Chapter 4

 

Motion

 

         Speed, velocity

 

         Acceleration    acceleration of gravity  independent of object’s mass

 

         Momentum

 

Force

 

         Mass vs. weight     weightlessness

 

 

Newton’s Laws

 

         1  Inertia

 

         2 Force  = change of momentum   = mass x acceleration

 

F = ma   newtons ( kg m /s2)

 

         Centripetal acceleration

 

         3 Action = reaction

 

Conservation of momentum

 

Conservation of angular momentum   for a circle  = m x v x r

 

ENERGY

Kinetic energy 1/2 m v2

 

Potential energy conversion gas cloud

 

Radiative energy

 

Temerature vs Heat

 

NEWTON 

 

         Gravity

 

         F =   G M1 M2/d2

 

attractive

 

Kepler’s Laws  according to Newton

1.   the orbit of each planet about the Sun is an ellipse with the Sun at one focus
size - semimajor axis; shape – eccentricity
orbits can be ellipses but also parabolas and hyperbolas
motion about center of mass

 

2.   as a planet moves around its orbit, it sweeps out equal areas in equal times.
closer is faster conservation of angular momentum

 

3.   (orbital period in year)2  = (average distance in AU)3   p2 = a3    movie   generalized for any two objects

 

p2 = a3 4 pi2 /( G (M1 +M2 )   or   M1 +M2  = a3 4 pi 2 / Gp2

 

a simpler version uses years, AU and solar masses

 

(M1 +M2 ) p2 = a3   or   M1 +M2  = a3 / p2

 

this can be used to measure mass.

 

 

  Escape velocity 

         Kinetic energy = potential energy

 

                 ½ m v2 = G m M / R

                          v2 =  2G M / R

 

                         v = SQRT (2G M / R)

  Simple orbits   escape velocity

         

         How to move slower in orbit

 

TIDES

 

Moons tides on the Earth

Timing

Why two tides?

 

Spring and Neap tides

 

 

Tidal friction  moon slows the earth

 

Synchronous rotation –Earth already slowed the moon.

Pluto-Charon also synchronous

Mercury just spin-orbit coupled