# Calculating Historical Positions of the Asteroid Belt's Orbit

Is it possible to calculate the historical whereabouts of the asteroid belt, as it seems to be moving ever outward due to the radiometer effect? Can it be calculated, for instance, where it was 1,000 years ago? 100,000 years ago? Etc.

In particular, I'm curious as to whether the science is solid enough to pin down at what time (if any) it would have shared the same orbit with the Earth.

Thanks!

Jack

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mfb
Mentor
Orbits of large objects (like everything detectable in the asteroid belt) usually change very slowly. The only way to get a significant modification is a fly-by at another object of at least comparable size. Remember: The astroid belt exists for 5 billion years now.

Therefore, just extrapolating the current orbits back 1000 years should give a good approximation for most objects. For 100 000 years, I would expect that the orbits of most objects had a similar shape, but the phase (the current position in this orbit) might be different, as it is more sensitive to small deviations.

If an object crossed the orbit of earth in the past, it is quite unlikely that it is part of the asteroid belt now. This would require some sort of capture process there.

MFB,
Thanks for the reply. Do you believe, then, that the radiometer effect is NOT constantly pushing the orbit of the asteroid belt outward?

Any drift in asteroid belt also has the Kirkwood gaps to contend with...
http://en.wikipedia.org/wiki/Kirkwood_gap

IIRC, the 'soft' outer edge of the asteroid belt has been offered as evidence that Jupiter has increased its orbital radius during the early aeons of solar system. YMMV.

mfb
Mentor
Do you believe, then, that the radiometer effect is NOT constantly pushing the orbit of the asteroid belt outward?
I do not say that there is no effect. I say that the effect is negligible. We had some thread about solar sails here, and if I remember correctly they feel a force of some newtons per square kilometer. The largest object, Ceres, would feel a force of some 10^6 N then. As comparison, the gravitational pull between Ceres and Earth is of the order of 10^12 N (current value), and the force between Ceres and Jupiter is even stronger.
In addition, a constant central force with 1/r^2 does not change orbits at all, as it can be added to gravity.

Thanks, MFB. Isn't there a difference, though, in the solar sail effect and the radiometer effect?
Jack

mfb
Mentor
There is - solar sails work in a vacuum as the radiation pressure is present there, the "radiometer effect" (at least what I found as definition) does not work in a perfect vacuum and is really small in space.

So what's the consensus here regarding whether historical positions of the asteroid belt can be calculated? Does anyone in physics suggest that the orbital radius of the belt has indeed moved over time? If so, what are the calculations about where it might have been at various intervals in the past?

mfb
Mentor
If the whole belt has moved in a significant way, this is something which happened on the time-scale of billions of years or during the formation of the planets (where things were a bit more unstable in general).

If the whole belt has moved in a significant way, this is something which happened on the time-scale of billions of years or during the formation of the planets (where things were a bit more unstable in general).
Thanks, MFB, but how do we know this? Are the assumptions at work here well-founded ones?

How do we know, for instance, that the asteroids were not created/introduced by some cataclysmic event that is outside the ordinary pattern of things that we observe today? Why must it have dated back to "the formation of the planets"? Indeed, if the planets were at one time "forming", then why didn't the material constituting the asteroids get pulled into those formations?

Nothing personal here in peppering you with these questions; I just want to be sure I'm not assuming anything unwarranted by the evidence or by sound physics.

Thanks again.
Jack

mfb
Mentor
Well, we cannot observe how our system looked some billion years ago. But it is possible to calculate the current changes in it and extrapolate both in the future and the past.

After the planets and the asteroid belt formed, they collected most of the material in the inner system. Since then, there is not enough mass in the inner solar system to modify the planetary orbits in a significant way. Jupiter had nearly the same orbit 3 billion years ago, and the other planets had similar orbits, too (luckily Pluto does not count as planet any more).

You can always create a scenario which leads to the current orbits with completely different initial conditions. But the chance that a lot of objects in chaotic orbits survive for ~2 billion years and arrange in the nice way we observe today afterwards is negligible. Unless you introduce some aliens, moving objects around ;).

Is it possible to calculate the historical whereabouts of the asteroid belt, as it seems to be moving ever outward due to the radiometer effect? Can it be calculated, for instance, where it was 1,000 years ago? 100,000 years ago? Etc.

In particular, I'm curious as to whether the science is solid enough to pin down at what time (if any) it would have shared the same orbit with the Earth.

Thanks!

Jack
This is impossible to compute. Yarkovsky effects are basically impossible to compute for a single body, because it depends on mass, albedo, rotation rate, sphericity of the object, etc. -- most of which are only tentatively known for asteroids. Also the effect is very weak with the more massive asteroids, and even for the smaller ones, other perturbations can easily be larger.