Garmaine asked 4 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.
$$\mathbf{\ddot{r}}=-\frac{\mu}{r^3}\mathbf{r} = -\frac{\mu}{r^2}\mathbf{\hat{r}} \tag{9.45}$$
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