentiating it. From time

t

{\displaystyle t}

 to

t
+
δ
t

{\displaystyle t+\delta t}

, the vector

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 keeps its beginning at the origin and rotates from angle

θ

{\displaystyle \theta }

 to

θ
+

θ
˙

δ
t

{\displaystyle \theta +{\dot {\theta }}\ \delta t}

 which moves its head a distance

θ
˙

δ
t

{\displaystyle {\dot {\theta }}\ \delta t}

 in the perpendicular direction

θ
^

{\displaystyle {\hat {\boldsymbol {\theta }}}}

 giving a derivative of

θ
˙

θ
^

{\displaystyle {\dot {\theta }}{\hat {\boldsymbol {\theta }}}}

.

text: We can now find the velocity and acceleration of our orbiting object.

text:
The coefficients of

r

^

{\displaystyle {\hat {\mathbf {r}}}}

 and

θ
^

{\displaystyle {\hat {\boldsymbol {\theta }}}}

 give the accelerations in the radial and transverse directions. As said, Newton gives this first due to gravity is

−
μ

/

r

2

{\displaystyle -\mu /r^{2}}

 and the second is zero.

text:
r
¨

−
r

θ
˙

2

=
−

μ

r

2

{\displaystyle {\ddot {r}}-r{\dot {\theta }}^{2}=-{\frac {\mu }{r^{2}}}}

(1)

text:
r

θ
¨

+
2

r
˙

θ
˙

=
0

{\displaystyle r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}=0}

(2)

text: Equation (2) can be rearranged using integration by parts.

text:
We can multiply through by

r

{\displaystyle r}

 because it is not zero unless the orbiting object crashes. Then having the derivative be zero gives that the function is a constant.

text:
r

2

θ
˙

=
h

{\displaystyle r^{2}{\dot {\theta }}=h}

(3)

text: which is actually the theoretical proof of Kepler's second law (A line joining a planet and the Sun sweeps out equal areas during equal intervals of time). The constant of integration, h, is the angular momentum per unit mass.

text:
In order to get an equation for the orbit from equation (1), we need to eliminate time.[8] (See also Binet equation.) In polar coordinates, this would express the distance

r

{\displaystyle r}

 of the orbiting object from the center as a function of its angle

θ

{\displaystyle \theta }

. However, it is easier to introduce the auxiliary variable

u
=
1

/

r

{\displaystyle u=1/r}

 and to express

u

{\displaystyle u}

 as a function of

θ

{\displaystyle \theta }

. Derivatives of

r

{\displaystyle r}

 with respect to time may be rewritten as derivatives of

u

{\displaystyle u}

 with respect to angle.

text: Plugging these into (1) gives

text: So for the gravitational force – or, more generally, for any inverse square force law – the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation (up to a shift of origin of the dependent variable). The solution is:

text:
where A and θ0 are arbitrary constants. This resulting equation of the orbit of the object is that of an ellipse in Polar form relative to one of the focal points. This is put into a more standard form by letting

e
≡

h

2

A

/

μ

{\displaystyle e\equiv h^{2}A/\mu }

 be the eccentricity, letting

a
≡

h

2

/

(
μ
(
1
−

e

2

)
)

{\displaystyle a\equiv h^{2}/(\mu (1-e^{2}))}

 be the semi-major axis. Finally, letting

θ

0

≡
0

{\displaystyle \theta _{0}\equiv 0}

 so the long axis of the ellipse is along the positive x coordinate.

text: Relativistic orbital motion[edit]

text: The above classical (Newtonian) analysis of orbital mechanics assumes that the more subtle effects of general relativity, such as frame dragging and gravitational time dilation are negligible. Relativistic effects cease to be negligible when near very massive bodies (as with the precession of Mercury's orbit about the Sun), or when extreme precision is needed (as with calculations of the orbital elements and time signal references for GPS satellites.[9])

text: Orbital planes[edit]

text: The analysis so far has been two dimensional; it turns out that an unperturbed orbit is two-dimensional in a plane fixed in space, and thus the extension to three dimensions requires simply rotating the two-dimensional plane into the required angle relative to the poles of the planetary body involved.

text: The rotation to do this in three dimensions requires three numbers to uniquely determine; traditionally these are expressed as three angles.

text: Orbital period[edit]

text: The orbital period is simply how long an orbiting body takes to complete one orbit.

text: Specifying orbits[edit]

text: Six parameters are required to specify a Keplerian orbit about a body. For example, the three numbers that specify the body's initial position, and the three values that specify its velocity will define a unique orbit that can be calculated forwards (or backwards) in time. However, traditionally the parameters used are slightly different.

text: The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his laws. The Keplerian elements are six:

text:
Inclination (i)
Longitude of the ascending node (Ω)
Argument of periapsis (ω)
Eccentricity (e)
Semimajor axis (a)
Mean anomaly at epoch (M0).

text: In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. However, in practice, orbits are affected or perturbed, by other forces than simple gravity from an assumed point source (see the next section), and thus the orbital elements change over time.

text: Orbital perturbations[edit]

text: An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time.

text: Radial, prograde and transverse perturbations[edit]

text: A small radial impulse given to a body in orbit changes the eccentricity, but not the orbital period (to first order). A prograde or retrograde impulse (i.e. an impulse applied along the orbital motion) changes both the eccentricity and the orbital period. Notably, a prograde impulse at periapsis raises the altitude at apoapsis, and vice versa, and a retrograde impulse does the opposite. A transverse impulse (out of the orbital plane) causes rotation of the orbital plane without changing the period or eccentricity. In all instances, a closed orbit will still intersect the perturbation point.

text: Orbital decay[edit]

text: If an orbit is about a planetary body with significant atmosphere, its orbit can decay because of drag. Particularly at each periapsis, the object experiences atmospheric drag, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body.

text: The bounds of an atmosphere vary wildly. During a solar maximum, the Earth's atmosphere causes drag up to a hundred kilometres higher than during a solar minimum.

text: Some satellites with long conductive tethers can also experience orbital decay because of electromagnetic drag from the Earth's magnetic field. As the wire cuts the magnetic field it acts as a generator, moving electrons from one end to the other. The orbital energy is converted to heat in the wire.

text: Orbits can be artificially influenced through the use of rocket engines which change the kinetic energy of the body at some point in its path. This is the conversion of chemical or electrical energy to kinetic energy. In this way changes in the orbit shape or orientation can be facilitated.

text: Another method of artificially influencing an orbit is through the use of solar sails or magnetic sails. These forms of propulsion require no propellant or energy input other than that of the Sun, and so can be used indefinitely. See statite for one such proposed use.

text: Orbital decay can occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the solar system are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years.

text: Orbits can decay via the emission of gravitational waves. This mechanism is extremely weak for most stellar objects, only becoming significant in cases where there is a combination of extreme mass and extreme acceleration, such as with black holes or neutron stars that are orbiting each other closely.

text: Oblateness[edit]

text: The standard analysis of orbiting bodies assumes that all bodies consist of uniform spheres, or more generally, concentric shells each of uniform density. It can be shown that such bodies are gravitationally equivalent to point sources.

text: However, in the real world, many bodies rotate, and this introduces oblateness and distorts the gravity field, and gives a quadrupole moment to the gravitational field which is significant at distances comparable to the radius of the body. In the general case, the gravitational potential of a rotating body such as, e.g., a planet is usually expanded in multipoles accounting for the departures of it from spherical symmetry. From the point of view of satellite dynamics, of particular relevance are the so-called even zonal harmonic coefficients, or even zonals, since they induce secular orbital perturbations which are cumulative over time spans longer than the orbital period.[10][11][12] They do depend on the orientation of the body's symmetry axis in the space, affecting, in general, the whole orbit, with the exception of the semimajor axis.

text: Multiple gravitating bodies[edit]

text: The effects of other gravitating bodies can be significant. For example, the orbit of the Moon cannot be accurately described without allowing for the action of the Sun's gravity as well as the Earth's. One approximate result is that bodies will usually have reasonably stable orbits around a heavier planet or moon, in spite of these perturbations, provided they are orbiting well within the heavier body's Hill sphere.

text: When there are more than two gravitating bodies it is referred to as an n-body problem. Most n-body problems have no closed form solution, although some special cases have been formulated.

text: Light radiation and stellar wind[edit]

text: For smaller bodies particularly, light and stellar wind can cause significant perturbations to the attitude and direction of motion of the body, and over time can be significant. Of the planetary bodies, the motion of asteroids is particularly affected over large periods when the asteroids are rotating relative to the Sun.

text: Strange orbits[edit]

text: Mathematicians have discovered that it is possible in principle to have multiple bodies in non-elliptical orbits that repeat periodically, although most such orbits are not stable regarding small perturbations in mass, position, or velocity. However, some special stable cases have been identified, including a planar figure-eight orbit occupied by three moving bodies. Further studies have discovered that nonplanar orbits are also possible, including one involving 12 masses moving in 4 roughly circular, interlocking orbits topologically equivalent to the edges of a cuboctahedron.[13]

text: Finding such orbits naturally occurring in the universe is thought to be extremely unlikely, because of the improbability of the required conditions occurring by chance.[13]

text: Astrodynamics[edit]

text: Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun).

text: Earth orbits[edit]

text:
Low Earth orbit (LEO): Geocentric orbits with altitudes up to 2,000 km (0–1,240 miles).[14]
Medium Earth orbit (MEO): Geocentric orbits ranging in altitude from 2,000 km (1,240 miles) to just below geosynchronous orbit at 35,786 kilometers (22,236 mi). Also known as an intermediate circular orbit. These are "most commonly at 20,200 kilometers (12,600 mi), or 20,650 kilometers (12,830 mi), with an orbital period of 12 hours."[15]
Both Geosynchronous orbit (GSO) and Geostationary orbit (GEO) are orbits around Earth matching Earth's sidereal rotation period. All geosynchronous and geostationary orbits have a semi-major axis of 42,164 km (26,199 mi).[16] All geostationary orbits are also geosynchronous, but not all geosynchronous orbits are geostationary. A geostationary orbit stays exactly above the equator, whereas a geosynchronous orbit may swing north and south to cover more of the Earth's surface. Both complete one full orbit of Earth per sidereal day (relative to the stars, not the Sun).
High Earth orbit: Geocentric orbits above the altitude of geosynchronous orbit 35,786 km (22,240 miles).[15]

text: Scaling in gravity[edit]

text: The gravitational constant G has been calculated as:

text: (6.6742 ± 0.001) × 10−11 (kg/m3)−1s−2.

text: Thus the constant has dimension density−1 time−2. This corresponds to the following properties.

text: Scaling of distances (including sizes of bodies, while keeping the densities the same) gives similar orbits without scaling the time: if for example distances are halved, masses are divided by 8, gravitational forces by 16 and gravitational accelerations by 2. Hence velocities are halved and orbital periods remain the same. Similarly, when an object is dropped from a tower, the time it takes to fall to the ground remains the same with a scale model of the tower on a scale model of the Earth.

text: Scaling of distances while keeping the masses the same (in the case of point masses, or by reducing the densities) gives similar orbits; if distances are multiplied by 4, gravitational forces and accelerations are divided by 16, velocities are halved and orbital periods are multiplied by 8.

text: When all densities are multiplied by 4, orbits are the same; gravitational forces are multiplied by 16 and accelerations by 4, velocities are doubled and orbital periods are halved.

text: When all densities are multiplied by 4, and all sizes are halved, orbits are similar; masses are divided by 2, gravitational forces are the same, gravitational accelerations are doubled. Hence velocities are the same and orbital periods are halved.

text: In all these cases of scaling. if densities are multiplied by 4, times are halved; if velocities are doubled, forces are multiplied by 16.

text: These properties are illustrated in the formula (derived from the formula for the orbital period)

text: for an elliptical orbit with semi-major axis a, of a small body around a spherical body with radius r and average density σ, where T is the orbital period. See also Kepler's Third Law.

text: Patents[edit]

text: The application of certain orbits or orbital maneuvers to specific useful purposes have been the subject of patents.[17]


document_title: Joel Berry II

question_text: what nba team did joel berry go to

question_tokens: what nba team did joel berry go to

text: Joel Berry II

text: High school career[edit]

text: Berry, a 6'0 point guard, played high school basketball at Lake Highland Preparatory School in Orlando, Florida. He led his team to two state titles and was the first player named Florida Mr. Basketball three times. He was named a Parade All-American and McDonald's All-American as a senior in 2014.[1]

text: College career[edit]

text: Berry's freshman season was hampered by injury. He averaged 4.2 points and 1.5 assists per game backing up junior Marcus Paige at point guard.

text: As a sophomore, Berry moved into the starting lineup at point guard, with Paige shifting over to shooting guard, resulting in a dramatic increase in Berry's offensive production.  Berry helped the team to an Atlantic Coast Conference (ACC) regular season title. He then helped the team to an ACC Tournament championship, averaging 17 points per game and coming away with Most Valuable Player honors.[2][3]  In the post-season, Berry and the Tar Heels made the Final Four and 2016 NCAA championship game. During the championship game, Berry scored 20 points and dished out four assists, but North Carolina fell short on a last-second shot to Villanova, 77-74.

text: As a junior, Berry led the Tar Heels to the ACC regular season title.  In the NCAA Tournament, despite playing with injuries to both ankles, Berry led the Tar Heels to a 2017 NCAA men's basketball championship.  In the national title game against Gonzaga, Berry scored 22 points and had six assists, and was thereafter named Most Outstanding Player of the Final Four, becoming the first player since Bill Walton to score 20 points or more in back-to-back title games.[4] While Berry was one out of 182 players that declared early entry into the 2017 NBA Draft, he ultimately decided to return to North Carolina for his senior season instead, announcing his decision on April 25, 2017.

text: In his Senior year, Berry led the Tar Heels to the ACC tournament final. Despite losing in the second round of the NCAA tournament, he averaged 17.1 points and 3.2 assists per game. He was named the winner of the Dean Smith Most Valuable Player award at the 2017-18 UNC men’s basketball awards ceremony, and was one of eight finalists for the James E. Sullivan Award, which is presented by the Amateur Athletic Union (AAU) to the top amateur athlete in the United States. He was also voted a third team All-American by the National Association of Basketball Coaches (NABC). Berry earned this distinction just two weeks after being named a 2018 first team All-ACC selection.

text: Professional career[edit]

text: Los Angeles Lakers (2018–present)[edit]

text: After going undrafted in the 2018 NBA draft, Berry signed with the Los Angeles Lakers summer league team. On July 19, 2018, he signed a rookie scale contract with the Lakers. [5]


document_title: Chase Field

question_text: when do they close the roof at chase field

text: Chase Field

text: History[edit]

text: The park was built during a wave of new, baseball-only parks in the 1990s. Although nearly all of these parks were open-air, it was taken for granted that a domed stadium was a must for a major-league team to be a viable venture in the Phoenix area. Phoenix is by far the hottest major city in North America; the average high temperature during baseball's regular season is 99.1 °F (37.3 °C), and game-time temperatures well above 100 °F (38 °C) are very common during the summer.

text: Stadium funding furor[edit]

text: In the spring of 1994, the Maricopa County Board of Supervisors approved a quarter percentage point increase in the county sales tax to pay for their portion of the stadium funding. This came about at a time that the county itself was facing huge budget deficits and lack of funding for other services. The sales tax being levied was very unpopular with local citizens, who were not allowed to vote on the issue of funding a baseball stadium with general sales tax revenue (usage of public subsidies for stadium projects was actually prohibited by a 1989 referendum). The issue was so controversial and divisive that in August 1997, Maricopa County Supervisor Mary Rose Wilcox was shot and injured while leaving a county board meeting by Larry Naman, a homeless man, who attempted to argue in court that her support for the tax justified his attack. In May 1998, Naman was found guilty of attempted first-degree murder.[10]

text: Costs for the stadium were originally estimated at $279 million in 1995,[11] but cost overruns (in part because of rising prices for steel and other materials) pushed the final price to $364 million.[12] As part of the original stadium deal, the Diamondbacks were responsible for all construction costs above $253 million. These extra expenses, combined with the Diamondbacks and their fellow expansion franchise, the Tampa Bay Devil Rays, not being allowed to share in the national MLB revenue for their first 5 years of operations, left the Diamondbacks in a less-than-desirable financial situation, which would come back to haunt team founder and managing partner Jerry Colangelo and his group later on.

text: Construction on the park began in 1996, and was finished just before the Diamondbacks' first season began, in 1998. It was the third MLB stadium to have a retractable roof and the first in the United States (at the time, only Toronto's SkyDome, now Rogers Centre and Montreal's Olympic Stadium had them; others are now at Minute Maid Park in Houston, Miller Park in Milwaukee, Safeco Field in Seattle and Marlins Park in Miami). It was also the first ballpark to feature natural grass in a retractable roof stadium.

text: The stadium hosted Games 1, 2, 6, and 7 of the 2001 World Series between the Arizona Diamondbacks and the New York Yankees. The Diamondbacks won all four home games, winning the world championship in seven games, and thus denying the Yankees a fourth consecutive championship. It was the first time since 1991 that the home team won all home games of a World Series. The only other incident was 1987, both by the Minnesota Twins.

text: Chase Field was originally named Bank One Ballpark after Bank One of Chicago, Illinois, giving rise to its nickname "BOB". After Bank One merged with New York-based JPMorgan Chase & Co., the name change was announced on September 23, 2005.

text: In March 2006, Chase Field played host to three first-round games of the World Baseball Classic.

text: Chase Field hosted the Major League Baseball All-Star Game in 2011.[9]

text: Chase Field will host the 2017 National League Wild Card Game.

text: Chase Field also has a swimming pool sponsored by Dodge, located in right-center field, which is rented to patrons as a suite holding 35 guests for $3,500 per game during the 2011 season. Mark Grace was the first player to "splash" a home run into the pool.[13] On September 19, 2013, after clinching the NL West, several members of the Los Angeles Dodgers climbed over the outfield wall and jumped into the pool after being asked by the Diamondbacks to not celebrate on the field after the game.

text: In addition to baseball, the pool has been used by Monster Jam's Jim Koehler to continue his tradition of swimming after Freestyle.[14] The ballpark also features a dirt strip between home plate and the pitcher's mound, one of only two current ballparks to do so (Comerica Park in Detroit is the other). This dirt strip, sometimes known as the "keyhole", was very common in old-time ballparks.

text: The park's foul territory is somewhat larger than is the case for most ballparks built in the 1990s. With 80% of the seats in foul territory, the upper deck is one of the highest in the majors. The park's suites are tucked far under the third deck, which keeps the upper deck closer to the action, with the exception of their Dugout Suites which sit next to the home and visitor's dugouts.

text: Before the 2008 season began, a brand new High Definition scoreboard was installed beyond center field, replacing the original. The new scoreboard is 46 ft (14 m) high and 136 ft (41 m) wide and it cost $14 million. It is the fifth largest HD screen in Major League Baseball behind Kauffman Stadium. The screen at Kauffman is larger by overall area and is square in shape but Chase Field's screen is larger by length and is rectangular.[15][16]

text: Premium seating includes 4,400 club seats, 57 suites, 6 party suites, Executive suite, batters box suite, two dugout suites, and the Ramtrucks.com Party Pool.

text: The Diamondbacks and St. Louis Cardinals game on April 3, 2013 lasted 16 innings. It was the longest game in Chase Field's 17-year history.[17]

text: Other events[edit]

text: The organizers of the Insight.com Bowl elected to move their game from Arizona Stadium in Tucson to Phoenix beginning in 2000, and Chase Field became the game's host. In 2006, the bowl game moved to Sun Devil Stadium, to replace the Fiesta Bowl, which moved to University of Phoenix Stadium in Glendale, Arizona. The football configuration was notable because of the lack of nets behind the goalposts and the dugout behind the south end zone. The final Insight Bowl played at Chase was between the hometown Arizona State Sun Devils and the Rutgers Scarlet Knights. The bowl, now known as the Cactus Bowl, returned to Chase Field in January 2016.

text: The stadium also hosts occasional concerts and international soccer games. For football and soccer, the field is set up with the end lines perpendicular to the third-base line and temporary bleachers added on the east side.

text: Chase Field has staged nine women's college basketball games. The second game, which was played on December 18, 2006, was shortened by rain with four minutes and 18 seconds remaining and Arizona State leading Texas Tech 61–45. Venue staff closed the roof in an effort to finish the game, but officials deemed the court unsafe. In 2000, ASU played the Tennessee Volunteers at the same facility.[18]

text: Chase Field was also the site of the "Challenge at Chase", a college baseball game between Arizona State and University of Arizona. Arizona won both contests.[19] There has been no game scheduled there since 2008.[19]

text: In February 2006, the Professional Bull Riders hosted a Built Ford Tough Series bull riding event at this venue. Chris Shivers won this event with a total score of 181.5 points (out of a possible 200) on two bulls, including an impressive 93.75 (out of 100) points on Taylor Made bucking bull, Smokeless Wardance, in the short-go round. During the long-go round, the roof was closed, but during the short-go, the roof was opened.

text: The stadium has hosted Monster Energy Supercross rounds from 1999 to 2015.[20] Monster Jam came to Chase Field every year in late January about two weeks after Monster Energy Supercross. Both events moved to the University of Phoenix Stadium in 2016.

text: Roof and cooling system[edit]

text: Chase Field's roof is opened or closed depending on the game-time temperature. When the decision is made to close the roof, it is left open for as long as possible before game time in order to keep the grass growing. Even when the roof is closed, the park's windows allow enough sunlight to play in true daylight without overheating the stadium.

text: The roof, which takes just 4½ minutes to open or close at a cost of $2–$3, is closed three hours before game time using two 200-horsepower motors triggered from a control room in the upper deck above left-center field.[9] A massive HVAC system then drops the temperature inside the park 30° by the time the gates open. The cooling system, which has the power equivalent of cooling 2,500 homes of 2,000 square feet, uses chilled water and is part of the same system that serves more than 30 buildings in downtown Phoenix.[9] The cooling plant is located in a separate building right outside the ballpark.[9] Originally, the HVAC system didn't work above row 25 of the upper level, exposing fans in the higher rows to the full force of the often-oppressive heat typical of Arizona summers. Recent changes keep virtually all of the facility in air-conditioned comfort.[21]

text: Transportation[edit]

text: Chase Field is served by Westbound METRO Rail's Washington at 3rd Street station and Eastbound METRO Rail's Jefferson at 3rd Street station.


document_title: Problem solving

question_text: who emphasized the processes of experience and problem solving

text: Problem solving

text: Definition[edit]

text: The term problem solving is used in many disciplines, sometimes with different perspectives, and often with different terminologies. For instance, it is a mental process in psychology and a computerized process in computer science. Problems can also be classified into two different types (ill-defined and well-defined) from which appropriate solutions are to be made. Ill-defined problems are those that do not have clear goals, solution paths, or expected solution. Well-defined problems have specific goals, clearly defined solution paths, and clear expected solutions. These problems also allow for more initial planning than ill-defined problems.[1] Being able to solve problems sometimes involves dealing with pragmatics (logic) and semantics (interpretation of the problem). The ability to understand what the goal of the problem is and what rules could be applied represent the key to solving the problem. Sometimes the problem requires some abstract thinking and coming up with a creative solution.

text: Psychology[edit]

text: Thomas J. D'Zurilla in 1988 defined problem solving as a “cognitive–affective–behavioral process through which an individual (or group) attempts to identify, discover, or invent effective means of coping with problems encountered in every day living”.[2] It is an evolutionary drive for living organisms and an important coping skill for dealing with a variety of concerns. Problem solving specifically in psychology refers to a state of desire for reaching a definite 'goal' from a present condition that either is not directly moving toward the goal, is far from it, or needs more complex logic for finding a missing description of conditions or steps toward the goal. In each case "where you want to be" is an imagined (or written) state in which you would like to be and the solutions are situation- or context-specific. This process includes problem finding or 'problem analysis', problem shaping, generating alternative strategies, implementation and verification of the selected solution. Distinguished feature of a problem is that there is a goal to be reached and how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis.[3] The nature of human problem solving processes and methods is a field of study and work for mental health professionals. Methods of studying problem solving include introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods.[4] Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills.[5]

text: Problem solving has two major domains: mathematical problem solving and personal problem solving both are seen in terms of some difficulty or barrier is encountered.[6] Empirical researches show that self-interest and interpersonal skills; collaborative and instrumental problem approach (it helps in reflective and expansive understanding of the problem situation and its preferable outcome); strategy fluency (the number and diversity of strategies) and conceptual clarity that can lead to an action-identification (Vallacher & Wegner, 1987);[7] temporal lifespan perspective that lead to selectivity in strategy (problem focused and emotion focused strategies);[8] self-efficacy and problem familiarity; formation of 'carry over' relationships (egalitarian friendship, romantic ties, cliques, hygge's, etc.) that helps individuals mutually move through life and provide a sense of identity (Antonucci, Birditt, & Ajrouch, 2011);[9] negotiation; type of relationships (obligatory vs. voluntary); gender typing; problem focused and emotion focused strategies as some strategies and factors that influence everyday problem solving. Neuropsychologists have studied that individuals with frontal lobe injuries with deficits in emotional control and reasoning can be remediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems (Rath, Simon, Langenbahn, Sherr, & Diller, 2003).

text: Interpersonal everyday problem solving is dependent upon the individual personal motivational and contextual components. One such component is the emotional valence of "real-world" problems and it can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving (D'Zurilla & Goldfried, 1971; D'Zurilla & Nezu, 1982), demonstrating that poor emotional control can disrupt focus on the target task and impede problem resolution and likely lead to negative outcomes such as fatigue, depression, and inertia (Rath, Langenbahn, Simon, Sherr, & Diller, 2004). In conceptualization, human problem solving consists of two related processes: problem orientation, the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. Studies conclude people's strategies cohere with their goals (Hoppmann & Blanchard-Fields, 2010, Berg et al., 1998)[10] and they are stemmed from the natural process of comparing oneself with others (Sonstegard and Bitter, 1998).

text: Cognitive sciences[edit]

text: The early experimental work of the Gestaltists in Germany placed the beginning of problem solving study (e.g., Karl Duncker in 1935 with his book The psychology of productive thinking[11]). Later this experimental work continued through the 1960s and early 1970s with research conducted on relatively simple (but novel for participants) laboratory tasks of problem solving.[12][13] Choosing simple novel tasks was based on the clearly defined optimal solutions and their short time for solving, which made it possible for the researchers to trace participants' steps in problem-solving process. Researchers' underlying assumption was that simple tasks such as the Tower of Hanoi correspond to the main properties of "real world" problems and thus the characteristic cognitive processes within participants' attempts to solve simple problems are the same for "real world" problems too; simple problems were used for reasons of convenience and with the expectation that thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research is the work by Allen Newell and Herbert A. Simon.[14] Other experts have shown that the principle of decomposition improves the ability of the problem solver to make good judgment.[15]

text: Computer science and algorithmics[edit]

text: In computer science and in the part of artificial intelligence that deals with algorithms ("algorithmics"), problem solving encompasses a number of techniques known as algorithms, heuristics, root cause analysis, etc. In these disciplines, problem solving is part of a larger process that encompasses problem determination, de-duplication, analysis, diagnosis, repair, etc.

text: Engineering[edit]

text: Problem solving is used in when products or processes fail, so corrective action can be taken to prevent further failures. It can also be applied to a product or process prior to an actual fail event, i.e., when a potential problem can be predicted and analyzed, and mitigation applied so the problem never actually occurs. Techniques such as Failure Mode Effects Analysis can be used to proactively reduce the likelihood of problems occurring.

text: Military science[edit]

text: In military science, problem solving is linked to the concept of "end-states", the desired condition or situation that strategists wish to generate.[16]:xiii, E-2 The ability to solve problems is important at any military rank, but is highly critical at the command and control level, where it is strictly correlated to the deep understanding of qualitative and quantitative scenarios. Effectiveness of problem solving is "a criterion used to assess changes in system behavior, capability, or operational environment that is tied to measuring the attainment of an end state, achievement of an objective, or creation of an effect".[16]:IV-24 Planning for problem-solving is a "process that determines and describes how to employ 'means' in specific 'ways' to achieve 'ends' (the problem's solution)."[16]:IV-1

text: Other[edit]

text: Forensic engineering is an important technique of failure analysis that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

text: Reverse engineering[17] attempts to discover the original problem-solving logic used in developing a product by taking it apart.

text: Other problem solving tools are linear and nonlinear programming, queuing systems, and simulation.[18]

text: Problem-solving strategies[edit]

text: Problem-solving strategies are the steps that one would use to find the problem(s) that are in the way to getting to one's own goal. Firend's problem solving model (PSM) is practical in application and incorporates the conventional 5WH approach, with a systematic process of investigation, implementation and assessment cycle.[19][non-primary source needed] Some would refer to this as the "problem-solving cycle" (Bransford & Stein, 1993). In this cycle one will recognize the problem, define the problem, develop a strategy to fix the problem, organize the knowledge of the problem cycle, figure out the resources at the user's disposal, monitor one's progress, and evaluate the solution for accuracy. The reason it is called a cycle is that once one is completed with a problem another usually will pop up.

text: Blanchard-Fields (2007) looks at problem solving from one of two facets. The first looking at those problems that only have one solution (like mathematical problems, or fact-based questions) which are grounded in psychometric intelligence. The other that is socioemotional in nature and are unpredictable with answers that are constantly changing (like what's your favorite color or what you should get someone for Christmas).

text: The following techniques are usually called problem-solving strategies'[20]

text:
Abstraction: solving the problem in a model of the system before applying it to the real system
Analogy: using a solution that solves an analogous problem
Brainstorming: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum solution is found
Divide and conquer: breaking down a large, complex problem into smaller, solvable problems
Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption
Lateral thinking: approaching solutions indirectly and creatively
Means-ends analysis: choosing an action at each step to move closer to the goal
Method of focal objects: synthesizing seemingly non-matching characteristics of different objects into something new
Morphological analysis: assessing the output and interactions of an entire system
Proof: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it
Reduction: transforming the problem into another problem for which solutions exist
Research: employing existing ideas or adapting existing solutions to similar problems
Root cause analysis: identifying the cause of a problem
Trial-and-error: testing possible solutions until the right one is found

text: Problem-solving methods[edit]

text:
Eight Disciplines Problem Solving
GROW model
How to Solve It
OODA loop (observe, orient, decide, and act)
PDCA (plan–do–check–act)
Root cause analysis
RPR problem diagnosis (rapid problem resolution)
TRIZ (in Russian: Teoriya Resheniya Izobretatelskikh Zadach, "theory of solving inventor's problems")
A3 problem solving
System dynamics
Hive mind

text: Common barriers to problem solving[edit]

text: Common barriers to problem solving are mental constructs that impede our ability to correctly solve problems. These barriers prevent people from solving problems in the most efficient manner possible. Five of the most common processes and factors that researchers have identified as barriers to problem solving are confirmation bias, mental set, functional fixedness, unnecessary constraints, and irrelevant information.

text: Confirmation bias[edit]

text: Within the field of science there exists a set of fundamental standards, the scientific method, which outlines the process of discovering facts or truths about the world through unbiased consideration of all pertinent information and through impartial observation of and/or experimentation with that information. According to this method, one is able to most accurately find a solution to a perceived problem by performing the aforementioned steps. The scientific method does not prescribe a process that is limited to scientists, but rather one that all people can practice in their respective fields of work as well as in their personal lives. Confirmation bias can be described as one's unconscious or unintentional corruption of the scientific method. Thus when one demonstrates confirmation bias, one is formally or informally collecting data and then subsequently observing and experimenting with that data in such a way that favors a preconceived notion that may or may not have motivation.[21] Research has found that professionals within scientific fields of study also experience confirmation bias. Andreas Hergovich, Reinhard Schott, and Christoph Burger's experiment conducted online, for instance, suggested that professionals within the field of psychological research are likely to view scientific studies that are congruent with their preconceived understandings more favorably than studies that are incongruent with their established beliefs.[22]

text: Motivation refers to one's desire to defend or find substantiation for beliefs (e.g., religious beliefs) that are important to one.[23] According to Raymond Nickerson, one can see the consequences of confirmation bias in real-life situations, which range in severity from inefficient government policies to genocide. With respect to the latter and most severe ramification of this cognitive barrier, Nickerson argued that those involved in committing genocide of persons accused of witchcraft, an atrocity that occurred from the 15th to 17th centuries, demonstrated confirmation bias with motivation. Researcher Michael Allen found evidence for confirmation bias with motivation in school children who worked to manipulate their science experiments in such a way that would produce their hoped for results.[24] However, confirmation bias does not necessarily require motivation. In 1960, Peter Cathcart Wason conducted an experiment in which participants first viewed three numbers and then created a hypothesis that proposed a rule that could have been used to create that triplet of numbers. When testing their hypotheses, participants tended to only create additional triplets of numbers that would confirm their hypotheses, and tended not to create triplets that would negate or disprove their hypotheses. Thus research also shows that people can and do work to confirm theories or ideas that do not support or engage personally significant beliefs.[25]

text: Mental set[edit]

text: Mental set was first articulated by Abraham Luchins in the 1940s and demonstrated in his well-known water jug experiments.[26] In these experiments, participants were asked to fill one jug with a specific amount of water using only other jugs (typically three) with different maximum capacities as tools. After Luchins gave his participants a set of water jug problems that could all be solved by employing a single technique, he would then give them a problem that could either be solved using that same technique or a novel and simpler method. Luchins discovered that his participants tended to use the same technique that they had become accustomed to despite the possibility of using a simpler alternative.[27] Thus mental set describes one's inclination to attempt to solve problems in such a way that has proved successful in previous experiences. However, as Luchins' work revealed, such methods for finding a solution that have worked in the past may not be adequate or optimal for certain new but similar problems. Therefore, it is often necessary for people to move beyond their mental sets in order to find solutions. This was again demonstrated in Norman Maier's 1931 experiment, which challenged participants to solve a problem by using a household object (pliers) in an unconventional manner. Maier observed that participants were often unable to view the object in a way that strayed from its typical use, a phenomenon regarded as a particular form of mental set (more specifically known as functional fixedness, which is the topic of the following section). When people cling rigidly to their mental sets, they are said to be experiencing fixation, a seeming obsession or preoccupation with attempted strategies that are repeatedly unsuccessful.[28] In the late 1990s, researcher Jennifer Wiley worked to reveal that expertise can work to create a mental set in persons considered to be experts in certain fields, and she furthermore gained evidence that the mental set created by expertise could lead to the development of fixation.[29]

text: Functional fixedness[edit]

text: Functional fixedness is a specific form of mental set and fixation, which was alluded to earlier in the Maier experiment, and furthermore it is another way in which cognitive bias can be seen throughout daily life. Tim German and Clark Barrett describe this barrier as the fixed design of an object hindering the individual's ability to see it serving other functions. In more technical terms, these researchers explained that "[s]ubjects become "fixed" on the design function of the objects, and problem solving suffers relative to control conditions in which the object's function is not demonstrated."[30] Functional fixedness is defined as only having that primary function of the object itself hinder the ability of it serving another purpose other than its original function. In research that highlighted the primary reasons that young children are immune to functional fixedness, it was stated that "functional fixedness...[is when]subjects are hindered in reaching the solution to a problem by their knowledge of an object's conventional function."[31] Furthermore, it is important to note that functional fixedness can be easily expressed in commonplace situations. For instance, imagine the following situation: a man sees a bug on the floor that he wants to kill, but the only thing in his hand at the moment is a can of air freshener. If the man starts looking around for something in the house to kill the bug with instead of realizing that the can of air freshener could in fact be used not only as having its main function as to freshen the air, he is said to be experiencing functional fixedness. The man's knowledge of the can being served as purely an air freshener hindered his ability to realize that it too could have been used to serve another purpose, which in this instance was as an instrument to kill the bug. Functional fixedness can happen on multiple occasions and can cause us to have certain cognitive biases. If we only see an object as serving one primary focus than we fail to realize that the object can be used in various ways other than its intended purpose. This can in turn cause many issues with regards to problem solving. Common sense seems to be a plausible answer to functional fixedness. One could make this argument because it seems rather simple to consider possible alternative uses for an object. Perhaps using common sense to solve this issue could be the most accurate answer within this context. With the previous stated example, it seems as if it would make perfect sense to use the can of air freshener to kill the bug rather than to search for something else to serve that function but, as research shows, this is often not the case.

text: Functional fixedness limits the ability for people to solve problems accurately by causing one to have a very narrow way of thinking. Functional fixedness can be seen in other types of learning behaviors as well. For instance, research has discovered the presence of functional fixedness in many educational instances. Researchers Furio, Calatayud, Baracenas, and Padilla stated that "... functional fixedness may be found in learning concepts as well as in solving chemistry problems."[32] There was more emphasis on this function being seen in this type of subject and others.

text: There are several hypotheses in regards to how functional fixedness relates to problem solving.[33] There are also many ways in which a person can run into problems while thinking of a particular object with having this function. If there is one way in which a person usually thinks of something rather than multiple ways then this can lead to a constraint in how the person thinks of that particular object. This can be seen as narrow minded thinking, which is defined as a way in which one is not able to see or accept certain ideas in a particular context. Functional fixedness is very closely related to this as previously mentioned. This can be done intentionally and or unintentionally, but for the most part it seems as if this process to problem solving is done in an unintentional way.

text: Functional fixedness can affect problem solvers in at least two particular ways. The first is with regards to time, as functional fixedness causes people to use more time than necessary to solve any given problem. Secondly, functional fixedness often causes solvers to make more attempts to solve a problem than they would have made if they were not experiencing this cognitive barrier. In the worst case, functional fixedness can completely prevent a person from realizing a solution to a problem. Functional fixedness is a commonplace occurrence, which affects the lives of many people.

text: Unnecessary constraints[edit]

text: Unnecessary constraints are another very common barrier that people face while attempting to problem-solve. This particular phenomenon occurs when the subject, trying to solve the problem subconsciously, places boundaries on the task at hand, which in turn forces him or her to strain to be more innovative in their thinking. The solver hits a barrier when they become fixated on only one way to solve their problem, and it becomes increasingly difficult to see anything but the method they have chosen. Typically, the solver experiences this when attempting to use a method they have already experienced success from, and they can not help but try to make it work in the present circumstances as well, even if they see that it is counterproductive.[34]

text: Groupthink, or taking on the mindset of the rest of the group members, can also act as an unnecessary constraint while trying to solve problems.[35] This is due to the fact that with everybody thinking the same thing, stopping on the same conclusions, and inhibiting themselves to think beyond this. This is very common, but the most well-known example of this barrier making itself present is in the famous example of the dot problem. In this example, there are nine dots lying in a square- three dots across, and three dots running up and down. The solver is then asked to draw no more than four lines, without lifting their pen or pencil from the paper. This series of lines should connect all of the dots on the paper. Then, what typically happens is the subject creates an assumption in their mind that they must connect the dots without letting his or her pen or pencil go outside of the square of dots. Standardized procedures like this can often bring mentally invented constraints of this kind,[36] and researchers have found a 0% correct solution rate in the time allotted for the task to be completed.[37] The imposed constraint inhibits the solver to think beyond the bounds of the dots. It is from this phenomenon that the expression "think outside the box" is derived.[38]

text: This problem can be quickly solved with a dawning of realization, or insight. A few minutes of struggling over a problem can bring these sudden insights, where the solver quickly sees the solution clearly. Problems such as this are most typically solved via insight and can be very difficult for the subject depending on either how they have structured the problem in their minds, how they draw on their past experiences, and how much they juggle this information in their working memories[38] In the case of the nine-dot example, the solver has already been structured incorrectly in their minds because of the constraint that they have placed upon the solution. In addition to this, people experience struggles when they try to compare the problem to their prior knowledge, and they think they must keep their lines within the dots and not go beyond. They do this because trying to envision the dots connected outside of the basic square puts a strain on their working memory.[38]

text: Luckily, the solution to the problem becomes obvious as insight occurs following incremental movements made toward the solution. These tiny movements happen without the solver knowing. Then when the insight is realized fully, the "aha" moment happens for the subject.[39] These moments of insight can take a long while to manifest or not so long at other times, but the way that the solution is arrived at after toiling over these barriers stays the same.

text: Irrelevant information[edit]

text: Irrelevant information is information presented within a problem that is unrelated or unimportant to the specific problem.[34] Within the specific context of the problem, irrelevant information would serve no purpose in helping solve that particular problem. Often irrelevant information is detrimental to the problem solving process. It is a common barrier that many people have trouble getting through, especially if they are not aware of it. Irrelevant information makes solving otherwise relatively simple problems much harder.[40]

text: For example: "Fifteen percent of the people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these people have unlisted phone numbers?"[41]

text: The people that are not listed in the phone book would not be among the 200 names you selected. The individuals looking at this task would have naturally wanted to use the 15% given to them in the problem. They see that there is information present and they immediately think that it needs to be used. This of course is not true. These kinds of questions are often used to test students taking aptitude tests or cognitive evaluations.[42] They aren't meant to be difficult but they are meant to require thinking that is not necessarily common. Irrelevant Information is commonly represented in math problems, word problems specifically, where numerical information is put for the purpose of challenging the individual.

text: One reason irrelevant information is so effective at keeping a person off topic and away from the relevant information, is in how it is represented.[42] The way information is represented can make a vast difference in how difficult the problem is to be overcome. Whether a problem is represented visually, verbally, spatially, or mathematically, irrelevant information can have a profound effect on how long a problem takes to be solved; or if it's even possible. The Buddhist monk problem is a classic example of irrelevant information and how it can be represented in different ways:

text: This problem is near impossible to solve because of how the information is represented. Because it is written out in a way that represents the information verbally, it causes us to try and create a mental image of the paragraph. This is often very difficult to do especially with all the irrelevant information involved in the question. This example is made much easier to understand when the paragraph is represented visually. Now if the same problem was asked, but it was also accompanied by a corresponding graph, it would be far easier to answer this question; irrelevant information no longer serves as a road block. By representing the problem visually, there are no difficult words to understand or scenarios to imagine. The visual representation of this problem has removed the difficulty of solving it.

text: These types of representations are often used to make difficult problems easier.[43] They can be used on tests as a strategy to remove Irrelevant Information, which is one of the most common forms of barriers when discussing the issues of problem solving.[34] Identifying crucial information presented in a problem and then being able to correctly identify its usefulness is essential. Being aware of irrelevant information is the first step in overcoming this common barrier.

text: Cognitive sciences: two schools[edit]

text: In cognitive sciences, researchers' realization that problem-solving processes differ across knowledge domains and across levels of expertise (e.g. Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily generalize to problem-solving situations outside the laboratory, has led to an emphasis on real-world problem solving since the 1990s. This emphasis has been expressed quite differently in North America and Europe, however. Whereas North American research has typically concentrated on studying problem solving in separate, natural knowledge domains, much of the European research has focused on novel, complex problems, and has been performed with computerized scenarios (see Funke, 1991, for an overview).

text: Europe[edit]

text: In Europe, two main approaches have surfaced, one initiated by Donald Broadbent (1977; see Berry & Broadbent, 1995) in the United Kingdom and the other one by Dietrich Dörner (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches share an emphasis on relatively complex, semantically rich, computerized laboratory tasks, constructed to resemble real-life problems. The approaches differ somewhat in their theoretical goals and methodology, however. The tradition initiated by Broadbent emphasizes the distinction between cognitive problem-solving processes that operate under awareness versus outside of awareness, and typically employs mathematically well-defined computerized systems. The tradition initiated by Dörner, on the other hand, has an interest in the interplay of the cognitive, motivational, and social components of problem solving, and utilizes very complex computerized scenarios that contain up to 2,000 highly interconnected variables (e.g., Dörner, Kreuzig, Reither & Stäudel's 1983 LOHHAUSEN project; Ringelband, Misiak & Kluwe, 1990). Buchner (1995) describes the two traditions in detail.

text: North America[edit]

text: In North America, initiated by the work of Herbert A. Simon on "learning by doing" in semantically rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains – such as physics, writing, or chess playing – thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of expertise (e.g. Anderson, Boyle & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981).

text: Areas that have attracted rather intensive attention in North America include:

text:
Reading (Stanovich & Cunningham, 1991)
Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)
Calculation (Sokol & McCloskey, 1991)
Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)
Managerial problem solving (Wagner, 1991)
Lawyers' reasoning (Amsel, Langer & Loutzenhiser, 1991)
Mechanical problem solving (Hegarty, 1991)
Problem solving in electronics (Lesgold & Lajoie, 1991)
Computer skills (Kay, 1991)
Game playing (Frensch & Sternberg, 1991)
Personal problem solving (Heppner & Krauskopf, 1987)
Mathematical problem solving (Pólya, 1945; Schoenfeld, 1985)
Social problem solving (D'Zurilla & Goldfreid, 1971; D'Zurilla & Nezu, 1982)
Problem solving for innovations and inventions: TRIZ (Altshuller, 1994)

text: Characteristics of complex problems[edit]

text: As elucidated by Dietrich Dörner and later expanded upon by Joachim Funke, complex problems have some typical characteristics that can be summarized as follows:[citation needed]

text:
Complexity (large numbers of items, interrelations and decisions)

enumerability
heterogeneity
connectivity (hierarchy relation, communication relation, allocation relation)

Dynamics (time considerations)

temporal constraints
temporal sensitivity
phase effects
dynamic unpredictability

Intransparency (lack of clarity of the situation)

commencement opacity
continuation opacity

Polytely (multiple goals)

inexpressiveness
opposition
transience

text: Collective problem solving[edit]

text: Problem solving is applied on many different levels − from the individual to the civilizational. Collective problem solving refers to problem solving performed collectively.

text: Social issues and global issues can typically only be solved collectively.

text: It has been noted that the complexity of contemporary problems has exceeded the cognitive capacity of any individual and requires different but complementary expertise and collective problem solving ability.[44]

text: Collective intelligence is shared or group intelligence that emerges from the collaboration, collective efforts, and competition of many individuals.

text: In a 1962 research report, Douglas Engelbart linked collective intelligence to organizational effectiveness, and predicted that pro-actively 'augmenting human intellect' would yield a multiplier effect in group problem solving: "Three people working together in this augmented mode [would] seem to be more than three times as effective in solving a complex problem as is one augmented person working alone".[45]

text: Henry Jenkins, a key theorist of new media and media convergence draws on the theory that collective intelligence can be attributed to media convergence and participatory culture.[46] He criticizes contemporary education for failing to incorporate online trends of collective problem solving into the classroom, stating "whereas a collective intelligence community encourages ownership of work as a group, schools grade individuals". Jenkins argues that interaction within a knowledge community builds vital skills for young people, and teamwork through collective intelligence communities contribute to the development of such skills.[47]

text: Collective impact is the commitment of a group of actors from different sectors to a common agenda for solving a specific social problem, using a structured form of collaboration.

text: After World War II the UN, the Bretton Woods organization and the WTO were created and collective problem solving on the international level crystallized since the 1980s around these 3 types of organizations. As these global institutions remain state-like or state-centric it has been called unsurprising that these continue state-like or state-centric approaches to collective problem-solving rather than alternative ones.[48]

text: It has been observed that models of liberal democracy provide neither adequate designs for collective problem solving nor handling the substantive challenges in society such as crime, war, economic decline, illness and environmental degradation to produce satisfying outcomes.[49]

text: Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved as well as systems of managing these suggestions that provide good results.[50] With the Internet a new capacity for collective, including planetary-scale, problem solving was created.[51]