Question

two satellite of mass M and 2 m are revolving into circular orbits of radii r and 2r around an imaginary planet on the surface of with gravitational force is inversely proportional to distance from his Centre. the ratio of Orbital speed of satellite is

Answer 1

Orbital speed = √GM/√R

Ratio= √m/√2m × √2r/√r

= 1/√2 × √2

= 1

Ratio = 1:1

Answer 2

Hey Bud,

◆ Answer -

v1:v2 = √2:1

◆ Explanation-

# Given-

r1 = r

r2 = 2r

m1 = m

m2 = 2m

# Solution-

Orbital speed of satellite is calculated by formula -

v = √(GM/r)

Where,

G = gravitational constant

M = mass of planet

r = orbital radius

As G,M are constants-

v ∝ 1/√r

Therefore,

v1/v2 = √(r2/r1)

v1/v2 = √(2r/r)

v1/v2 = √2 = 1.414

Hence, ratio of orbital velocities of two satellites is √2:1 .

Hope this helps...