Please I want someone to answer it clearly and step by step A 500-kg satellite i
ID: 1609370 • Letter: P
Question
Please I want someone to answer it clearly and step by step
A 500-kg satellite is put into a circular orbit around the earth at an altitude equal to the radius R_E of the earth, i.e., it circles at a distance of 2R_E from the center of the earth. (The mass of the earth is 6.0 times 10^24 kg, and the radius of the earth is 6.4 times 10^6 m). (a) Find the acceleration of the satellite at this distance. (b) Find the velocity of the satellite in its orbit. (c) How long does it take the satellite to make one revolution around the earth?Explanation / Answer
a) acceleration of the satellite, g' = G*Me/r^2
= G*Me/(2*Re)^2
= (1/4)*(G*Me/Re^2)
= g/4
= 9.8/4
= 2.45 m/s^2
b) use, g' = v^2/r
v = sqrt(g'*r)
= sqrt(g'*2*Re)
= sqrt(2.45*2*6.4*10^6)
= 5600 m/s
c) Time period, T = 2*pi*r/v
= 2*pi*2*Re/v
= 2*pi*2*6.4*10^6/5600
= 14361 s or 240 min or 4.0 hours