Newton’s Universal “Law” of Gravitation and Planetary Data

View of Mars from the Hubble Space Telescope (March 1997).  Notice Mars’ thin atmosphere (~1% of Earth’s atmospheric mass), the wispy and mysterious clouds high in Mars’ atmosphere, and the polar ice caps.

Image Source: NASA

One of the most tangible of Isaac Newton’s contributions to physics is his Universal “Law” of Gravitation. I put “law” in quotes because first of all equations don’t ever govern natural phenomenon — they are simply mathematical descriptions of nature — and second, there are situations in which this relationship doesn’t really apply, such as at extremely small spatial scales or at very high speeds (such as near the speed of light).

But it will work for most situations that people will look at, such understanding the acceleration due to gravity on the various planets in our solar system, or in modeling the motions of our atmosphere and ocean, or in predicting the trajectory that a missile will follow in Earth’s gravitational field.

In any case, here is one form of Newton’s Universal “Law” of Gravitation:

g = GM/r^2

where g = the acceleration due to gravity from an object in m/s^2, G = the Universal Gravitational Constant = 6.67E-11 m^3/kg/s^2, M is the mass of the object in kg, and r is the distance from the center of mass of the object, in m.

When I refer to “the object,” I may be talking about a planet, or a rock, or a moon, or anything that has mass.

With this equation, the mass of the Earth or the Moon or any other solar system body can be estimated if the acceleration due to gravity g and the radius of the object r are known. Just solve the equation symbolically for M, plug in your numbers (as long as they have the correct units), and calculate.

By the way, just in case you never noticed my earlier blog entry, an excellent source of physical data about the planets in our solar system (compiled by Raymond T. Pierrehumbert at the University of Chicago) can be found here.