Question

Why can’t we include all the appropriate gravitational forces for an interplanetary trajectory in a single equation of motion and solve it directly?

Answer 1

To put all the appropriate gravitational forces into a single equation, we need to define a single reference coordinate system to fit all the forces. Now, we know every planet is different having different trajectories around the other central objects (like the sun). The different motion of every object in our equation makes our equation 'highly nonlinear vector differential equation' which is very hard to solve. In fact, there’s no closed form solution to even a three-body problem.

answered by: anonymous