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3

1) and 2) are easy to show, the bonus is very hard and I will not attempt it. A $L$iberation point can be seen as a balance between three accelerations in a rotating frame of reference. Gravity from $M_1$ Gravity from $M_2$ Centrifugal acceleration. For $L_2$, the first two are $-\frac{(1 - \delta)M_1}{(R + r_2)^2}$ and $-\frac{M_2}{r_"^2}$ respectively. ...

3

Given the radial distance $r$, velocity $v$, flight path angle $\gamma$ in radians, gravitational parameter $\mu$, and specific orbital energy $\epsilon$, the specific relative angular momentum is $$h= \|{\overrightarrow{r} \times \overrightarrow{v}}\| = rv\sin\left(\frac{\pi}{2}+ \gamma\right) =rv\cos\left( \gamma\right)$$ Then the orbital eccentricity ...

3

A detective story, not an answer I pulled the historical TLEs for the ISS from Space-Track.org. On 16 May 2016, it experienced a rev rollover. The TLEs around the rollover have rev's 99,989, 99,992, 1, 6 I then pulled up the historical TLEs for Explorer 7 in the time frame you suggested around 21 Aug 2019 - 27 Aug 2019. It includes the two TLEs you ...

2

There are a couple of potential solutions to this problem. One would be to place the mirrors at a distance just a little closer to Mars than the L2 point and let the radiation pressure counter the weak Mars net gravity field. One doesn't have to be right in line either, but a "halo" orbit circling the Mars/Sun line would allow you to balance forces while ...

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