Planet-X has a mass of 5.89×1024 kg and a radius of 8190 km. What is the First C
ID: 1460634 • Letter: P
Question
Planet-X has a mass of 5.89×1024 kg and a radius of 8190 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.) 6.93 km/s You are correct. Your receipt no. is 150-893 Help: Receipt What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet? 9.79 km/s You are correct. Your receipt no. is 150-1063 Help: Receipt If the period of rotation of the planet is 19.8 hours, then what is the radius of the synchronous orbit of a satellite? Can not figure out last question. Show work please.
Explanation / Answer
time period T = orbital distance / orbital speed
T = (2*pi*r)/(vo)
vo = sqrt(GM/r)
T = 2*pi*r/(sqrt(GM/r)
T = 2*pi*r^(3/2)/sqrt(GM)
given T = 19.8 hours = 19.8*60*60 = 71280 s
71280 = (2*pi*r^(3/2))/(sqrt(6.67*10^-11*5.89*10^24))
r = 3.698*10^7 m