Question

Good morning,

so I was reading this problem and I think i have an idea of how to do it, but I have to formulas in mind. I think F=GM+m/r^2 (solves for the gravitational force on the surface?) or G= Gm/r^2 ( where m is the mass of the satellite?)

a 200.0 kg artificial satellite circling the Earth completes each orbit in 240.0 minutes. Find the gravitational force on the satellite.

Answer 1

mass of satellite=m=200 kg

mass of earth=M=5.972*10^24 kg

let radius of the orbit is R.

if speed of the satellite is v,

then time period of each revolution=circumference of the orbit/speed

==>240*60 seconds=2*pi*R/v

==>v=4.3633*10^(-4)*R m/s....(1)

now, to stay in equilibrium in the orbit, centripetal force has to be balanced by the gravitational force.

then G*M*m/R^2=m*v^2/R

where G=universal gravitational constant=6.673*10^(-11)

then v^2=G*M/R

using equation 1,

(4.3633*10^(-4)*R)^2=G*M/R

==>1.90383*10^(-7)*R^2=G*M/R

using value of G and M,

1.90383*10^(-7)*R^3=3.9851*10^14

==>R^3=2.09321*10^21

==>R=12.79*10^6 m

then gravitational force=G*M*m/R^2

=487.225 N