Question

Kinematics, Force: You did so well in your physics course that you decided to try to get a summer job working in a physics laboratory at the University. You got the job as a student lab assistant in a research group investigating the ozone depletion at the Earth's poles. This group is planning to put an atmospheric measuring device in a satellite which will pass over both poles. To collect samples of the upper atmosphere, the satellite will be in a circular orbit 200 miles above the surface of the Earth which has a radius of about 4000 miles. To adjust the instruments for the proper data taking rate, you need to calculate how many times per day the device will sample the atmosphere over the South pole.

Answer 1

Calculate how many times per day the device will sample the atmosphere over the South pole is the same that launch the device from the South pole and calculate its angular speed in rpd (revolutions per day). The angular speed of the device can be expressed as

Since the device is in a circular orbit, we can find its tangetial speed using

inserting eq. (2) into (1), we obtain

we can get the centripetal acceleration of the device using Newton's second law,

inserting eq. (4) into (3),

inserting data given and known constants,

First we will convert miles to meter,

thus,

we want the angular speed in rpd so,

Then,

or

Therefore, the device will sample the atmosphere over the South pole 15 times per day.