How Does the Mass of a Moon Affect Its Orbital Speed Around a Planet?

[Hasan Ribin]

Hi. Tell me pls how does the mass of moons effect their speed around planets?
I know that in case of satellites their speeds depend on planet Mass and ٌ R+h only (R is a radius of the planet and h is satellite's height from the planet surface), but in that case we do not measure satellites' mass because of its insignificance.. But if a satellite for instance has the same mass as the Moon, we should take into account its gravitational effect to the planet as well I guess.. Please help (and if it is possible - with necessary formula). Thanks ))

P.S.: Sorry for English.. Long time without practice :)

I've also added that question http://http://answers.yahoo.com/question/index?qid=20110525032837AAL59Xi" , maybe someone wishes to answer on the site

 

[tiny-tim]

Welcome to PF!

Hi Hasan! Welcome to PF!

The acceleration of the moon depends only on the distance L between the moon and the planet: GM_planet/L².

The speed of the moon depends on the distance R of the moon from the centre of mass (assuming a circular orbit): centripetal acceleration = v²/R.

The rest of the calculation I'll leave to you. ​

 

[Hasan Ribin]

Thanks ))

The acceleration of the moon depends only on the distance L between the moon and the planet: GMplanet/L2.

Yeah.. that is what I tried to talk about but.. You mean that if we reduce the Moon's mass, say, to 3.5 × 10^22 kg but the distance between the Earth's and the Moon's mass centers leave the same there will be no changes regarding its velocity during moving around the planet? I mean the orbital period of the Moon will remain about 27 days?

I thought it is right only for planet sattelites or planets within solar system because their mass is negligible relative to the sun or other globes they are moving around.. But what if the mass of a sattelite or a moon is insignificantly different from the globe it is moving around? Say, the Moon and the Earth.. (or if we significantly in- decrease the Moon mass )?

 

[tiny-tim]

Hi Hasan!

You mean that if we reduce the Moon's mass, say, to 3.5 × 10^22 kg but the distance between the Earth's and the Moon's mass centers leave the same there will be no changes regarding its velocity during moving around the planet? I mean the orbital period of the Moon will remain about 27 days?

No, because the speed depends on both L and R, and if you change the mass of the moon, then the position of the centre of mass changes, ie R changes.

 

[Hasan Ribin]

if you change the mass of the moon, then the position of the centre of mass changes, ie R changes.

Ok, thank you very much, now I see.. Dear, would you explain this stuff as well please? How does the position change, I guess that the more mass moves the Moon closer to the center of mass, is there anything that this prosess depend on also? How to calculate it?