Question
Two satellites A and B are in different circular orbit about the earth. If the orbital speed of satellite A is twice that of satellite B what is the ratio (TA/TB) of the period of satellites ?
Answers
Anonymous
m Ac = m v^2/R
m Ac = G m Me/R^2
so
v^2/R = G Me/R^2
v^2 R G Me = constant
Va^2 Ra = Vb^2 Rb
if Va = 2 Vb
4 Vb^2 Ra = 1 Vb^2 Rb
so
Rb = 4 Ra
now period = 2piR/V
Ta = 2 pi Ra / Va
Tb = 2 pi Rb / Vb = 2 pi (4Ra) / (Va/2) = 8 * Ta
Ta/Tb = 1/8
m Ac = G m Me/R^2
so
v^2/R = G Me/R^2
v^2 R G Me = constant
Va^2 Ra = Vb^2 Rb
if Va = 2 Vb
4 Vb^2 Ra = 1 Vb^2 Rb
so
Rb = 4 Ra
now period = 2piR/V
Ta = 2 pi Ra / Va
Tb = 2 pi Rb / Vb = 2 pi (4Ra) / (Va/2) = 8 * Ta
Ta/Tb = 1/8