A spacecraft of mass 500 kg is in orbit around an asteroid ``the size
of the Isle of Wight'', which you can assume to be a sphere of radius 10 km
consisting of rock with a density 2700 kg m
.
The spacecraft's orbit has
a semimajor
axis of 330 km and an eccentricity of 0.4. What is the distance of closest
approach that the spacecraft makes to the asteroid?
[5 marks]
Find the period of the orbit in days.
[7 marks]
If the spacecraft approached the asteroid initially along a parabolic orbit, how much energy did it have to lose to be inserted into its present orbit?
[8 marks]
What is the maximum speed of the spacecraft in its present orbit?
[5 marks]
[Hints can be found here, but do not follow this link until you have attempted the question on your own.]