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## Homework Statement

R is Earth radius.

A satellite is launched 2R from the center of the earth, vertically above the northpole, at an angle of 60° to the vertical.

The satellite crashes on the southpole. Find the launch velocity and the maximum distance to the center of the Earth from its trajectory.

## Homework Equations

Energy conservation.

Angular momentum is also conserved.

## The Attempt at a Solution

I tried using those two conservation laws to first get the launch velocity.

Energy conservation:

[itex]\frac{mv^{2}}{2}+\frac{GMm}{2R}=\frac{mu^{2}}{2}+\frac{GMm}{-R}[/itex]

Angular momentum conservation:

[itex]v \cdot 2R \cdot sin(Pi/3) = u \cdot -R [/itex]

Solving first equation for u and plugging into the second gives me [itex]9684.37 m/s [/itex]

Can I find the maximum distance by using the same equations?