### gravitational potential model

**(gravitational model, gravity model)**
(mathematical model of an astronomical body's gravitational field)

I use the term **gravitational potential model** for a common
type of model of the gravitational potential of
an astronomical body (e.g., a planet or moon),
essentially defining a map showing the acceleration that the
body's gravity would produce in different directions and altitudes,
describing this map in terms of spherical harmonics.
The term **geopotential model** is common specifically for Earth,
and the terms **gravitational model** and **gravity model** are also used
(but be warned *gravity model* is more often seen regarding economics models
with a similarity to the effects of gravitational potential).
Such *gravitational potential models*
use spherical harmonic coefficients to describe the gravitational pull
in each direction in terms of overall patterns in the variation
in different directions,
in a similar manner to that in which a Fourier transform
describes a periodic function (or equivalently, a function over an interval).
The coefficients are generally derived from many measurements,
e.g., with gravimeters, or by tracking objects orbiting
the body, such as space probes, or are modeled and calculated based
on analysis of factors such as rotation period and constituents.

The coefficients used generally are based on harmonics aligned
with the body's rotation, and the coefficients most likely to be
significant and of interest for objects massive enough to be
nearly spherical are **zonal coefficients**
(**C**_{n 0}, for n=1,2,3,..., often written C_{00},
C_{10}, etc., for small integer),
corresponding to patterns that are the same along any meridian, the
other coefficient of most interest being one particular
**sectorial coefficient**, **C**_{2 2} (often written C_{22}).
C_{0 0} is merely the average gravity, and
C_{1 0} is generally minor.
C_{2 0} indicates the oblateness (greater or lesser gravity
around the equator), and C_{2 2} is similar, but "sideways",
indicating some greater or lesser amount at two opposite points on
the equator, such as from extra mass toward the end points of a line
between them.
The zonal coefficients are also commonly cited
as J_{n} (the J_{n} value is defined so as to be the
negative of the C_{n 0} value), **J**_{2} being the most
significant.

(*gravity,physics,planets*)
**Further reading:**

http://en.wikipedia.org/wiki/Geopotential_model

**Referenced by pages:**

J_{2}

Index