You are making a trip in a space shuttle, and your friend Jimmy is in another space shuttle. He shares the same circular orbit with you, which is 420 km above the Earth, but he is 21 km ahead of you.
(a) How long will it take you to catch up with your friend if you reduce your orbital radius by 1.4 km? ("Catch up" here means to lie along a line that passes through the center of the earth.)
(b) By how much must you reduce your orbital radius to catch up in 9 hours?
Thank you!
Being in a 261 mile high orbit, your orbital velocity is 25,125 fps. The orbital period is 92.95 minutes.
Assuming that the 21km (68,901 ft.) distance is along the circumference of the orbit, your friend is only 2.75 sec. ahead of you. Clearly, you need only slow down a minute amount to shorten your period and meet up with your friend in less than 92.95 minutes.