# Change orbit from circle to parabola

1. Nov 23, 2012

### athrun200

1(a) The problem statement, all variables and given/known data

A space ship travels in a circular orbit around a planet. It applies a sudden
thrust and increases its speed by a factor f . If the goal is to change the
orbit from a circle to a parabola, what should f be if the thrust points in the tangential direction?

in some other direction? What is the distance of closest approach if the
thrust points in the radial direction?

2. Relevant equations
Kepler’s laws

3. The attempt at a solution
We know that for circle, ε=0; for parabola ε=1
We also know that $ε=\sqrt{1+\frac{2EL^{2}}{m\alpha^{2}}}$
So $E=-\frac{m\alpha^{2}}{2L^{2}}$ for ε=0
$E=0$ for ε=1

But I don't know what to do next in order to find the increased factor f

2. Nov 23, 2012

### TSny

Hello. Could you please define the symbols $\alpha$ and $L$?

Can you express the kinetic energy of the ship in terms of $m$, $\alpha$ and $L$ before and after the thrust?

Last edited: Nov 23, 2012
3. Nov 23, 2012

### athrun200

$V(r)=-\frac{\alpha}{r}$
So $\alpha=GMm$

$L$ is angular momentum.

I think it is possible to express KE in terms of m and L but not $\alpha$.
But what should I do next?

4. Nov 23, 2012

### TSny

ok. Express kinetic energy in terms of $\alpha$ and $r$ using E= KE + V
You can assume $r$ remains constant during the thrust. So you should be able to relate initial and final speeds since you know how E changes. Instead of expressing E in terms of L, try to express E in terms of r for a circular orbit.