Orbital Velocity: Why Mass Doesn't Matter

[Muhammad Sabih]

why orbital velocity of a satellite is independent of mass?

 

[CWatters]

Have you looked at the maths? Write down the equation for the required centripetal force and for the gravitational attraction that provides it. Equate the two.

 

[HallsofIvy]

An "orbit" is just like falling with enough side-ways velocity that you keep "missing" the earth. That does not depend upon mass for the same reason the speed, at any time, of a falling object does not depend upon mass- the gravitational force is a multiple of mass so it cancels out of "F= ma".

 

[tfr000]

why orbital velocity of a satellite is independent of mass?

Well, if the satellite's mass is large enough, it's not (independent of mass). For instance, the Moon.
However, if the satellite's mass is something like 1 ten-billionth of the mass of the body it's orbiting, and another satellite's mass is 5 ten-billionths, then you will see negligible difference in their motion about the body.

 

[DaveC426913]

Well, if the satellite's mass is large enough, it's not (independent of mass). For instance, the Moon.
However, if the satellite's mass is something like 1 ten-billionth of the mass of the body it's orbiting, and another satellite's mass is 5 ten-billionths, then you will see negligible difference in their motion about the body.

Are you asserting that a small object in the same orbit as the Moon's would orbit at a different speed than the Moon?

 

[tfr000]

Are you asserting that a small object in the same orbit as the Moon's would orbit at a different speed than the Moon?

Well, yes. Newton says the force between them (the Earth and whatever) is proportional to the product of their masses. Therefore, the Moon orbits a little faster, in the same orbit than say, a baseball. A basketball's orbit would not be noticeably different from the baseball's.
What are you saying?

 

[russ_watters]

Are you asserting that a small object in the same orbit as the Moon's would orbit at a different speed than the Moon?

Note that two objects orbit their combined center of mass, which for the Earth-Moon system is 4,671 km from the center of the Earth. So a small object will have an orbit around Earth more centered around Earth's center, have a different distance or radius (pick one) and a different speed.

 

[Janus]

Are you asserting that a small object in the same orbit as the Moon's would orbit at a different speed than the Moon?

Yes. Such an object could orbit as much as ~ 6 m/s slower than the Moon. ( and have a period ~4 hrs longer)

 

[CWatters]

Just in case the OP is lost...

If one of the masses (m₂) is very small compared to the other (M₁) then the maths simplifies to ..

Centripetal force = gravitational attraction

m₂v²/r = GM₁m₂/r²

M₂ cancels which is why V is independent of mass.

If m₂ isn't small then see the last few posts above.

 

[DaveC426913]

Note that two objects orbit their combined center of mass, which for the Earth-Moon system is 4,671 km from the center of the Earth. So a small object will have an orbit around Earth more centered around Earth's center, have a different distance or radius (pick one) and a different speed.

Yeah, I thought maybe that was the confounding factor.

I was imagining small objects in simultaneous orbit, ahead of the Moon, being overtaken and swept up by Moon.