Question

Consider two satellites A and B orbiting around earth in uniform circular motion.

• The acceleration of satellite A is 16 times that of satellite B.

• The period of satellite B is 4 times the period of satellite A.

Using the concept of Fg as Fc, and the corresponding equations for orbital period, calculate the ratio of the radius of the motion of satellite A to that of satellite B (rA/rB = ?).

Answer 1

By force balance on acceleration,

m*a = Fc = m*w^2*R

a = w^2*R

here, w = 2*pi/T

then, a = 4*pi^2*(R/T^2)

So, a1/a2 = (R1/R2)*(T2/T1)^2

given, acceleration of satellite A(a1) is 16 times that of satellite B(a2), then

a1/a2 = 16

also, period of satellite B(T2) is 4 times the period of satellite A(T1), then

T2/T1 = 4

So, the ratio of the radius of the motion of satellite A(R1) to that of satellite B(R2) will be,

R1/R2 = (a1/a2)*(T1/T2)^2

R1/R2 = 16*(1/4)^2

R1/R2 = 1

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