To solve this problem it is necessary to use the concepts related to the Gravitational Force and Newton's Second Law, as far as we know:
[tex]F_g = \frac{GMm}{r^2}[/tex]
Where,
G = Gravitational constant
M = Mass of earth (in this case)
m = mass of satellite
r = radius
In the other hand we have the second's newton law:
[tex]F = ma[/tex]
Where,
m = mass
a = acceleration
Equation both equations we have,
[tex]ma = \frac{GMm}{r^2}[/tex]
For the problem we have that,
Satellite A:
[tex]ma_A = \frac{GMm}{r^2}[/tex]
Satellite B:
[tex]ma_B = \frac{GMm}{(2r)^2}[/tex]
The ratio between the two satellites would be,
[tex]\frac{ma_A}{ma_B}= \frac{\frac{GMm}{r^2}}{\frac{GMm}{(2r)^2}}[/tex]
Solving for a_B,
[tex]a_B = \frac{a_A}{4}[/tex]
Therefore the centripetal acceleration of [tex]A_B[/tex] is a quarter of [tex]a_A[/tex]
