alleryStart learning →Earth's radius is 6.37 x 10^6 m, and g at its surface is about 9.8 m/s^2. Using G = 6.673 x 10^-11 N.m^2/kg^2, what is Earth's mass?
A5.96 x 10^22 kg
B5.96 x 10^24 kg
C9.35 x 10^24 kg
D3.79 x 10^31 kg
Answer & Solution
Correct answer: B. 5.96 x 10^24 kg
1. Rearrange g = GM/r^2 to get M = g r^2 / G.
2. M = (9.8)(6.37 x 10^6)^2 / (6.673 x 10^-11) = (9.8)(4.058 x 10^13) / (6.673 x 10^-11).
3. M = 3.977 x 10^14 / 6.673 x 10^-11 = 5.96 x 10^24 kg.
_Source: OpenStax Physics (CC BY 4.0), Ch 7 "Newton's Law of Gravitation", section 7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity_
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