AST 307 · Introductory Astronomy
Fall 2003

AST 307
Homework #3
Due Friday Sep. 19

  1. Look up the period and semimajor axis of the orbit of a moon of Jupiter in Table 11.1 in your text (pick any one but say which one you picked). Calculate the mass of Jupiter by using these numbers with Newton's version of Kepler's third law:       2     3
              P = a / M

    Note that you will have to put P and a into appropriate units for this formula, and M will be in units of the Sun's mass.
    Compare your answer with the actual mass of Jupiter.

  2. The Earth's gravity causes the Moon to orbit the Earth, approximately following a circular path with a radius equal to the distance from the Earth to the Moon, given in the back of your book.

    Using the period and size of the Moon's orbit, calculate the acceleration of the Moon.

    Compare that acceleration to the acceleration due to gravity on the surface of the Earth, g = 9.8 m/s^2. Why is the acceleration of the Moon smaller than the acceleration at the surface of the Earth by the factor that it is?

    (This is the argument that Newton used to figure out his law of gravity.)

  3. Assume you are in a spaceship with a mass of 1000 kg, orbiting in a circular orbit with a radius of 1 AU around the Sun.

    Calculate your speed, your kinetic energy, and your potential energy.

    Assume you fire your rocket long enough to bring you up into a circular orbit 2 AU from the Sun. What are your speed, kinetic energy, and potential energy now?

    How much total energy did your rocket engine have to give to your spaceship to get you into the bigger orbit? How does this compare to the change in your kinetic and potential energies?

    (This is an example of what it called the Virial Theorem, which we will use in understanding atoms and stars, as well as orbits.)

15 September 2003
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