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PBL: Orbits

Kepler's laws

(1) All planets move about the Sun in elliptical orbits, having the Sun as one of the foci.

(2) A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time.

(3) The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.

  • Using Excel design an iterative model to show that these 3 laws are a consequence of Newton's universal law of gravity.
  • Show that the total energy of an orbiting planet is constant.
  • Use your knowledge of circular motion to predict the velocity for a circular orbit, use your model to test the prediction.

Elastic orbits

A mass is made to travel in a circle on the end of an elastic string.

  • Derive an equation for the relationship between the time period and radius.
  • Design an experiment to test your hypothesis.

Algodoo orbits

In the Algodoo universe where G = 1 Nm2kg-2 there are two bodies with diameter 1m and mass 1kg separated by 50 m.

  • Is it possible to project a small body from the surface of one so that it orbits the other?

Escape velocity

Use your different models to show that the escape velocity 1m from a body of mass 1 kg in a universe with  G = 1 Nm2kg-2 is √2 ms-1

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