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Last Modified: 2:01pm 10 Aug 11

Gravitational Potential Energy and Orbits

You can use the conservation of energy to analyze the motion of bodies in orbit around the Sun. For example, consider Halley's comet. It has a mass of about m = 10^(14) kg, and a very eccentric orbit:

At aphelion, the comet is roughly Ra = 5250 million km from the Sun (between the orbits of Uranus and Neptune) and is moving at roughly Va = 880 m/s.

  1. What is the kinetic energy of the comet at aphelion?
  2. What is the gravitational potential energy of the comet at aphelion? Use the standard astronomical convention that GPE = 0 at a distance of infinity, so the GPE is less than zero at any non-infinite distance. 
    
                                   G*M(sun)*m
                   GPE(r)  =   -  ------------
                                       r
  3. What is the comet's total energy at aphelion?

At perihelion, the comet is only Rp = 86 million km from the Sun (between the orbits of Mercury and Venus).

  1. What is the gravitational potential energy of the comet at perihelion?
  2. What is the kinetic energy of the comet at perihelion?
  3. What is the comet's speed at perihelion?

  4. What is the ratio of the fastest to the slowest orbital speed?
  5. What is the ratio of the largest to the smallest orbital distance?
  6. What do you notice about the ratios of speed and distance?

Astronomers noticed some of these connections between the various properties of planets in the solar system before Newton devised his Law of Universal Gravitation. Johannes Kepler came up with a set of laws describing orbital motion which turn out to be perfectly consistent with gravity. You can read about Kepler's Laws in many places, such as

Sorry, we could not find this page | RIT CIS - Center for Imaging Science

Sorry, we could not find this page

We apologize, but the page you were looking for is not available. Most of our material is available from the menus above.

Last Modified: 2:01pm 10 Aug 11

Adapted from Prof. Michael Richmond.