Calculating Angle & Speed to Reach Planet's Moon from Station Orbit

[dirb]

Homework Statement

Find angle and velocity

Relevant Equations

Unsure

A station is orbiting a planet at a distance R₁, a moon is orbiting the planet at distance R₂ with the period T. The planet itself has a radius r_p and a mass m_p. We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase. Determine the angle $\theta$ and additional speed so that the station reaches the moon of the planet.

I was thinking that it has something to do with tangential velocity, and conservation of energy but I don't know how to write the maths? Which concepts should I use in this problem? thanks!

 

[haruspex]

Homework Statement:: Find angle and velocity
Relevant Equations:: Unsure

We know that when an object adds its velocity at a point in the orbit, the height of the opposite orbit will increase.

Unsure what is meant by "when an object adds its velocity". Do you mean "when an impulse is given to an object in orbit so as to increase its speed"?
And what is the "opposite orbit"? Is this a translation?

As to reaching the moon, a one time impulse to an object in a circular orbit will produce an elliptical one. And even if we got the station into the same circular orbit as the moon, it would necessarily be at the same period as the moon, so still might never reach it. I don't see how the question can be answered without knowing the initial angular separation of the bodies.

Edit: assuming the two given radii are different, the periods are different. Maybe we are to assume the impulse is given at the ideal point (the one requiring the least impulse) in their relative motions.