A spacecraft is initially in a circular orbit of the sun at the Earth's orbital radius. It uses a single brief rocket thrust parallel to it's velocity to put it in a new orbit with aphelion distance equal to the radius of Jupiter's orbit.
What is the ratio of the spacecraft's speeds just after and just before the rocket thrust?
Assume Earth and Jupiter have cicular orbits, with radii 1.5 x 10^11m and 7.8x10^11m respectively. The mass of the sun is 1.99 x10^30kg and G = 6.672x10^-11 m^3kg^-1s^-2. Ignore gravitational attraction between the spacecraft and planets.
The Attempt at a Solution
Using L = [r x mv]
I equate the angular momentum at earths orbit and at jupiters orbit.
1.5x10^11 * mV1 = 7.8 x10^11 *mV2
So the m's cancel and V2/V1 = 1.5/7.8
Now im very unsure about this because i am asked for the ratio of velocities just before and after the thrust. But what i have calculated is the velocity of the spacecraft when it is in jupiters orbit. So this means that my V2 is slower than V1 but V2 just after the thrust is going to be faster than V1. Perhaps i just invert the fraction to show the change in velocity?
So i would get V2/V1 = 7.8/1.5
Any ideas guys? There is a second part to this question which is where i am to use G and the mass of the sun so i didnt think id need them for this part.