Question

You found your physics course so interesting that you decided to get a job working 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 that will pass over both poles. To collect samples of molecules escaping from the upper atmosphere, the satellite will be put into a circular orbit 150 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. You do not remember the values of G (Newton’s Gravitational Constant) or the mass of the Earth, but you do remember the acceleration with which objects fall at the surface of the Earth

Answer 1

given
radius of orbit of satellite, r = 4000 miles

= 4000*1609 m

= 6.436*10^6 m

Re = (4000 - 150) miles

= 3850*1609 m

= 6.195*10^6 m

on the surface, g = G*Me/Re^2

at the location of satellite,

g' = G*Me/r^2

g'/g = (Re/r)^2

g' = g*(Re/r)^2

= 9.8*(6.195/6.436)^2

= 9.08 m/s

we know, g' = v^2/r

==> v = sqrt(g'*r)

= sqrt(9.08*6.436*10^6)

= 7644 m/s

time period of satellite, T = 2*pi*r/v

= 2*pi*6.436*10^6/7644

= 5290 s

= 5290/(60*60)

= 1.469 hours

the number of times the satellite sample = 24/T

= 24/1.469

= 16.3 times <<<<<<<-----------------Answer