Question

2 satellites a and b go around a planet p in circular orbits having radius 4r and respective the speed of

Answer 1

Circular orbit with uniform motion.

let the satellite with the orbiting radius 4 R have a mass m1.

its speed in the orbit = 3 v.

let the satellite with the orbit radius R have a mass m2.

let its speed = v2.

let the mass of planet = M

The gravitational force of attraction is equal to the centripetal force acting on the satellite making it go around in a circle.

centripetal force formula is = m V²/r --- (1)

satellite 1: m1 * (3v)² / (4 R) = G M m1 / (4 R)² --- (2)

v² = G M / (36 R) --- (3)

satellite 2: m2 * v2² / R = G M m2 / R² --- (4)

v2² = G M / R ---(5)

from (3), GM /R = 36 v²

from (5), v2² = 36 v²

v2 = 6 v

Answer 2

F=GMm/R2,

now force of Gravitation provide centripetal force

therefore mv2/R=GMm/R2

v=[GM/R]1/2

Now, according to question

3v=[GM/4R]1/2

3v=1/2[GM/R]1/2 ----------(1)

and

let the velocity of the other planet be x,

x=[GM/R]1/2 -------------(2)

from (1) and (2)

3v=x/2,

x=6v

hence solved