A satellite is in circular orbit around an unknown planet. The satellite has a speed of 1.70*10^4 m/s and the radius of the orbit is 5.25*10^6 m.
A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60*10^6 m. What is the orbital speed of the second satellite?
A satellite orbiting a planet has a centripetal force acting on it that keeps the satellite in the circular path and prevents it from moving in a straight line. This force is provided by the gravitational force of attraction between the planet and the satellite.
If the mass of the satellite is m, the mass of the planet is M and the radius of the orbit is r the gravitational force of attraction is `F = (G*M*m)/r^2` . The centripetal acting on the satellite in terms of its speed v is `m*v^2/r`
`(G*M*m)/r^2 = m*v^2/r`
=> `(G*M)/r = v^2`
=> `G*M = r*v^2`
The value of G and M is the same for both the satellites. This gives:
`(1.7*10^4)^2*(5.25*10^6) = v^2*8.6*10^6`
=> `v^2 = (1.7*10^4)^2*(5.25*10^6)/(8.6*10^6)`
=> v = 13282.48 m/s
The orbital speed of the second satellite is 13282.48 m/s