1. The starship \"Exercise\" is in a circular orbit of radius ro about a star, a
ID: 1770215 • Letter: 1
Question
1. The starship "Exercise" is in a circular orbit of radius ro about a star, as depicted in 1 Captain Leeway fires the rocket thruster briefly so as to give the ship an instan taneous impulse directed toward the star (the resulting decrease in the mass of the ship is negligible) (a) Calculate the semi-latus-rectum (a) and the eccentricity for the new orbit. Ex- press the results as simply as possible in terms of I, ro, m, and k GMm (where m is the mass of the ship: M is the mass of the star (M m); and G is the universal gravitational constant) (b) Sketch the new orbit in relation to the original cicular orbit. Make a similar sketch for the case in which the impulse is applied in the opposite direction, away from the star.Explanation / Answer
Energy of the spaceship= k/2ro
k/2ro = mv2/2
also , v=I/m
v=sqrt(k/mro)
ro=a(1+e)
using energy conservation
and angular momentum conservation
e=(rv2/GM -1)
this implies, e= (I2r/k -1) (using above)
semi latus rectum= a(1-e2)
=r/(1+e) * (1-e2)
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