Planet-X has a mass of 3.06×10 24 kg and a radius of 5620 km. What is the First
ID: 2031779 • Letter: P
Question
Planet-X has a mass of 3.06×1024 kg and a radius of 5620 km. What is the First Cosmic Speed i.e. the speed of a satellite on a low lying circular orbit around this planet? (Planet-X doesn't have any atmosphere.)
6.03 km/s
What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet?
8.52 km/s
If the period of rotation of the planet is 14.0 hours, then what is the radius of the synchronous orbit of a satellite?
(I need help with this last question, I've tried so many different equations!)
You are correct.Your receipt no. is 161-7754 Previous Tries
Explanation / Answer
given
M = 3.06*10^24 kg
T = 14 hours
= 14*60*60 s
radius of orbit, r = ?
we know,
T = 2*pi*r^(3/2)/sqrt(G*M)
T^2 = 4*pi^2*r^3/(G*M)
==> r^3 = G*M*T^2/(4*pi^2)
r = (G*M*T^2/(4*pi^2))^(1/3)
= (6.67*10^-11*3.06*10^24*(14*60*60)^2/(4*pi^2))^(1/3)
= 2.36*10^7 m or 23600 km