Another Impact on Jupiter

[CRGreathouse]

Yes, but two bodies will have stable orbits. Once you get into more than that the system becomes chaotic, right? I mean, it's locally stable, but as soon as things get close enough to be interesting all that goes out the window.

But perhaps mass isn't an issue -- model the planets as massless spheres orbiting a point mass (the sun). Would that make collision probability proportional to cross-sectional area? Cross-sectional area divided by distance from the sun?

[cheesehead]

Originally Posted by plandon

Assume it is just 2 bodies with point masses,

But here we have at least 3 bodies, with two of them in orbit around the Sun.

This set of simplifying assumptions is too simple to be useful here.

The masses make no difference.

They do when M1 (Sun) >> M2 (planet) >> M3 (meteoroid/comet).

Cancel now the assumption of point masses and the only problem that occurs is if the material radius (solid + atmosphere) overlaps the other.

Yes, but this is "only" just what we're considering: the problem of nonplanetary bodies impacting planets in our solar system -- when their radii overlap.

The perpendicular (to the original unaffected path) effect of gravity does not make that much difference.

It does in the cases we're really considering.

[Spherical Cow]

Originally Posted by plandon

The masses make no difference.
One body will orbit another elliptically, parabolicly or hyperbolicly.
Cancel now the assumption of point masses and the only problem that occurs is if the material radius (solid + atmosphere) overlaps the other.
The perpendicular (to the original unaffected path) effect of gravity does not make that much difference.

Maybe I'm misunderstanding- are you saying that neither the masses nor gravity make any difference to future collisions? Seems like if you cranked up gravity to be significantly stronger, you'd have more collisions sooner; weaken gravity to zero, and relatively few collisions will happen. (All that hinges on what everything is doing when you adjust the gravity, of course.) That suggests that gravity and mass are important. Or am I not following what you're saying?

Norm

[Primeinator]

Originally Posted by plandon

Just my counter-intuitive disputable tuppence worth...

Assume it is just 2 bodies with point masses,
(point masses may be found in all school physics labs, next to the perfectly rigid massless unit length rods)

The masses make no difference.
One body will orbit another elliptically, parabolicly or hyperbolicly.
Cancel now the assumption of point masses and the only problem that occurs is if the material radius (solid + atmosphere) overlaps the other.
The perpendicular (to the original unaffected path) effect of gravity does not make that much difference.

When I mentioned this puzzle to an amateur astronomer he waffled on about "spiralling in" which is a fallacy.

To actuality hit gravitationally (as opposed to colliding because the paths cross anyway), the relative velocity must be exactly right in a small range.

Originally Posted by Spherical Cow

Maybe I'm misunderstanding- are you saying that neither the masses nor gravity make any difference to future collisions? Seems like if you cranked up gravity to be significantly stronger, you'd have more collisions sooner; weaken gravity to zero, and relatively few collisions will happen. (All that hinges on what everything is doing when you adjust the gravity, of course.) That suggests that gravity and mass are important. Or am I not following what you're saying?

Norm

Spherical Cow,

Mass DOES matter, but it is not quite as significant as some might think. Many asteroids and comets have such a high velocity that their path will not be altered much by a body such as a planet (as plandon is pointing out). However, planets could potentially alter the path of an asteroid or comet by a small degree, depending on how close the object is to the planet and the differences between their respective gravity. For a collision to occur, one or more of the following conditions must be met:

1. The object is moving slow enough that the planet's gravity does more work...pulling the object in.
2. The object hits the planet directly.
3. The planet's gravity is SO massive that the object really can't cross anywhere in gravitational influence (though this would be like black holes, planets are no where near massive enough).

[cheesehead]

Originally Posted by Primeinator

For a collision to occur, one or more of the following conditions must be met:

1. The object is moving slow enough that the planet's gravity does more work...pulling the object in.
2. The object hits the planet directly.
3. The planet's gravity is SO massive that the object really can't cross anywhere in gravitational influence (though this would be like black holes, planets are no where near massive enough).

Actually, only #2 is necessary and sufficient (and you could omit "directly" -- if it hits, it hits).

#1 and #3 are too vague to have meaning here, and you've disqualified #3 already.

[cheesehead]

Originally Posted by Spherical Cow

Maybe I'm misunderstanding- are you saying that neither the masses nor gravity make any difference to future collisions?

Post #11's simplifying assumptions take the example too far down for the statements there to mean anything to this discussion.

[Primeinator]

Originally Posted by cheesehead

Actually, only #2 is necessary and sufficient (and you could omit "directly" -- if it hits, it hits).

#1 and #3 are too vague to have meaning here, and you've disqualified #3 already.

Yes, this is why I said a planet would not qualify under this category. I should be more clear on the first one. An incoming asteroid or comet (or any other comparable object) is moving through space with a given velocity that is small enough that it does not meet the escape velocity of the planet at a given radius.

I used the word "directly" on number two to illustrate the fact that the object would have hit the planet regardless of the planet's gravity- they would have crossed paths irregardless, where in the other two examples gravity is a key factor.

[cheesehead]

Here are two articles with a photo of Anthony Wesley (the amateur who first saw and reported the new spot) and his own-design 14.5-inch short-focus Newtonian telescope:

http://www.independent.co.uk/news/sc...r-1755868.html

http://www.timesonline.co.uk/tol/new...cle6721504.ece

- - -

BTW, as The Independent explains, we have Tom Watson's drama at the British Open to thank for keeping Anthony up late enough to see the spot after it had rotated to within his view.

- - -

Edit:

But now I see that the article linked from the OP has links to an even better photo:

http://jupiter.samba.org/AnthonyWesley.jpg

and to Wesley's observing log:

http://jupiter.samba.org/jupiter-impact.html

which has detailed specs for his scope:

Scope: Homebrew GEM mounted Newtonian using a 14.5" Royce conical mirror
(link to images removed until the slashdot tsumani retreats)

Mount: Losmandy Titan
Optics:
- 14.5" f/5 Royce conical primary
- 1/30 wave Antares Optics secondary
- Televue 5x powermate , working at 7.7x

[cheesehead]

An article of the sort that predictably follows such events:

"Could Earth Be Hit, Like Jupiter Just Was?"

http://news.yahoo.com/s/space/200907...jupiterjustwas

I'm not going to make a habit of noting any other similar articles.

[CRGreathouse]

Originally Posted by cheesehead

Actually, only #2 is necessary and sufficient (and you could omit "directly" -- if it hits, it hits).

#1 and #3 are too vague to have meaning here, and you've disqualified #3 already.

I believe the intent of #2 was "the object would have hit the planet even if the planet's mass were 0" and the intent of #1 was "the object would not have hit the planet if the planet's mass were 0, but hits it because the planet's gravity altered its course".

[Primeinator]

Originally Posted by CRGreathouse

I believe the intent of #2 was "the object would have hit the planet even if the planet's mass were 0" and the intent of #1 was "the object would not have hit the planet if the planet's mass were 0, but hits it because the planet's gravity altered its course".

Correct assumption on number two, incorrect on number one. For the first statement, I meant to say that the object passing by the planet was not moving with enough kinetic energy (i.e. at or beyond the escape velocity for that planet) with the given radius from the planet the object was passing. If the object passes with a velocity less than the escape velocity, it will be pulled into orbit and eventually will enter the planet's atmosphere and collide.