同济大学：《大学物理》课程教学资源（电子教案，英文版）第七章 引力

Gravity

Gravity

Agenda Today 1 Kepler's Laws 2 Newton's Law of gravity 3 gravitational field and potential energy 4 Einstein's theory of gravity

Agenda Today 1 Kepler’s Laws 2 Newton’s Law of gravity 3 gravitational field and potential energy 4 Einstein’s theory of gravity

天何所沓？十二焉分？ 日月安属？列星安陈？ Sphere of the Fixed Stars Celestial Region Sphere of the Moon (Terrestrial Region) Fire A标 Water

天何所沓？十二焉分？ 日月安属？列星安陈？

Ptolemy's model of universe motion

Ptolemy’s model of universe

The heroes OANNIS KETTLER Cilgi tmbgu soi N R山G-+s

The heroes

Kepler's laws The law of orbit:All planets move in elliptical with the sun at one focus The Law of area:A line joining any planet to the sun sweeps out equal areas in equal times vdt Planet 11

Kepler’s laws The law of orbit: All planets move in elliptical with the sun at one focus The Law of area: A line joining any planet to the sun sweeps out equal areas in equal times

Angular momentum(角动量) L=rxp The law of period: the square of the period of any planet is proportional to the cube of the planet's mean distance from the sun. T R

Angular momentum（角动量）: The law of period: the square of the period of any planet is proportional to the cube of the planet’s mean distance from the sun

Newton's Law of gravity: G RR / G:gravitational constant

Newton’s Law of gravity: G： gravitational constant

For any planet, GMML-MT 2 r2 20 V= T We have: 4z2 Kepler's law of GM. period

For any planet, T r v r v M r GM M p s p 2 2 2   We have: 3 2 2 4 r GM T s   Kepler’s law of period

B Credit:Richard Mushotzky (GSFONASA),ROSAT,ESA,NASA A Distance The existence of dark matter

The existence of dark matter