Gravitational acceleration and orbits
Newton wondered if the same force that caused objects to fall 9.8 m/s/s on earth could explain the Moon’s orbit around earth
- Newton (calculus) calculated the moon’s acceleration amoon
- from distance and velocity (sidereal period)
- amoon = 0.027 m/s/s vs. 9.8 at earth
- ratio of accelerations 9.8/0.027 = 3600
- ratio of distance to moon to radius of earth = 60
- Therefore a circular orbit could be explained if the gravitational force varied inversely with the square of distance
- considering also his laws of motion, Newton came up with:
the Universal law of Gravity
- FM<m = (GMm)/r2 -- attractive and radial
- what is the force of M on m?