- #1

brijmohan3

- 5

- 0

## Homework Statement

A rocket ship is in circular orbit of radius R around a planet. Its velocity is doubled by a sudden engine burst. Calculate the furthest distance from the planet on the new trajectory.

## Homework Equations

Elliptical energy equation: E = Ek +Ep = -GMm/2a (a=semi major axis)

With Ek = (1/2)mv^2 and Ep = -GMm/R

## The Attempt at a Solution

Sorry for not being very user friendly.

From applying the elliptical energy equation to the initial circular orbit, I deduced

(1) v^2 = GM/R where v = initial velocity, M = mass of planet.

After the impulse, I have:

(2) E = (1/2)*m*(2v)^2 -GMm/R = -GMm/2(r+R)

where r = length to planet from furthest distance

Combining (1) and (2) gives r = -2R

I have two questions in regards to this:

1) Is the method correct?

2) If the answer is right, how is it possible that I get a negative value? Does this just mean it is taken in the 'negative' direction to the original 'R'?

Thanks, and sorry for the lack of friendliness in the equations again.