3.3 Newton’s Law of Universal Gravitation Warm Up The Moon orbits Earth about once every 28 days. Why doesn’t the Moon crash into Earth? ___________________________________________________________________________________________ ___________________________________________________________________________________________ ___________________________________________________________________________________________
From Kepler to Newton
Kepler’s three laws describe the orbits of the planets around the Sun. Newton used Kepler’s laws to derive a law describing the nature of the gravitational forces that cause the planets to move in these orbits. Newton concluded that the force that keeps planets in orbit is the same force that makes an apple fall to the ground. He stated that there is a gravitational force between any two bodies in the universe. Like all other forces, gravity is a mutual force. That is, the force with which Earth pulls on a falling apple is equal to the force with which the apple pulls on Earth, but in the opposite direction. Earth pulls on your body with a force of gravity that is commonly referred to as your “weight.” Simultaneously, your body exerts a force on planet Earth of the same magnitude but in the opposite direction. Relative to each other, Earth “weighs” the same as your body! Newton was able to use Kepler’s laws as a starting point for showing that the force of gravity between the Sun and the planets varied as the inverse of the square of the distance between the Sun and the planets. He was convinced that the inverse square relation would apply to everyday objects near the surface of Earth as well. He produced arguments suggesting that the force should depend on the product of the masses of the two bodies being attracted to one another. The mathematical details of how Newton arrived at his famous law of universal gravitation can be found in many references, but are too lengthy to reproduce here. Newton’s Law of Universal Gravitation Every body in the universe attracts every other body with a force that is (a) directly proportional to the product of the masses of the two bodies and (b) inversely proportional to the square of the distance between the centres of mass of the two bodies. The equation for Newton’s law of universal gravitation is: F = G
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Chapter 3 Circular Motion and Gravitation 169