Now assume that a satellite of mass m is orbiting the earth at a distance r from the center of the earth with speed ve. A satellite of mass 2m is orbiting mars, also at a distance r from the center of mars, with a speed vm. What is the ratio tmte , the time it takes the satellite circling mars to make one revolution divided by the time it takes the satellite orbiting the earth to make one revolution? the mass of the earth is me and the mass of mars is mm.

Question

21-10-2022
Physics

Answered

Now assume that a satellite of mass m is orbiting the earth at a distance r from the center of the earth with speed ve. A satellite of mass 2m is orbiting mars, also at a distance r from the center of mars, with a speed vm. What is the ratio tmte , the time it takes the satellite circling mars to make one revolution divided by the time it takes the satellite orbiting the earth to make one revolution? the mass of the earth is me and the mass of mars is mm.

Answer :

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Qwbox Qwbox · Answer 1 · 2022-10-26T08:21:34-04:00

The ratio of the time it takes the satellite circling mars to make one revolution divided by the time it takes the satellite orbiting the earth to make one revolution is (Rm/Re)^3/2.(Me/Mm)^1/2

The orbital velocity of the satellite is given by,

V = √(GM/R)

Where,

V is orbital velocity,

G is gravitational constant,

M is the mass of planet,

R is the distance from the centre of the planet to the satellite.

According to given condition,

Ve = √(GMe/Re)

Ve it the orbital velocity of earth,

Me is mass of the earth,

Re is the radius of the earth.

Also,

Vm = √(GMm/Rm)

Vm it the orbital velocity of mars,

Mm is mass of the mars,

Rm is the radius of the mars.

We know, time period of revolution,

T = distance/velocity

Time period od revolution of satelite of earth,

Te = 2πRe/√(GMe/Re)

Time period of revolution of satelite of mars,

Tm = 2πRm/√(GMm/Rm)

Now, dividing the time time period of revolution of mars by time period of revolution of earth,

Te/Tm = [2πRe/√(GMe/Re)]/[2πRm/√(GMm/Rm)]

Te/Tm = (Rm/Re)^3/2.(Me/Mm)^1/2

So the final ratio of both the time periods is (Rm/Re)^3/2.(Me/Mm)^1/2.

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