A space craft is initially in a circular orbit close the Earth. An engine fires so that the space craft rapidly increases its speed and transfers to an elliptical orbit with an apogee distance equal to the radius of the Moon's orbit around the Earth. This apogee distance is 60 times the radius of the initial circular orbit of the space craft. Find the necessary fractional increase in speed which must be produced by the engine. What will happen if the engine produces a fractional increase in speed which is 1% too large?
[Hints can be found here, but do not follow this link until you have attempted the question on your own.]