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The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
Thus, the gravitational acceleration at this radius is [14] = (). where G is the gravitational constant and M(r) is the total mass enclosed within radius r. If the Earth had a constant density ρ, the mass would be M(r) = (4/3)πρr 3 and the dependence of gravity on depth would be
The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude of the force between a point mass, M {\displaystyle M} , and another point mass, m {\displaystyle m} , is given by Newton's law of gravitation : [ 3 ] F = G M m r 2 {\displaystyle F={\frac {GMm}{r^{2}}}}
Geopotential is the potential of the Earth's gravity field.For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation.
Conversely, as two massive objects move towards each other, the motion accelerates under gravity causing an increase in the (positive) kinetic energy of the system and, in order to conserve the total sum of energy, the increase of the same amount in the gravitational potential energy of the object is treated as negative. [1]
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level (assumed zero geopotential) that represents the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. [1]
A gravitational potential function can be written for the change in potential energy for a unit mass that is brought from infinity into proximity to the Earth. Taking partial derivatives of that function with respect to a coordinate system will then resolve the directional components of the gravitational acceleration vector, as a function of ...
For this the gravitational force, i.e. the gradient of the potential, must be computed. Efficient recursive algorithms have been designed to compute the gravitational force for any N z {\displaystyle N_{z}} and N t {\displaystyle N_{t}} (the max degree of zonal and tesseral terms) and such algorithms are used in standard orbit propagation software.
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