Gravitation - Changing Orbit Dynamics

[Lord Anoobis]

Homework Statement

A spaceship is in a circular orbit of radius $r_0$ about a planet of mass M. A brief but intense firing of its engine in the forward direction decreases the spaceship's speed by 50%. This causes the spaceship to move into an elliptical orbit.
a) What is the spaceship's, just after the rocket burn is completed, in terms of M, G and $r_0$?
b) In terms of $r_0$, what are the spaceship's minimum and maximum distance from the planet in its new orbit?

Homework Equations

The Attempt at a Solution

Let's look at part a first. This is an even numbered problem and I'm not sure about the answer.
Let $v_i = 2v_f$ and the mass of the ship be m
Just after firing, the movement can still be considered circular and the ship experiences a centripetal acceleration of
$a_r = \frac{F}{m}$, leading to
$\frac{GmM}{r_0^2} = m\frac{(2v_f)^2}{r_0}$
$v_f = \sqrt{\frac{GM}{4r_0}}$
Is this correct?

 

[mfb]

Just after firing, the movement can still be considered circular

This statement is a bit misleading. Just calculate the initial velocity in terms of M, G and r₀, then you don't need assumptions about the orbit (you know the initial orbit) to find v_f.

The answer is right.

 

[Lord Anoobis]

This statement is a bit misleading. Just calculate the initial velocity in terms of M, G and r₀, then you don't need assumptions about the orbit (you know the initial orbit) to find v_f.

The answer is right.

Looking at now I can see just how obvious and simple it is. But that's what happens when doing physics problems as the time approaches midnight. Thanks for the input.