How Does a Rocket's Trajectory Change Near a Star?

[skizm240]

A rocket is 1.00x10^10m from a moving star moving at a speed of 1.00x10^5 m/s with a total energy of -1.67x10^17 J when it experiences a gravitational force magnitude of 6.67x10^7 N. It turns on its thrusters and its speed as well its distance to the star doubles by the time the thrusters are turned off.

Find the rocket's mass, the star's mass
Prove the fist trajectory is elliptical and not circular.
If a=1.11x10^10 m for the first trajectory, find the period.
Find the work done by the thrusters in changing trajectories.

How would I star this problem? It is the first part of physics ( Mech)

I know r'= 2r and v'=2v
would I use the orbtial formulas to find the mass or something else. Any hints or anything will be helpful thank you.

 

[SpaceTiger]

Find the rocket's mass, the star's mass

What's the expression for the total energy of an object in orbit about a central mass? What's the expression for the gravitational force between two objects?

Prove the fist trajectory is elliptical and not circular.

What's the velocity of an object in a circular orbit at this distance? How does it compare to the rocket's velocity?

If a=1.11x10^10 m for the first trajectory, find the period.

What is Kepler's Third Law?

Find the work done by the thrusters in changing trajectories.

What is the energy of the new orbit? Where did this energy come from?