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Using G, Earth's mass, and Earth's radius, what value does Newton's law of gravitation predict for the acceleration due to gravity at Earth's surface?
A0.980 m/s^2
B6.67 m/s^2
C98.0 m/s^2
D9.80 m/s^2
Answer & Solution
Correct answer: D. 9.80 m/s^2
1. Substituting G, Earth's mass of 5.98 x 10^24 kg, and Earth's radius of 6.38 x 10^6 m into g = GM/r^2 gives a numerical value for g.
2. Carrying out that substitution and the arithmetic gives g = 9.80 m/s^2.
3. This matches the familiar surface value of g used in other calculations, confirming that the law of gravitation reproduces the everyday acceleration due to gravity.
4. 0.980 m/s^2 and 98.0 m/s^2 shift the decimal point by one place, and 6.67 m/s^2 mistakes the numeric part of G itself for the acceleration.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.5 Newton's Universal Law of Gravitation_
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