# The Naked Scientists Forum

### Author Topic: What happens to a planet's orbit when mass changes?  (Read 6203 times)

#### anshul singh

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##### What happens to a planet's orbit when mass changes?
« on: 17/06/2010 14:30:04 »
anshul singh  asked the Naked Scientists:

Hi the naked scientists,

What happens if mass of a planet reduces to its half without exerting any thrust (force) on it, what will happen to its orbit?

Thanks

What do you think?
« Last Edit: 17/06/2010 14:30:04 by _system »

#### graham.d

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##### What happens to a planet's orbit when mass changes?
« Reply #1 on: 17/06/2010 14:37:30 »
Nothing happens. The orbit of a planet is not dependent on its mass, only the mass of the sun.

#### syhprum

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##### What happens to a planet's orbit when mass changes?
« Reply #2 on: 17/06/2010 18:00:14 »
I guess this is true if the mass of the planet is small relative to the Sun but would not the situation be different if the mass was increased so that it was the same as the Sun ?.

#### Geezer

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##### What happens to a planet's orbit when mass changes?
« Reply #3 on: 17/06/2010 18:21:57 »
Nothing happens. The orbit of a planet is not dependent on its mass, only the mass of the sun.

er well, strictly speaking, don't they both orbit each other? (although the Sun's orbit is more like a slight wobble because of the very large difference in mass)

That being the case, there would be a slight change in the Sun's orbit.

#### tommya300

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##### What happens to a planet's orbit when mass changes?
« Reply #4 on: 17/06/2010 22:10:12 »
anshul singh  asked the Naked Scientists:

Hi the naked scientists,

What happens if mass of a planet reduces to its half without exerting any thrust (force) on it, what will happen to its orbit?

Thanks

What do you think?

OK I'll bite guys, I can't resist learning, beat me up without exerting force...

Can Mass be dismissed from the essential formulas related to orbit?
The formula for centripetal force is: F = (mv2)/r
The formula for the gravitational force between two bodies of mass M and m is (GMm)/r2

Force is not exerted here it is a resultant with a direct relationship to the mass? Isn't it?
Wouldn't the orbit need to be recalculated, using the new mass with the same force?

Isn't it In the Principia, Newton defined the force of gravity in the following way (translated from the Latin)?
"Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them?"

Is the sun and the earth act as a binary star system? What happens to the rest of the planets?
.

.
http://en.wikipedia.org/wiki/Orbit
.

#### Geezer

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##### What happens to a planet's orbit when mass changes?
« Reply #5 on: 17/06/2010 23:03:09 »
Is the sun and the earth act as a binary star system? What happens to the rest of the planets?

They make it a lot more complicated

Each planet has some effect on the Sun, so the Sun's "orbit" must be quite complex.

#### syhprum

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##### What happens to a planet's orbit when mass changes?
« Reply #6 on: 18/06/2010 05:51:51 »
http://en.wikipedia.org/wiki/Orbit
I read thru this article and was very pleased to see that the path of a cannon ball fired from a mountain top at sub orbital speed was described as elliptical.
Almost invariably such sub orbits are described as parabolic in the press and scientific articles and that was what I was taught at school but this would only be true if the earth was flat and of infinite extent.

#### graham.d

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##### What happens to a planet's orbit when mass changes?
« Reply #7 on: 18/06/2010 08:42:11 »
I was assuming that the planet is much lighter than the Sun. However I think it fair to say that, in the spirit of the question (I thought), that you could define the orbit of a body around the sun to be relative to the sun. In this case the orbit still does not depend on the mass of the planet. If you take a solar system, with multiple bodies, the problem if analysed very strictly and to high accuracy, is indeed complex and probably cannot actually be analysed mathematically at all, but a solution would be reliant on computer modelling.

Gm1m2/r2 = m22

So  ω2 = Gm1/r3

where ω = 2π/T where T is the time for a complete orbit (1 year for the earth)
Note that m2 (the mass of the planet) cancels out.

This is the relationship between distance to the the sun and orbit time that was derived empirically by Kepler.

#### tommya300

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##### What happens to a planet's orbit when mass changes?
« Reply #8 on: 20/06/2010 13:37:32 »
I was assuming that the planet is much lighter than the Sun. However I think it fair to say that, in the spirit of the question (I thought), that you could define the orbit of a body around the sun to be relative to the sun. In this case the orbit still does not depend on the mass of the planet. If you take a solar system, with multiple bodies, the problem if analysed very strictly and to high accuracy, is indeed complex and probably cannot actually be analysed mathematically at all, but a solution would be reliant on computer modelling.

Gm1m2/r2 = m22

So  ω2 = Gm1/r3

where ω = 2π/T where T is the time for a complete orbit (1 year for the earth)
Note that m2 (the mass of the planet) cancels out.

This is the relationship between distance to the the sun and orbit time that was derived empirically by Kepler.

Well Graham.d that settles that 2 simultaneous equations tells it always.

#### The Naked Scientists Forum

##### What happens to a planet's orbit when mass changes?
« Reply #8 on: 20/06/2010 13:37:32 »