Orbital Motion Circular Orbits Keplers Laws Energy in Elliptical - - PowerPoint PPT Presentation

Orbital Motion

• Circular Orbits
• Kepler’s Laws
• Energy in Elliptical Orbits
• Homework

Circular Orbits

• Consider a mass

in a circular orbit of radius

about a mass

• The relationship between the gravitational force on

due to

and the acceleration of

is given by Newton’s second law of motion as

Circular Orbits (cont’d)

• The velocity of the mass

can also be written in terms of the orbital period

(the time to 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

• f 350 km. (a) What is the mechanical energy

• f the ball in its orbit? (b) What is the

mechanical energy

• f 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.

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.

Energy in Elliptical Orbits

• The total mechanical energy for a mass

in an elliptical orbit about a mass

is

where

is the semimajor axis of the orbit

Homework Set 11 - Due Mon. Feb. 9

• Answer Questions 11.5 & 11.6
• Do Problems 11.13, 11.18, 11.20 & 11.22