Another Impact on Jupiter
 

A new impact on Jupiter- Twice in one lifetime! (Makes you wonder how many we've missed.)

[URL="http://thelede.blogs.nytimes.com/2009/07/21/amateur-astronomer-finds-new-earth-size-impact-mark-on-jupiter/"]http://thelede.blogs.nytimes.com/2009/07/21/amateur-astronomer-finds-new-earth-size-impact-mark-on-jupiter/[/URL]

Norm

Quite impressive and somewhat harrowing that these extremely large objects can go undetected.

[QUOTE=Primeinator;182086]Quite impressive and somewhat harrowing that these extremely large objects can go undetected.[/QUOTE]

I was going to refute this by showing how much larger Jupiter is than Earth, but a quick calculation gives it a cross-sectional area only 125 times that of Earth. To some extent collisions are also determined by the gravity well -- Jupiter pulls in more objects because it's more massive -- but it's only 318 times the mass of the Earth. Those don't seem like very good safety margins to me! Anyone want to try an explanation like 'Jupiter is in a good spot to be hit and we're not'?

[QUOTE=CRGreathouse;182095]I was going to refute this by showing how much larger Jupiter is than Earth, but a quick calculation gives it a cross-sectional area only 125 times that of Earth. To some extent collisions are also determined by the gravity well -- Jupiter pulls in more objects because it's more massive -- but it's only 318 times the mass of the Earth. Those don't seem like very good safety margins to me! Anyone want to try an explanation like 'Jupiter is in a good spot to be hit and we're not'?[/QUOTE]

I think saying we are not in a "good" spot to be hit is incorrect. We have had major collisions in the past, but for the most part we have been very lucky. Planets like Neptune, Uranus, Saturn and Jupiter that have masses many times that of earth (especially Jupiter) can help protect the inner planets by swallowing up incoming objects, but only to an extent. I think the reason we have had historically few major collisions is that 1) Earth is a very small region in space so statistically it is unlikely to cross the path of another object. 2) I think the moon helps some and 3) Luck.

Back when Shoemaker-Levy 9 hit Jupiter, I remember reading about observers who had seen similar features on Jupiter in the past (a very few times), but no one suspected that they were the result of impact, until they saw S-L 9 and realized what an impact looks like. Maybe two impacts in 15 years (S-L 9 in 1994 and now this new one) isn't an anomalously short time. And maybe we're luckier than we think.

Norm

[quote=CRGreathouse;182095]To some extent collisions are also determined by the gravity well -- Jupiter pulls in more objects because it's more massive -- but it's only 318 times the mass of the Earth. Those don't seem like very good safety margins to me! Anyone want to try an explanation like 'Jupiter is in a good spot to be hit and we're not'?[/quote]Okay -- Yes, Jupiter is in a good spot to be hit. So are we.

Here's a casual argument (that might well overlook some factors):

Consider a set of random orbits that "cross" both E's orbit and J's orbit. ("Cross" means being, at some point, the same distance from the Sun, even if orbital tilt means it's always millions of miles from ever meeting the planet.) Call these EJ-crossing orbits, and the objects in them, EJ-crossers.

Consider two spheres centered on Sun, of 1 AU radius (E's distance from Sun), and 5 AU (J's distance from Sun). Each EJ-crossing orbit intersects both spheres twice. Each intersection is, on average, 5 times as far from another EJ or planetary orbit at J's distance than at E's distance. The EJ objects are, on average, 5 times as far from J at J's distance as they are from E at E's distance from the Sun.

Gravitational attraction is proportional to inverse square of distance, so the average ratios are 1-to-25 at J and E. However the mass ratio is 318-to-1. Overall, an EJ object is pulled towards J at J's distance 318/25 times (roughly 13:1) as well as towards E at E's distance.

Furthermore, EJ objects will, on average, be travelling faster at 1 AU than at 5 AU. IIRC, the ratio will be the square root of 5 = ~ 2.2. This means E has that much less time to attract an object near it than J does.

13 * 2.2 = ~29.

So I'd estimate J attracts EJ objects 29 times as well as E does (but there's probably at least one factor left out).

Further, there are probably more J-crossers than E-crossers. Anything with an aphelion > 5 AU and perihelion between 5 AU and, say, 1.2 AU will be a J-crosser but not an E-crosser.

Support your local search for Near Earth Objects.

Huh. So ignoring the implicit assumptions and generalizing that argument, here's how much other debris planets will attract compared to Earth:

Jupiter: 27x
Saturn: 3.2x
Venus: 1.3x
Earth: 1x
Mercury: 23%
Uranus: 18%
Neptune: 10%
Mars: 5.7%
Ceres: 0.0035%
with the other minor planets attracting less than 1e-5.

Put another way, Earth gets about 3% of the planet-object collisions in this model.

[QUOTE]So I'd estimate J attracts EJ objects 29 times as well as E does (but there's probably at least one factor left out).[/QUOTE]

So, continuing the arm-waving (we should attain human-powered flight soon...), and assuming one Jupiter impact per 15 years (1994, and then 2009), that means we might expect an Earth impact every 435 years (15X29). If Tunguska counts, then maybe we're safe for awhile.

Norm

[QUOTE=Spherical Cow;182136]If Tunguska counts, then maybe we're safe for awhile.[/QUOTE]

Gambler's fallacy?

[QUOTE]Gambler's fallacy? [/QUOTE]

aacckk. Touche'. I'll dust off my hard hat.

Norm

Just my counter-intuitive disputable tuppence worth...

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

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.