- #1
Lord Anoobis
- 131
- 22
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?