# Working with Newton's law of gravitation

Mars has a mass of about 6.4 x 10^23 kg, and its moon Phobos has a mass of about 9.6 x 10^15 kg. If the magnitude of the gravitational force between the two bodies is 4.6 x 10^15 N, how far apart are Mars and Phobos?

Please show the work, answer and the formulas you used. Thanks!

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

According to Newton's law of gravitation, the gravitational force of attraction between two bodies of mass m1 and m2 is given by,

F = (G m1 m2)/R^2

where G = 6.673*10^-11 m3 kg-1 s-2 is the gravitational constant and m1 and m2 are the masses.

We will now substitute the values

F = (6.673*10^-11 * 6.4*10^23 * 9.6*10^15)/R^2

it is given that, F = 4.6*10^15 N

thus,

4.6*10^15 = (6.673*10^-11 * 6.4*10^23 * 9.6*10^15)/R^2

or, R^2 = (6.673*10^-11 * 6.4*10^23 * 9.6*10^15)/4.6*10^15

= 89128069565217.39

or R = 9440766.36 m

= 9440.7 Km

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:50 pm ad1c9bdddf>https://brainmass.com/physics/work/working-newtons-law-gravitation-10464