Last edited 28Apr08 by Mike Hutches Find this document at http://cheer.math.edu/reulab/web/hutches2

# Voyager: Traversing the Modern Orrery

## Abstract

In this part of a joint project with Will Davis to create a modern orrery of our solar system in the CUBE, the date will be set to August 20, 1977. On this date NASA lauched Voyager II, and soon thereafter, Voyager I. These missions were designed to explore the far reaches of the solar system and will soon be leaving it, becoming humanity's first intergalactic space crafts. The project illustrates the maneuver of "gravity assist" to propel a small mass around a large.

## History and Math

The Voyager missions make use of a spacecraft manuever called a gravity assist to reach the edge of our solar system. This is a method that takes advantage ofthe two body method of determining orbits. When sufficiently close to a large body (ie Jupiter, Saturn) the craft's orbit can be detiremined entirely by the gravitational pull of that body only. This is called being in that planet's Sphere of Influence (SOI).

If the craft approaches the planet on a hyperbolic orbit it will have the velocity Vinf as it enters the planet's SOI. Due to the conservation of energy in a hyperbolic orbit the craft will also leave the planet's SOI with the velocity Vinf.

This does not seem to give any benefit to the craft if it leaves with the same speed that it left with, but that is because we are looking in the wrong frame of reference. When the craft enters the planet's SOI it is traveling Vinf with respect to the sun, but it is traveling towards the planet then. Afterwards it will be traveling away from the planet, so the craft's velocity with respect to the sun is actually Vinf+Vplanet.

Thus the craft gain velocity relative to the sun and this is how the Voyager missions got enough velocity to exit the solar system. This is what we will model inside our orrery. You will be able to watch and ride on the voyager craft as they leave Earth, garner speed at Jupiter and Saturn, and leave the solar system!

## Finished Project

Please write mikehutches@gmail.com if interested in the source code.

## Misc.

Diagram of voyager.

Here is a picture of me!

Here is a picture of what my project is about.

This is why I am not there today.

## References

Prussing, John E. and Conway, Bruce A., "Orbital Mechanics", Oxford University Press, New York, New York, 1993.

Hamilton, Calvin J. "The Voyager Planetary Mission" Jet Propulsion Laboratory, 1997 http://www.solarviews.com/eng/vgrfs.htm.