Question

What is the ratio of the orbital velocities of two satellites, each in circular orbit around Earth, given that satellite A orbits 2.40 times as far from Earth’s center of gravity as satellite B? Give your answer in terms of B’s velocity to A’s velocity.

Answer 1

ratio of velocity is 3:2

Step-by-step explanation:

given data

orbits A = 2.40 B

to find out

What is the ratio of the orbital velocities of two satellites

solution

we know here orbit velocity formula that is

V =
`\sqrt{(G*M)/(r)}`

here V is velocity and G is gravitational constant and M is mass of earth and r is distance from object to center of earth

so we calculate it for B that is V1

V1 =
`\sqrt{(G*M)/(B)}` .........................2

here r is B

and

for orbit A velocity is V2

V2 =
`\sqrt{(G*M)/(2.40 B)}`

so here r is 2.40 B

sop from equation 2 and 3

`(V1)/(V2) = \sqrt{((G*M)/(B) )/((G*M)/(2.40 B))}`

solve it we get

`(V1)/(V2)  = √(2.40)`

`(V1)/(V2)  =(3)/(2)`

so ratio is 3:2