Two satellites are in orbit around the same planet. Satellite A has a mass of 1.5 x 10^2 kg, and satellite B has a mass of 4.5 x 10^3 kg. The mass of the planet is 6.6 x 10^24 kg. Both satellites have the same orbital radius of 6.8 x 10^6 m. What is the difference in the orbital periods of the satellites?
A. No difference
B. 1.5 x 10^2 s
C. 2.2 x 10^2 s
D. 3.0 x 10^2 s
Thanks.
A. No difference
B. 1.5 x 10^2 s
C. 2.2 x 10^2 s
D. 3.0 x 10^2 s
Thanks.
-
Gravity giving centripetal force, so
>>
GmM/r square = m (v square )/ r Where r is the distance between the centers of any two masses
So we get
V= sq root( GM/ r)
Time period = 2 x pi x r / v. Distance / velocity
Time period = 2 x pi x sq root ( r ^3 / GM)
T(a) -T(b)= ( 2 x pi. /sq root GM(planet). ) x ( R(a)^3/2 - R(b)^3/2)
=0 as R(a) is equal to R(b)
Note time period doesnot depends on the mass of satellite
Only depends on mass of earth(planet) and radius of satellite (joining centers of both, planet and satellite)
ANSWER IS 'A'
>>
GmM/r square = m (v square )/ r Where r is the distance between the centers of any two masses
So we get
V= sq root( GM/ r)
Time period = 2 x pi x r / v. Distance / velocity
Time period = 2 x pi x sq root ( r ^3 / GM)
T(a) -T(b)= ( 2 x pi. /sq root GM(planet). ) x ( R(a)^3/2 - R(b)^3/2)
=0 as R(a) is equal to R(b)
Note time period doesnot depends on the mass of satellite
Only depends on mass of earth(planet) and radius of satellite (joining centers of both, planet and satellite)
ANSWER IS 'A'