# Does a planet's size/mass affect location?

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#### bdewoody

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I read that there may be earth sized planets way out beyond Pluto which began to make me wonder about whether a planet's size/mass controls where it lies in relation to it's parent star and other planets in the same system. How far out can our sun capture and hold an object in a basically circular orbit.

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#### MeteorWayne

##### Guest
Unless it is comparable to the mass of the sun (in which case it would be a Brown Dwarf at least) the mass of the orbiting body is almost completely irrelevant. It is so small that in most orbital calculations, unless very extreme precision is needed, the mass of the smaller body is ignored.

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#### bdewoody

##### Guest
So it is a body's speed that determines how far away from it's parent star a planet will orbit?

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#### MeteorWayne

##### Guest
In a sense, that's correct. It's really a bit more complicated, since in an elliptical orbit (which all of them are, really) the speed constantly changes. It's more about the energy of the orbit.

For example, the earth, in a relatively circular orbit (and getting more circular for the next 10 or 20 thousand years) we do about 30 km/sec at 1 AU. Meanwhile a comet in a highly elliptical orbit from the Oort clud will be doing about 41 km/sec at 1 AU. If it's going faster than that at 1 AU, it won't be coming back

Wayne

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#### GraemeH

##### Guest
Hi bdewoody

Lets break your questions down a little bit ....

....... How far out can our sun capture and hold an object in a basically circular orbit.
In a completely isolated system, there would be no easily definable outer orbital limit as Sol's gravity diminishes with 1/d^2, (where d is the distance to the object) so long as the orbitial velocity of the planet does not exceed the escape velocity.

In reality, the sun has many neighbours so the orbital limit can be defined as the point at which another star's gravitional field exceeds that of Sol. For example, let's say the nearest star is alpha Cen, that alpha Cen has the same mass as Sol and the distance is 4 ly (I'm ignoring beta Cen, Promixa Cen and obvious differences of the systems). We could then define a maximum stable orbital distance of 1.99999 ly, so long as the planetary orbital velocity is below the escape velocity.

I read that there may be earth sized planets way out beyond Pluto
It certainly is a possibility, although such planets are extremely unlikely to have formed at that orbital distance. A star may however capture a "rogue planet" (ejected from another planetary system) or hold on to an inner planet that had been promoted to a larger orbital distance through perturbation - see below. In both cases, such a planet's orbit would most likely be highly eliptical with high inclination.

.... which began to make me wonder about whether a planet's size/mass controls where it lies in relation to it's parent star and other planets in the same system.
Have you come across Bode's Law? (see http://en.wikipedia.org/wiki/Bode%27s_law ) This is a scaling law, so no theoretical basis was used in it's derivation, but it does a good job in closely matching the semi major axis of several planets.

If our planetary formation models were well defined and the resultant dynamic equations were invariant to minor differences to the intial starting conditions, we should be able to model and predict planetary system formation with a reasonable level of accuracy.

At present all we can indicate is that in a well behaved ordered planetary system formation scenario, the scheme will most likely be;

terrestrial - gas giants - icy planetoids (possibility of asteroid belts fomed at orbital resonance between star and gas giant)

The terrestrial-gas giant boundry is defined by the frost line (point at which volatiles can condense to solids) and the early clearing of the circumstellar disk from in fall to star or outward migration as a consequence of stellar winds. Icy planetoids size is limited by the rarefied outer dust disk and that chance encounters, between planetoids, are minimal given the distance between them.

This pattern is expected to be repeated for all stellar classes, with the semi major axis of the different planet types scaled proportionally with the stellar mass (larger stars are hotter, therefore frost line is further away).

It is a lot harder to indicate what a planetary system would be for more chaotic system formation when, for example, a gas giant migrates inwards due to interaction (drag) with the initial gas/dust disk. Migration my be so extreme that the resultant system is of the "Hot Jupiter" type and any inner terrestrial planets initially formed have been ejected or spiralled into the parent star, due to orbital perturbation by the migrating gas giant.

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#### neilsox

##### Guest
As the others posted size/ mass does affect location, but several other mechanisms may predominate, so there are many possibilities.
Two or three light years is likely about right for maximum orbiting distance in our solar system, but very long term a star mass will pass closer than one light year, so outer planets, asteroids comets etc. will be perturbed from orbit. I don't think we have identified any comets that we expect to return from more than 1% of a light year, so perhaps a close approach of a star mass or more, has occurred sometime several billion years ago. Neil

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