Garmaine Staff asked 2 years ago

The purpose is to study the motion of two celestial bodies analytically. What is the closed-form of the two-body problem if I was to solve it analytically without using a numerical approximation technique.

An example where this would be useful is this question from the book Analytical Mechanics of Space Systems by Hanspeter Schaub.

Write a numerical simulation that integrates the differential equations of motion in Eq. (9.45) using a fourth-order Runge Kutta integration scheme. Using the subroutine of task (b), compare the answer of the numerical integration to the analytical two-body solution.

$$\mathbf{\ddot{r}}=-\frac{\mu}{r^3}\mathbf{r} = -\frac{\mu}{r^2}\mathbf{\hat{r}} \tag{9.45}$$