To learn more gravitational slingshots: The physics behind the notion of how we would expand the earth's orbit is called the "gravitational slingshot," using the gravity of a massive object to accelerate or move another object. NASA's Cassini, Voyager and Galileo missions all make use of this phenomenon to accelerate the satellites deeper into space.

The long story behind gravitational slingshots
NASA uses "slingshots" for to catapult almost all of its space-exploring craft to great distances. And they've written very in-depth descriptions of how gravity assists work, and how bodies in the solar system effect each other. You can either learn all the basics of space flight , or skip right to the gravitational assist description .

Does the slingshot effect slow planets down?
ScienceNet answers this and other questions about gravitational slingshots.

A demonstration of how the slingshot works (math included)
ScienceNet answers this and other questions about gravitational slingshots.