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