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Newton compared the acceleration due to Earth's gravity at the Moon's distance, about 2.70 x 10^-3 m/s^2, with the centripetal acceleration needed to keep the Moon in its orbit, about 2.72 x 10^-3 m/s^2. What did this close agreement support?
AThe Moon would need to have no mass at all for this
BEarth's gravity supplies the Moon's centripetal acceleration
CThe Moon orbits with zero acceleration at constant speed
DGravity and centripetal force are unrelated, independent forces
Answer & Solution
Correct answer: B. Earth's gravity supplies the Moon's centripetal acceleration
1. The acceleration due to gravity at the Moon's distance and the centripetal acceleration required to keep the Moon moving on its orbital circle agree to within less than 1%.
2. Because these two independently calculated accelerations nearly match, the clear implication is that Earth's gravitational force is the very force supplying the Moon's centripetal acceleration.
3. The Moon clearly has mass, since it is being accelerated at all, and an object moving on a circular orbit is never at zero acceleration, since its direction is constantly changing.
4. Gravity is not some separate, unrelated force alongside centripetal force here; in this situation gravity is the centripetal force acting on the Moon.
_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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