Transcript week 11

Chapter 13: Gravitation
Newton’s Law of Gravitation
A uniform spherical shell shell
of matter attracts a particles
that is outside the shell as if
all the shell’s mass is
concentrated at its center!
G = 6.67  10–11 N m2/kg2
Superposition Principle
Gravitation Near Earth’s Surface
Gravitational acceleration
1. Earth is not uniform.
2. Earth is not a sphere.
3. Earth is rotating.
Mean Earth surface (0 km, 9.83 m/s2), Mt. Everest (8.8 km, 9.80 m/s2), highest
manned balloon ( 36.6 km, 9.71 m/s2), Space Shuttle orbit (400 km, 8.70 m/s2),
and communications satellite (35,700 km, 0.225 m/s2)
Kepler’s Laws
1. The Law of Orbits: All planets move in elliptical
orbits, with the Sun at one focus.
2. The Law of Areas: A line that connects the planet
to the Sun sweeps out equal areas in the plane of
the planet’s orbit in equal times, i.e., the rate dA/dt
at which it sweeps out area A is constant.
3. The Law of Periods: The square of the period is
proportional to the cube of the semimajor axis of
its orbit.
Potential and Kinetic Energy
Potential Energy
Kinetic Energy
Total Energy
Einstein and Gravitation
Sample Problems 13-4, 13-5, 13-6