A satellite travels around the Earth at 7.5 km/s at an altitude of 320 nautical miles...?

Question

a) How long does the satelite take to make one revolution around the Earth?

b) How long does it take the satellite to travel between LA and NY (3000 miles)?

This is a question asked in my geometrical optics course, so I'm not sure if there is some kind of optics principle used here or if it's more suited towards a physics class approach.

I found that 1 nautical mile = 1852 m if that helps at all.

Answer 1

The formula to calculate the period of orbit for an earthly satellite is:

p = sqrt((4 * π^2 * r^3) / (3.986005x10^14 m^3 / s^2) where r is the radius of orbit from the center of mass of the earth and that big divisor is the universal gravitational constant times the mass of the earth, more details in source below).

This gives p^2 = (4.870*10^24 m^3) / (3.986*10^14 m^3 / s^2) =

1.222*10^10 s^2, so p = 111,000 s = 30.71 hours

Since the distance of 3000 miles is about 4800km and the circumference of the earth is about 40,000 km, the span is about 12% of the circumference and thus the satellite would take about 0.12 * 30.17 hours = 3.62 hours to transit from above LA to NY.