Answer:
The ratio of the orbital time periods of A and B is [tex]\frac{1}{2}[/tex]
Solution:
As per the question:
The orbit of the two satellites is circular
Also,
Orbital speed of A is 2 times the orbital speed of B
[tex]v_{oA} = 2v_{oB}[/tex] (1)
Now, we know that the orbital speed of a satellite for circular orbits is given by:
[tex]v_{o} = \farc{2\piR}{T}[/tex]
where
R = Radius of the orbit
Now,
For satellite A:
[tex]v_{oA} = \farc{2\piR}{T_{a}}[/tex]
Using eqn (1):
[tex]2v_{oB} = \farc{2\piR}{T_{a}}[/tex] (2)
For satellite B:
[tex]v_{oB} = \farc{2\piR}{T_{b}}[/tex] (3)
Now, comparing eqn (2) and eqn (3):
[tex]\frac{T_{a}}{T_{b}} = \farc{1}{2}[/tex]
