UNIVERSAL GRAVITATION Who are the main contributers to our understanding of gravity, and what did they do?

TYCHO BRAHE Spent most of his life star gazing. Tycho was an early astronomer who cataloged the positions of the planets and stars for decades.

Kepler used Tycho Brahe's data to develope 3 Laws of Planetary Motion

1. The Planet's Orbits are Ellipses. With the Sun at one Focal Point.

A line drawn from the Sun to a Planet will sweep out equal areas in equal times. A1 A2 A1 = A2 t1 t2 t1 = t2 2.

The radius of a planet’s orbit cubed ( r3 ) Divided by the period of orbit squared ( T2 ) IS A CONSTANT ! 3. r3 T2 = k

NEWTON used the Centripetal Force Equation and Kepler’s 3rd Law to determine:

m1m2 d2 Fg 

SO IF: m1 m2 d THEN: Fg = F d 2m1 m2 Fg = 2F 2d m1 m2 Fg = F/4 d/2 2m1 2m1 Fg= 16F

BUT: This was not overly useful, in order to use the equation to calculate the forces of attraction between two objects, a constant was needed.  = Is theoretically very important Gets you something you can really use!

Henry Cavendish Determined the UNIVERSAL GRAVITATIONAL CONSTANT By finding the force needed to twist the torsion fiber created by the movement of the small masses ( m ) toward the large masses ( M ) over a known distance. Here’s how it worked.

Using Newton’s equation we can state that: d2 m1m2 = K Fg Rearranging to solve for K we get: K = Fg d2 m1m2

Cavendish set up his experiment with m1, m2, d, and Fg as known quantities. He was then able to solve for K. He renamed it G, the UNIVERSAL GRAVITATIONAL CONSTANT G = 6.67 x 10-11 N m2 Kg2