# Orbital velocity

1. Oct 10, 2015

why orbital velocity of a satellite is independent of mass?

2. Oct 10, 2015

### 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.

3. Oct 11, 2015

### 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".

4. Oct 12, 2015

### tfr000

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.

5. Oct 12, 2015

### DaveC426913

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

6. Oct 12, 2015

### tfr000

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?

7. Oct 12, 2015

### Staff: Mentor

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.

8. Oct 12, 2015

### Janus

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

9. Oct 13, 2015

### 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.

10. Oct 13, 2015

### DaveC426913

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.