### Why isn't the asteroid belt affected by Jupiter's gravitational field?

• Jupiter's mass is just about a 1000th of the sun's and the asteroid belt is slightly closer to Jupiter than it is to the sun.

If the heavier the object, the more curvy space is around it, why isn't the asteroid belt's movement more turbulent owing to the effect of both Jupiter and the sun?

https://i.gifer.com/4EfK.mp4 Looks pretty affected to me

To be quite honest, what made you think that they **aren't** somewhat affected by Jupiter?

@JollyJoker I'm not an astronomer, but as I understand it, that's not the asteroid belt, which exists in a ring outside the orbit of mars (and not depicted in that animation).

@mattdm: All the asteroids in that graphic are outside the orbit of Mars.

@wireman: Consider in the future when phrasing questions to not assume that the laws of physics are being broken in your question. "How are asteroids affected by Jupiter's gravity?" phrases the question in a way that does not make the non-physical suggestion, as your question does, that asteroids are somehow immune to Jupiter's gravity.

@Eric Obviously. But I mean in the "empty" area on the graphic.

Isn't everything affected by everything else's gravity? In the entire universe?

@mattdm: I misunderstood the thrust of your comment. Yes, that diagram only shows asteroids whose orbits are enormously perturbed by Jupiter in a way that keeps their unusually-shaped orbits stable. You are correct that there are a great many asteroids that do not have this property, and that they are distributed in a ring more or less immediately outside the orbit of Mars.

And to clarify my previous comment: the individual orbits of those asteroids are more or less ordinary ellipses; they are not triangles. Jupiter perturbs those orbits such that the perhelions of those orbits correspond to the middles of the triangles. I should have said unusually-distributed orbits.

@JollyJoker: Those are the Hildas (red) and the Trojans (green), not the main-belt asteroids.

3 years ago

The asteroid belt is affected by Jupiter's gravity.

There are stable orbits inside of Jupiter's orbit. Jupiter's Hill Sphere has a radius of 53 million km. If you are more than 53 million km from Jupiter, then the Sun's gravity dominates and you can orbit the sun. But Jupiter orbits 780 million km from the Sun, so there is plenty of space between Mars and Jupiter for asteroids to have stable orbits.

As they pass Jupiter on their orbit they will get first a pull forward, and then a pull back but as these pulls happen at different locations on each orbit they tend to cancel out and result in effects like precession of the asteroid's perehelion or periodic variations in eccentricity. These effect act on the Earth and other planets too.

However if the time the asteroid takes to orbit the sun happens to be an exact fraction of the time that Jupiter takes, then it might receive the same pull at the same location. Resonant orbits like this tend to be unstable. The asteroid will be nudged out of the resonant orbit and into one that doesn't match up with Jupiter. This creates the Kirkwood Gaps in the asteroid belt.

Source

Very interesting, thanks! I wonder why orbital resonances only occur at these 'simple' ratios. For the 2:1 example stated in the source link you provided, it says _Once every two orbits, the relative positions between the asteroid and Jupiter will be the same, and the repeated tugs from Jupiter at this point will change the orbital elements of the asteroid_. However, I'd imagine this similarity of relative positions would occur at any ratio? (and not just simple ones)

Well if there was a 17:5 ratio, you would only get an repetition after 85 orbits. That isn't enough to cause a large gap, at the other 84 orbits there is another tug, but those are all in different directions

In fact, I think you'll probably find that those other unmarked dips in the curve probably also correspond to slightly less simple ratios. E.g. I'd guess that dip between 3:1 and 5:2 might be around 8:3. The one between 7:3 and 2:1 might be 11:5. The gaps are deepest where the ratios are simplest because those have more effect. (Note that even the 7:3 gap is less dominant than the 5:2, which in turn is less than the 3:1 and 2:1 gaps.) Harmonics are fun.

@wireman yeah, every fraction is a resonance, but the strength of the effect is inversely proportional to the least common multiple of the numerator and the denominator. Or maybe its square, even.

Might add that some of the asteroids orbit on Jupiter's orbit at the Lagrange points P4 and P5 ... in all .. Jupiter structured the distribution of asteroids in the belt - and prevented them from forming a small planet (although the whole mass is less than that of our Moon if I remember correctly)

There are also the Hilda Asteroids, which are in a 3:2 resonance with Jupiter and reach aphelions coinciding with the passage of Sun-Jupiter L4, L3, and L5 in succession.

@eagle275 Jupiter's Trojans *etc*: https://en.wikipedia.org/wiki/Jupiter_trojan