Mass vs. weight weightlessness
2 Force = change of momentum = mass x acceleration
F = ma newtons ( kg m /s2)
3 Action = reaction
Conservation of angular momentum for a circle = m x v x r
Kinetic energy 1/2 m v2
F = G M1 M2/d2
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
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.
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
Why two tides?
Tidal friction moon slows the earth
Synchronous rotation –Earth already slowed the moon.
Pluto-Charon also synchronous
Mercury just spin-orbit coupled