- #1
Leo Liu
- 353
- 156
- Homework Statement
- none
- Relevant Equations
- F=ma
The answer to (c) is ##-2\pi AGMm##.
Answer to (d)
For sub-question d, I used a different approach and I don't know why the solution to (d) is an appropriate approximation.
What I did was that I use Newton's laws to obtain two differential equation in polar coordinate, as shown:
$$\text{Assume that the planet moves counterclockwise}$$
$$-\frac{GMm}{r^2}\boxed{\hat r}-Amv^2\boxed{\hat\theta} =m(\ddot r-r\dot\theta ^2)\boxed{\hat r}+m(r\ddot\theta+2\dot r \dot\theta)\boxed{\hat\theta}$$
$$\begin{cases}
-A(r\dot\theta)^2=r\ddot\theta+2\dot r\dot\theta\\
-GM/r^2=\ddot r-r\dot\theta^2\\
\end{cases}$$
I would like to know if my solution is correct, and why the official solution works. Thanks a lot.
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