Voyager Applets:
Involved Physics

Tour Home

The physics of this applet are pretty simple -- orbits in a Keplerian (i.e., point mass) gravitational potential. For this problem, analytic solutions exist for the position and velocity of an orbiting object as a function of time, given its orbital properties. See the "Links" section for references describing orbital calculations.

We do make a few simplifying assumptions, most notably:

  • The orbits of the planets are circular (they're close to circular, but not perfectly so).
  • The planets all move in single plane (again, they're close to coplanar in the ecliptic, but not perfectly so).

For Grand Tour, we calculate energy in an admittedly simplistic fashion. Each time the spacecraft needs to change velocity (to leave a planet, or to rendezvous with a planet), the energy used is considered simply to be the difference in the kinetic energy between those two velocities. So there's energy used each time it leaves a planet (where it needs to be boosted into a higher orbit) and each time it arrives at a planet (where it needs to match the planet's orbital speed).