Gravity Equation

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 = Gm1m2/r2,
where F is the force due to gravity, between two masses (m1 and m2), 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/r2,
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/c4 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 = ?(GMa0/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 a0 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

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: JeanTate.UT@gmail.com

Recent Posts

This is What the Solar System Really Looks Like

At first glance, it looks like something from an alien autopsy. A strange organ cut…

15 hours ago

Beyond the Fermi Paradox V: What is the Aestivation Hypothesis?

Is it possible that the aliens are not hiding, but sleeping and waiting for the…

16 hours ago

Meteors of August: Our Guide to the 2020 Perseids

It's August and that means the Perseid meteors are inbound, starting this weekend this shower…

21 hours ago

Antarctica Is the Best Place On Earth for a Telescope, Is Also the Hardest Place to Put a Telescope

Twinkling stars might make for spectacular viewing on a hot summer’s night, but they are…

1 day ago

A Strange Planet has been Found that’s Smaller than Neptune But 50% More Massive

Astronomers have found another strange exoplanet in a distant solar system. This one's an oddball…

2 days ago

Martian Features Were Carved by Glaciers, not Flowing Rivers

Orbiters are giving us a chance to study the surface of Mars closely, and some…

2 days ago