Help With Satellites

Question

The mass of a planet is 5.00x10^23 kg its radius is R =6.40x10^6 m

An imaginary satellite orbits around this planet at a height (above the surface of the planet) H = 1.50x10^7 m. I found the satellites speed to be 1248.36m/s

The question is What is the period (in days) of the satellite's motion?

Any help would be appreciated!

Answer 1

I will set this up for you, but YOU do the math.

R = radius of planet in meters (given)

H = height of orbit in meters (given)

G = constant of gravitation (look it up in your book in units of Nm²/kg²)

M = mass of planet in kg (given)

Assuming the satellite is in a circular orbit, get the speed v in m/s by setting the gravitational force equal to the centripetal force, and solve for v. Note you do not need to know the mass of the satellite, since it cancels out.

GM / (R + H)² = v² / (R + H) ⇒

v = √[GM / (R + H)]

Get period P in seconds from

v = 2π(R + H) / P ⇒

P = 2π(R + H) / v

Now plug in R, H, and v to get P in seconds, convert seconds to days, and you are done.