Gravitation

Chronology Nicolaus Copernicus (1543): First to propose a system of planetary orbits. He argued that planets were in circular orbit around the sun. Johannes Kepler (1571) Worked as an assistant to Tycho Brahe making accurate measurements of the planets, after Brahe died he continued his work calculating planetary orbits with unprecedented accuracy.

Issac Newton (1643) Invented calculus, based on Kepler’s empirical observations he developed the laws of motion and developed the law of gravitational attraction Kepler showed that a planet moves round the Sun in an elliptical orbit which has the Sun in one of its two foci. He also showed that a line joining the planet to the Sun sweeps out equal areas in equal times as the planet describes its orbit. Both these laws were first formulated for the planet Mars

Kepler’s First Laws of Orbital Motion Planets follow elliptical orbits with the sun at one focus of the ellipse Ellipse r 1 + r 2 = 2a focus AphelionPerihelion b a c

Kepler’s Laws of Orbital Motion cont. Second Law: As a planet moves in its orbit, it sweeps out an equal amount of area in an equal time

Kepler’s Laws of Orbital Motion cont. The period T, of a planet increases as its mean distance from the Sun, r, raised to the 3/2 power: average distances

Newton’s Law of Universal Gravitation r Based on Kepler’s observations (empirical laws) Newton realizes that the same force that makes object fall on earth is the force that governs the orbits of the moon around the earth, or in general the movement of celestial bodies

Cavendish Experiment: Measurement of G

Gravitational attraction Gravity is the weakest of the fundamental forces (electromagnetic, weak, and strong (nuclear) The net force exerted by a rigid body on a mass m is the same as if all the mass was concentrated at its center of mass.

Gravitational Attraction on Earth’s “surface” For a mass on the surface of the Earth, we calculate the force of attraction using –M E = 5.97x10 24 kg –r Eb = 6.37x10 6 m Mass cancels of equation (every mass falls at the same rate) It has a small dependence on the height ( r E ) where it is calculated

Apparent Weight

Tides Tides are the rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans.