# Motion

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)

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

NEWTON

Gravity

F =   G M1 M2/d2

attractive

weight on other planets

# 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

if units are 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)

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