Chapter 9: Gravity Gravity is the force most familiar to us, and yet, is the least understood of all the fundamental forces of nature.

Four Fundamental Forces of Nature Gravity Electromagnetism Strong Nuclear Force (This holds atomic nuclei together) Weak Nuclear Force (Allows for radioactive decay)

Kepler’s Three Laws of Planetary Motion Go Columbia!! Johannes Kepler (1571-1630)

First Law Each planet moves in an elliptical orbit with the Sun at one focus.

An Ellipse Foci r1+r2 = constant a Minor Axis r2 r1 Semi-major Axis (a) Major Axis

Orbiting planet Sun at one focus

The Second Law The line from the sun to any planet sweeps out equal areas in equal times.

Orbiting planet A A Sun

The Third Law The square of the orbital period is proportional to the cube of the semi-major axis For a circular orbit, the semi-major axis is the radius

Newton’s Law of Universal Gravitation Every body in the universe exerts a force on every other body which is proportional to the product of their masses and inversely proportional to the square of the distance between them

R M1 M2

The Tides

Einstein’s Theory of Gravity

a =g a =g/2 a = 0 a =g/2 a =g