


Newton found the Moon’s inward acceleration in its orbit to be 0.0027 metre per second per second, the same as (1/60) 2 of the acceleration of a falling object at the surface of Earth. The Moon’s orbit has a radius of about 384,000 km (239,000 miles approximately 60 Earth radii), and its period is 27.3 days (its synodic period, or period measured in terms of lunar phases, is about 29.5 days). He calculated that the circular orbital motion of radius R and period T requires a constant inward acceleration A equal to the product of 4π 2 and the ratio of the radius to the square of the time: When Newton discovered that the acceleration of the Moon is 1/3,600 smaller than the acceleration at the surface of Earth, he related the number 3,600 to the square of the radius of Earth. He realized that this force could be, at long range, the same as the force with which Earth pulls objects on its surface downward. By invoking his law of inertia (bodies not acted upon by a force move at constant speed in a straight line), Newton concluded that a force exerted by Earth on the Moon is needed to keep it in a circular motion about Earth rather than moving in a straight line. Newton assumed the existence of an attractive force between all massive bodies, one that does not require bodily contact and that acts at a distance. By his dynamical and gravitational theories, he explained Kepler’s laws and established the modern quantitative science of gravitation. Newton discovered the relationship between the motion of the Moon and the motion of a body falling freely on Earth.
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