Planet between Mars and Jupiter

[Moontanman]

It has been long said that Jupiter prevented a planet from forming between Mars and Jupiter, in fact some sources seem to indicate the Jupiter may be the reason Mars is so small.

Thought experiment, if it was possible to move a planet between Mars and Jupiter, for the sake of this thought experiment lets assume a planet about the mass of Earth.

Would such a planet be stable in that orbit? (ignoring the asteroid impacts it would attract of course)

[Nicholas Kang]

Jupiter`s formation during the early infant years of our solar system is indeed the cause of prevention of terrestrial planets after Mars. Strong Jovian gravitational perturbation results in remnants of protoplanetary disc forming asteroid belt. Here is an article, somewhat old, but still informative. Maybe it will answer your question.

 

http://www-personal.umich.edu/~equintan/Other_Publications/Asteroid_Lissauer.pdf

[Robittybob1]

 

It has been long said that Jupiter prevented a planet from forming between Mars and Jupiter, in fact some sources seem to indicate the Jupiter may be the reason Mars is so small.

Thought experiment, if it was possible to move a planet between Mars and Jupiter, for the sake of this thought experiment lets assume a planet about the mass of Earth.

Would such a planet be stable in that orbit? (ignoring the asteroid impacts it would attract of course)

 

The missing planet is evidenced by the Asteroid Belt the failed planet build in my opinion. In my calculations it was the Sun becoming main sequence that stripped the terrestrial planets and disrupted the formation of Mars and the Asteroid belt. The surplus material was blown out to the torus of dust and gas out of which Jupiter was formed.

[Moontanman]

Jupiter`s formation during the early infant years of our solar system is indeed the cause of prevention of terrestrial planets after Mars. Strong Jovian gravitational perturbation results in remnants of protoplanetary disc forming asteroid belt. Here is an article, somewhat old, but still informative. Maybe it will answer your question.

 

http://www-personal.umich.edu/~equintan/Other_Publications/Asteroid_Lissauer.pdf

 

 

Your publication was not available, but my question was not if Jupiter caused the asteroid belt

 

The missing planet is evidenced by the Asteroid Belt the failed planet build in my opinion. In my calculations it was the Sun becoming main sequence that stripped the terrestrial planets and disrupted the formation of Mars and the Asteroid belt. The surplus material was blown out to the torus of dust and gas out of which Jupiter was formed.

 

 

Again, my question was not how or why the asteroid belt formed but if a planet could orbit there, not form there..

[Robittybob1]

 

 

Your publication was not available, but my question was not if Jupiter caused the asteroid belt

 

 

 

Again, my question was not how or why the asteroid belt formed but if a planet could orbit there, not form there..

Well the Asteroid Belt objects, and some are named, have survived. I don't see why if the planet formation process hadn't advance a bit more i.e. the Sun's mass was down a bit, then a planet sized body would have formed and survived just as Ceres has done. The size of Jupiter would be a way less too then IMO of course.

If Jupiter was less massive and Ceres had finished building would it survive long term. I have seen a program that could analyse such situations but they are beyond thinking the problem through.

It is depended on the timing of the Sun (stars in general) going thermonuclear that determines the size of the planets closer in, and that depends on the mass of the star, that depends on the size of the nebula cloud, and its angular momentum. They are all interconnected.

Lump all the Asteroid Belt bodies together. Would that have enough mass to be called a planet? http://en.wikipedia.org/wiki/Asteroid_belt

 

The total mass of the asteroid belt is estimated to be 2.8×10^21 to 3.2×10^21 kilograms, which is just 4% of the mass of the Moon.[2] The four largest objects, Ceres, 4 Vesta, 2 Pallas, and 10 Hygiea, account for half of the belt's total mass, with almost one-third accounted for by Ceres alone.[3][4]

....but also:

The current asteroid belt is believed to contain only a small fraction of the mass of the primordial belt. Computer simulations suggest that the original asteroid belt may have contained mass equivalent to the Earth.[37] Primarily because of gravitational perturbations, most of the material was ejected from the belt within about a million years of formation, leaving behind less than 0.1% of the original mass.

Edited January 31, 2015 by Robittybob1

[Moontanman]

Well the Asteroid Belt objects, and some are named, have survived. I don't see why if the planet formation process hadn't advance a bit more i.e. the Sun's mass was down a bit, then a planet sized body would have formed and survived just as Ceres has done. The size of Jupiter would be a way less too then IMO of course.

If Jupiter was less massive and Ceres had finished building would it survive long term. I have seen a program that could analyse such situations but they are beyond thinking the problem through.

It is depended on the timing of the Sun (stars in general) going thermonuclear that determines the size of the planets closer in, and that depends on the mass of the star, that depends on the size of the nebula cloud, and its angular momentum. They are all interconnected.

Lump all the Asteroid Belt bodies together. Would that have enough mass to be called a planet? http://en.wikipedia.org/wiki/Asteroid_belt

 

 

Let me make sure we are on the same page, if we could move an earth sized planet into the orbit between Mars and Jupiter it would be at least as stable as the other inner planets?

[Robittybob1]

 

 

Let me make sure we are on the same page, if we could move an earth sized planet into the orbit between Mars and Jupiter it would be at least as stable as the other inner planets?

"such situations ...... are beyond thinking the problem through." Can you predict what amounts to the chaotic behaviour of the "Three body problem"? The situation would need to be run through a computer using something like Wolfram Mathematica "Three body problem".

But since the Asteroid ring has survived at all bodes well for an Earth sized planet there, in my opinion, but I'm not a computer!

Edited February 1, 2015 by Robittybob1

[Enthalpy]

There are already minor planets between Mars and Jupiter so some orbits are stable. As long as these planets don't perturb Jupiter, they can be much heavier than Ceres and the orbit will be just as stable.

 

Only a few distances to Sun are made unstable by Jupiter's influence. It's where no asteroid is present: at 2.50, 2.82, 2.96, 3.27AU from te Sun, where the period resonates with Jupiter's one. See

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

 

That tells that a planet could last there. Whether it could form is an other story... My gut feeling is that we have only computer simulations up to now, which is an extremely weak evidence. The same simulations also claimed that no planet could stay around a double star, but meanwhile they are observed, so I'd say: wait until we know what exists or not at other planetary systems, and forget any prediction meanwhile.

 

You know, past theories also claimed that giant planets are gaseous and far from the star, but meanwhile giant planets are known very close to their star, and some are rocky. It's just that a viable theory can't result from a single observation, and what we imagine to be necessity is merely a fit to the observation.

[Airbrush]

..... if it was possible to move a planet between Mars and Jupiter, for the sake of this thought experiment lets assume a planet about the mass of Earth.

Would such a planet be stable in that orbit? (ignoring the asteroid impacts it would attract of course)

 

 

Since the total mass of the asteroid belt is far lower than the mass of the Earth, in fact Ceres is only 600 miles across and it contains a third of the mass of the asteroid belt, I would suspect that an Earth-sized object orbiting in the asteroid belt would NOT be stable because it is so much more massive than the asteroid belt.

Edited February 4, 2015 by Airbrush

[Robittybob1]

 

Since the total mass of the asteroid belt is far lower than the mass of the Earth, in fact Ceres is only 600 miles across and it contains a third of the mass of the asteroid belt, I would suspect that an Earth-sized object orbiting in the asteroid belt would NOT be stable because it is so much more massive than the asteroid belt.

I reasoned the mass of Ceres would not matter. In your opinion if it was more massive what difference would that make?

[Airbrush]

Earth is over 2,000 times the mass of the entire asteroid belt (1) in that relatively small region between Mars and Jupiter. Don't you think Jupiter would pull such a huge mass off balance and slam it into either Mars or Jupiter is short order?

 

(1) http://en.wikipedia.org/wiki/Ceres_(dwarf_planet)

Edited February 4, 2015 by Airbrush

[Robittybob1]

Earth is over 2,000 times the mass of the entire asteroid belt (1) in that relatively small region between Mars and Jupiter. Don't you think Jupiter would pull such a huge mass off balance and slam it into either Mars or Jupiter is short order?

 

(1) http://en.wikipedia.org/wiki/Ceres_(dwarf_planet)

There is rather a large gap between Mars and Jupiter. Since gravitational acceleration is proportional to mass, a small planet (Ceres) would be affected by gravity from another body the same (in one locality all objects fall the same rate due to gravity), hence I say size does not matter.

[imatfaal]

There is rather a large gap between Mars and Jupiter. Since gravitational acceleration is proportional to mass, a small planet (Ceres) would be affected by gravity from another body the same (in one locality all objects fall the same rate due to gravity), hence I say size does not matter.

 

 

When talking about gravitation you have to careful and specify which mass you mean. Acceleration due to gravity is independent of the mass of the object being described; the force of gravity is directly proportional to the mass of both objects but the acceleration is only proportional to the mass of the "other object" ie

 

[latex]F_{sun} = F_{object} = -\frac{G\cdot M_{sun}\cdot M_{object}}{r^2}[/latex]

 

[latex]a_{object} = -\frac{G\cdot M_{sun}}{r^2}[/latex]

[Robittybob1]

 

 

When talking about gravitation you have to careful and specify which mass you mean. Acceleration due to gravity is independent of the mass of the object being described; the force of gravity is directly proportional to the mass of both objects but the acceleration is only proportional to the mass of the "other object" ie

 

[latex]F_{sun} = F_{object} = -\frac{G\cdot M_{sun}\cdot M_{object}}{r^2}[/latex]

 

[latex]a_{object} = -\frac{G\cdot M_{sun}}{r^2}[/latex]

Fair enough, you've said exactly what I tried to say. So do you agree it is not the size of Ceres that matters the most when it comes to stability but rather its resonance based on the orbital frequency of the nearby planets

[imatfaal]

Fair enough, you've said exactly what I tried to say. So do you agree it is not the size of Ceres that matters the most when it comes to stability but rather its resonance based on the orbital frequency of the nearby planets

 

Not really no. It is a multi-body dynamic problem - and they just resist simplification. You could work out the orbit of Ceres around the sun. Add in Jupiter and it becomes very difficult - add in Mars as well...

 

Poincare showed that there is no normal analytical solution to these sort of problems (in that case just three body) - and in the vast amount of situations a non-repeating trajectory is the outcome

[Airbrush]

The material in the asteroid belt orbit is spread out evenly, like clothes evenly distributed in a washing machine. If you put a mass the size of Earth in one place it becomes an off balanced washing machine. Every orbit Jupiter will pull the Earth more and more, maybe throwing the Earth-size mass out of the solar system.

Edited February 5, 2015 by Airbrush

[Enthalpy]

The asteroids are distributed along a few distances and inclinations in the belt, and this suggests that they result from few previous massive bodies.

 

Jupiter destabilizes only some orbits in the belt, which it resonates with. These are the locations void of asteroids. The observation confirms this simple theory.

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

Elsewhere, asteroids stay up to now. A heavier body would do it equally well; it's attracted more strongly by Jupiter and the sun, and is has more inertia, so its own mass has no effect - as long as it influences Jupiter little.

 

What's possible is that Jupiter perturbs the formation of a planet by creating collisions in the material; until we observe enough planetary systems, this remains just weak models. The stability of an already formed planet is not in doubt.

[Robittybob1]

 

Not really no. It is a multi-body dynamic problem - and they just resist simplification. You could work out the orbit of Ceres around the sun. Add in Jupiter and it becomes very difficult - add in Mars as well...

 

Poincare showed that there is no normal analytical solution to these sort of problems (in that case just three body) - and in the vast amount of situations a non-repeating trajectory is the outcome

I think "Enthalpy" has a program that will run the 3 body problem.

[imatfaal]

I think "Enthalpy" has a program that will run the 3 body problem.

 

In special cases, or with limitations, or through simulation; but not a general analytic solution

[Robittybob1]

 

In special cases, or with limitations, or through simulation; but not a general analytic solution

That is OK he/she would then be able to plug in different mass planets at the distance of the Asteroid Belt region and see how stable they behave.

Edited February 6, 2015 by Robittybob1