Two satellites are in orbit around the Earth. The first is in a geostationary orbit, the second satellite at radius half that of the first. What is the (approximate) period, in hours, of the second satellite?

A geostationary satellite is one that remains above the same location on Earth. This means it has to be above the equator, and its orbit period is exactly 24 hours! The period of a circular orbit is distance/speed, which is 2piradius/(tangential velocity). If the radius is halved, to remain in orbit the velocity has to go up. Now by equating Newton's gravitational equation with F=mv2/r, we have F=mv2/r=GMEarthm/r2 So v2=GMEarth/r Halving r means v must go up by sqrt(2). So our new period is Tnew=24*(1/2)*(1/sqrt(2))=8.5 hrs.

HA
Answered by Hubert A. PAT tutor

6694 Views

See similar PAT University tutors

Related PAT University answers

All answers ▸

How do I sketch a function from its equation without using my graphical calculator?


Given that during a total solar eclipse the Sun is fully hidden by the Moon, calculate the radius of the Moon. (You may use the following: Solar radius 700,000 km, Sun-Earth distance 150,000,000 km, Moon-Earth distance 400,000 km)


a boat is in a still lake with its anchor up in the boat, it then drops its anchor till it hits the bottom of the lake. Is the water level highest a) when the anchor is in the water. b) when the anchor is in the boat. c) it makes no difference.


How do I evaluate something like 3070^2-3069^2?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences