4 ms·
A very well known stable case is the restricted 3-body problem. It is where one of the objects out of the 3 are so light that you can ignore it when calculating
by krisoft 2y ago
A very well known stable case is the restricted 3-body problem. It is where one of the objects out of the 3 are so light that you can ignore it when calculating the orbits of the other two.
It is of practical use often with spacecrafts, where the spacecraft is much much smaller than the Sun-Planet or Planet-Moon it orbits around. Jokingly one could say this is why you don't need to worry about the Sun-Earth system blowing up every time we boost the international space station to a higher orbit.
- me_me_me 2y agoDoesnt it make it 2-body problem then? If one variable is so insignificant that it is ignored whats the point of including it all together?
- krisoft 2y ago> If one variable is so insignificant that it is ignored whats the point of including it all together? The variable is not ignored. The effect of that 3rd light mass on the other two is ignored. The effect of the two massive bodies on the 3rd is not ignored. As an example when you are planning orbital manoeuvres for the JWST space telescope you assume that the movements of the telescope won't affect the Moon or the Earth. But the Moon and the Earth will effect the position of the JWST. While this is not "true", it is accurate enough to work in practice. And of course the significance is that the 3rd light object is the only one the engineer controls. We can't change what the Earth or the Moon does, but we can make our spacecraft burn engines in a direction of our choosing. That gives a changed velocity vector. And then we can use the restricted 3-body problem to efficiently calculate where it will end up as a function of time.