                                            ## 2. Gravity and Motion

• According to Keplers first law, the planets move in elliptical orbits with the Sun at one focus of the ellipse.

• According to Keplers second law, a planet sweeps out equal areas in equal times, which means that a planet moves faster when closest to the Sun, at the perihelion of the planets orbit.

• According to Keplers third law, the squares of the orbital periods of the planets are in proportion to the cubes of their average distances from the Sun.

• Two masses attract each other with a gravitational force that varies in proportion to the product of the masses and the inverse square of their separation.

• Mass is an intrinsic property of an object; weight decreases with increasing distance from the source of gravity.

• The Moons gravitational pull produces two tidal extensions, or bulges, of the ocean water. As the Earth rotates, the tidal bulges sweep toward and away from the beaches, producing the rise and fall of the tides twice each day.

• The Suns gravitational attraction produces ocean tides that are about one quarter the size of the Moons ocean tides.

• Due to tidal friction in shallow ocean waters, the Earth is slowing down and the days are getting longer, at about 0.002 seconds per century.

• The Moon is moving away from the Earth, and the distance between the Earth and the Moon is increasing at the rate of about 0.04 meters every year.

• If a large satellite moves closer to a planet than the Roche limit, the tidal forces of the planets gravity will tear the satellite apart.

• Motion holds the planets up against the relentless pull of the Suns gravity.

• When the speed of a small object is greater than the escape velocity of a larger object, the smaller object can escape the gravitational pull of the larger one.

• The escape velocity depends only on the mass of the large object and the distance separating the centers of the two objects.

• The orbital speed of the planets is equal to the Suns escape velocity at their distance.

• The orbital period of the Earth, one year, and the mean distance between the Earth and the Sun, 1 AU, can be used to determine the mass of the Sun M  = 1.989 x 1030 kg.

• The gravity of an object is caused by its curvature of nearby space-time.

• The Suns curvature of nearby space explained the precession of Mercurys perihelion and predicted the bending of starlight that passes near the Sun  first observed during the total solar eclipse of May 29, 1919.

Copyright 2010, Professor Kenneth R. Lang, Tufts University     