Universe Today
There is not one, not two, not even three gravity equations, but many!
The one most people know describes Newton's universal law of gravitation:
F = Gm
1
m
2
/r
2
, where F is the force due to gravity, between two masses (m
1
and m
2
), which are a distance r apart; G is the gravitational constant.
From this is it straightforward to derive another, common, gravity equation, that which gives the acceleration due to gravity, g, here on the surface of the Earth:
g = GM/r
2
, Where M is the mass of the Earth, r the radius of the Earth (or distance between the center of the Earth and you, standing on its surface), and G is the gravitational constant.
With its publication in the early years of the last century, Einstein's theory of general relativity (GR) became a much more accurate theory of gravity (the theory has been tested extensively, and has
passed all tests, with flying colors
, to date). In GR, the gravity equation usually refers to Einstein's field equations (EFE), which are not at all straight-forward to write, let alone explain (so I'm going to write them … but not explain them!):
G
??
= 8?G/c
4
T
??
G (without the subscripts) is the gravitational constant, and c is the speed of light.
Finally, here's a
acceleration of gravity
equation you've probably never heard of before:
a = ?(GMa
0
/r),
where a is the acceleration a star feels, due to gravity under MOND (MOdified Newtonian Dynamics), an alternative theory of gravity, M is the mass of a galaxy, r the distance between the star in the outskirts of that galaxy and its center, G the gravitational constant, and a
0
a new constant.
Some websites which contain more on gravity equations, for your interest and enjoyment:
Newton's Theory of "Universal Gravitation"
(NASA),
Einstein's equation of gravity
(University of Wisconsin Madison - heavy), and
Gravity Formula
(University of Nebraska-Lincoln).
Universe Today, as you would expect, has several stories relevant to gravity equations; here are a few:
See the Universe with Gravity Eyes
,
A Case of MOND Over Dark Matter
, and
Flyby Anomalies Explained?
. Here's an article about 0 gravity.
Gravity
, an Astronomy Cast episode, has more on gravity equations, as do several Astronomy Cast Question Shows, such as
September 26th, 2008
, and
March 31st, 2009
.
Sources:
University of Nebraska-Lincoln
NASA
UT-Knoxville