Interplanetary Transfers When more than one planet is involved, the problem is no longer a two-body problem. Nevertheless, it is common(at least to get a good approximation)to decompose the problem into a series of two body problems Consider, for example, an interplanetary sfer in the solar system. For each planet we define the sphere of influence(SOI). Essentially, this is the region where the gravitational attraction due to the planet is larger than that of the sun The mission is broken into phases that are connected by patches where each patch is the solution of a two body problem. This is called the patched conic approach. Consider, for instance, a mission to Mars. The first phase will consist of a geocentric hyperbola as the spacecraft escapes from earth sol. The second phase rould start at the edge of the earths SOl, and would be an elliptical trajectory around the sun while the spacecraft travels to Mars. The third phase would start at the edge of Mars'sol, and would be a hyperbolic approach trajectory with the gravitational field of mars as the attracting force For long missions, the situation can become very complex as one often tries to take advantage of the gravita tional fields of the planets encountered on the way, by entering into their SOIs with the objective of either changing direction or gaining additional impulse. This technique is often referred to as gravity assist. References [1 F.J. Hale, Introduction to Space Flight, Prentice-Hall, 1994Interplanetary Transfers When more than one planet is involved, the problem is no longer a two-body problem. Nevertheless, it is common (at least to get a good approximation) to decompose the problem into a series of two body problems. Consider, for example, an interplanetary transfer in the solar system. For each planet we define the sphere of influence (SOI). Essentially, this is the region where the gravitational attraction due to the planet is larger than that of the sun. The mission is broken into phases that are connected by patches where each patch is the solution of a two body problem. This is called the patched conic approach. Consider, for instance, a mission to Mars. The first phase will consist of a geocentric hyperbola as the spacecraft escapes from earth SOI. The second phase would start at the edge of the earth’s SOI, and would be an elliptical trajectory around the sun while the spacecraft travels to Mars. The third phase would start at the edge of Mars’ SOI, and would be a hyperbolic approach trajectory with the gravitational field of Mars as the attracting force. For long missions, the situation can become very complex as one often tries to take advantage of the gravita￾tional fields of the planets encountered on the way, by entering into their SOI’s with the objective of either changing direction or gaining additional impulse. This technique is often referred to as gravity assist. References [1] F.J. Hale, Introduction to Space Flight, Prentice-Hall, 1994. 6