Answer :
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
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
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