You did so well in your physics course that you decided to try to get a summer j

Question

1. 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.

Explanation / Answer

As the satellite is in circular orbit the Centripetal force needed will be given by gravity .

So equate the two

m*w^2*r = Gm(Me)/r^2

Me is mass of Earth

r = 4200 miles = 6759245 m

w^2 = G*Me/r^3 = (6.67*10^-11)*(5.97*10^24) / (6759245)^3 = 1.29*10^-6

w = 1.136*10^-3 rad/s

Time to cover one revolution = Time to pass south pole = 2*pi/w = 5530.9 s

Time in 1 day = 24*60*60 = 86400 s

No of times it pass = 86400/5530.9 = 15.7 or approx 16 Times

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