# Voyager: The mathematics of interstellar space travel

One of the key equations needed to understand spacecraft navigation is Newton's inverse square law of gravity:

We learned this in Physics 101 in the university as engineers. Essentially, the force measured (F) is gravity’s (G) work attracting two masses (m_{1}, m_{2}) that weakens/strengthens as the square of the distance between those two bodies changes. So gravity’s attraction effect is virtually infinite according to the inverse square law. The Sun’s mass is pretty huge.

Grasping this law we can further derive equations which describe the motion of the sun, the planets and the Voyager spacecraft flying between them. These equations are fairly trivial if we only consider two bodies---the Earth and the Sun. So we can find a simple solution which predicts exactly where the Earth and Sun will be at any point in time given information about their positions and velocities at some starting point. This two body problem, as it is called, is well known and fairly straightforward, but not very practical as the whole picture emerges.

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