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_{μν} = 8πG/c^{4} T_{μν}

G (without the subscripts) is the gravitational constant, and c is the speed of light.

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.

By Jean Tate
Hi! When I was only six (or so), I went out one clear but windy night with my uncle and peered through the eyepiece of his home-made 6" Newtonian reflector. The dazzling, shimmering, perfect globe-and-ring of Saturn entranced me, and I was hooked on astronomy, for life. Today I'm a freelance writer, and began writing for Universe Today in late 2009. Like Tammy, I do like my coffee, European strength please.
Contact me: [email protected]

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