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Orbital Motion
Circular Orbits
Kepler’s Laws
Energy in Elliptical Orbits
Homework
Circular Orbits
in a circular orbit of radius about a mass
Consider a mass
and the acceleration of
due to
is
The relationship between the gravitational force on
given by Newton’s second law of motion as
Circular Orbits (cont’d)
can also be written in terms of the orbital period
(the time to
The velocity of the mass
complete one orbit) as
Substituting this into the previous expression for
yields
The total mechanical energy of the orbiting satellite is
Example 1
A playful astronaut releases a bowling ball, of mass = 7.20 kg, into circular orbit about Earth at
an altitude of 350 km. (a) What is the mechanical energy of the ball in its orbit? (b) What is the
mechanical energy
of the ball on the launch pad at Cape Canaveral? (c) What is the change in the
ball’s mechanical energy between the launch pad and the orbit?
Kepler’s First Law
All planets move in elliptical orbits, with the Sun at one focus.
Kepler’s Second Law
A line that connects a planet to the Sun sweeps out equal areas in the plane of the planet’s orbit
in equal times.
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Kepler’s Third Law
The square of the orbital period of any planet is proportional to the cube of the semimajor axis of
the orbit.
4
1 2
5
3
6
Energy in Elliptical Orbits
in an elliptical orbit about a mass
The total mechanical energy for a mass
where is the semimajor axis of the orbit
is
Homework Set 11 - Due Mon. Feb. 9
Answer Questions 11.5 & 11.6
Do Problems 11.13, 11.18, 11.20 & 11.22