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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.

Respuesta :

Answer:

ratio of velocity  is 3:2

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 = [tex]\sqrt{\frac{G*M}{r}}[/tex]

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 =  [tex]\sqrt{\frac{G*M}{B}}[/tex]     .........................2

here r is B

and

for orbit A velocity is V2

V2 = [tex]\sqrt{\frac{G*M}{2.40 B}}[/tex]

so here r is 2.40 B

sop from equation 2 and 3  

[tex]\frac{V1}{V2} = \sqrt{\frac{\frac{G*M}{B} }{\frac{G*M}{2.40 B}}}[/tex]

solve it we get

[tex]\frac{V1}{V2}  = \sqrt{2.40}[/tex]

[tex]\frac{V1}{V2}  =\frac{3}{2} [/tex]

so ratio is 3:2

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