Two satellites of masses M and 9M are orbiting a planet in a circular orbit of radius r . Their frequency of revolution will be in the ratio of

Question

Two satellites of masses M and 9M are orbiting a planet in a circular orbit of radius r . Their frequency of revolution will be in the ratio of (A) 1:9 (B) 1:3 (C) 1:1 (D) 3:1

Tardigrade Admin · Accepted Answer

Using Kepler's IIIrd law of planetary motion, T=2π √(r3/GM) or T2 propto r3 Frequency, f=(1/T)=(1/2 π )√(GM/r3) Frequency is independent of the mass of the satellite. Hence, required ratio = 1: 1

Q. Two satellites of masses $M$ and $9 M$ are orbiting a planet in a circular orbit of radius $r$ . Their frequency of revolution will be in the ratio of

$1 : 9$

$1 : 3$

$1 : 1$

$3 : 1$

Using Kepler's III^rd law of planetary motion,
$T = 2 π \frac{r ^{3}}{GM}$ or $T^{2} \propto r^{3}$
Frequency, $f = \frac{1}{T} = \frac{1}{2 π} \frac{GM}{r ^{3}}$
Frequency is independent of the mass of the satellite.
Hence, required ratio $= 1 : 1$

Q. Two satellites of masses M and 9M are orbiting a planet in a circular orbit of radius r . Their frequency of revolution will be in the ratio of

1:9

1:3

1:1

3:1