Jupiter's New Impact Scar (2009 July 23)

[NoelC]

You note a 50/50 chance of losing or gaining energy... Can you describe each scenario very briefly?

I'm glad you mentioned this... It's something I always wondered idly about but never found the time to grok. I had (without much thought) vaguely assumed that objects approaching a more massive body most often gain energy, because they spend more time approaching and accelerating than they do leaving at acclerated (higher) velocity. On critical reflection this sounds way too simplistic or at worst just plain wrong.

Is there any way you can describe the "gravitational slingshot effect" in layman's terms? I know we sometimes use it with the inner planets to sling probes into the outer solar system... I just can't seem to get my head around the dynamics in 4 dimensions without a good solid nudge.

Thanks.

-Noel

[Chris Peterson]

Is there any way you can describe the "gravitational slingshot effect" in layman's terms? I know we sometimes use it with the inner planets to sling probes into the outer solar system... I just can't seem to get my head around the dynamics in 4 dimensions without a good solid nudge.

It works by transferring orbital angular momentum from the planet to the slingshot object. If you're coming up on a planet in a retrograde direction (opposite the direction the planet is moving), swing around the planet and head back in the direction you came from, you will steal a little of the planet's velocity relative to the Sun. That might sound odd, but keep in mind we are talking relative to the Sun, not to the planet. If you view things from the planet's frame of reference, the slingshot object enters and leaves at the same speed (that is, whatever it gains on the way in, it loses again on the way out).

Think of it like this: you're riding along the street on a skateboard, and a car passes you. You toss a rope out and snag the bumper. You quickly speed up (a lot) and the cars slows down (a little). Later you release the rope. You've still got all that new speed.

You note a 50/50 chance of losing or gaining energy... Can you describe each scenario very briefly?

At the simplest, you could approach a planet in a retrograde orbit, in which case you'll pick up some of the planets orbital angular momentum in the form of increased orbital speed. Relative to the Sun, you've increased your energy- possibly enough to exceed the Sun's escape velocity, in which case you'll now be in a parabolic or hyperbolic orbit. Or, you could approach the planet in a prograde orbit, in which case you will add energy to the planet's orbit, and lose some of your own. This could be enough to convert an object in a parabolic or hyperbolic orbit (which would otherwise leave the Solar System) into an elliptical orbit.

Whether the likelihood of an energy increase or decrease is 50/50, however, is another question. The inclination of comets isn't random- different populations (based primarily on position) are more likely to be in prograde or retrograde orbits. This is an area of ongoing research. And objects which are dragged into elliptical orbits by Jupiter remain subject to significant perturbations which may well keep them from becoming periodic with respect to Jupiter. So I think the question of these energy statistics remains open.

[Pete]

i know impacts happen on all celestial bodies, would i be correct in thinking impacts are a lot more common or likely with jupiter because of its huge gravitational pull?

That's an interesting question, one I've thought about a lot in the past. I don't know a good way to answer it without some sort of simulation. My thinking is that Jupiter's gravity isn't a factor, however. Objects with strong gravitational fields certainly affect the orbits of objects passing by, but they don't necessarily increase the chance of a collision. Jupiter is a large planet, of course (as you noted), so it has a much larger collisional cross-section than other planets. That means it will collide with more debris than the other planets, regardless of its gravitational field.

The increase in collisional cross-section due to the target body's gravity is called gravitational focusing. A back-of-a-piece-of-scrap-paper-while-slacking-off-at-work calculation to go with the diagram in the link:

Picture a spherical target body of mass M and radius R.
Before: a small body approaches at speed v on a trajectory whose closest approach would be b if the target were massless. (b is the so-called impact parameter.)
After: the small body has been deflected by the target's gravity and just grazes the target body surface tangentially at speed v_coll.
Specific (i.e. per unit mass) angular momentum, v dot-product r, is conserved: v b = v_coll R
So is specific energy (until the impact itself of course): v^2/2 - GM/[r_initial ~= infinity] = v_coll^2/2 - GM/R
Rearrange this and use v_esc = sqrt(2GM/R) to get:

v_coll = sqrt(v^2 + v_esc^2) (...Pythagoras? I guess this line follows immediately from simple velocity vector geometry)
b = R sqrt(1 + v_esc^2 / v^2)

The effective cross section that a large spherical body presents to incoming small bodies is larger for slower initial closing speeds and also for larger target mass, which seems intuitive. Doesn't seem to make a HUGE difference in Jupiter's case... Closing speed of v = v_esc ~= 59.5 km/s "only" increases the planet's collisional x-section by a factor of 4.

[EDIT: ...by a factor of 2, not 4! Also, the above doesn't account for the Sun's gravity.]

(LaTeX would be nice in here )

[The Code]

Copy and paste the hole text except the last line.. nice link pete. http://www.stsci.edu/~webdocs/AnnualReport/ar04.pdf

Thank you..

mark

[BMAONE23]

Space.com shows a good comparitive image in their article. Hubble has awoken

[fugfar]

i want to thank the community for all these great answers, bottom line for me i guess, is what a great mind blower, and if anyone has a link to the guy in Australia, id like to add to his fanmail.

chris and nuefer, you guys are shedding so much light on something we all take for granted. every bit is interesting, to me at least.
thanx

-fug

[bystander]

i want to thank the community for all these great answers, bottom line for me i guess, is what a great mind blower, and if anyone has a link to the guy in Australia, id like to add to his fanmail.

From: Jupiter another impact

The discoverer & his gear:
http://jupiter.samba.org/AnthonyWesley.jpg

And his site's announcement & followup:
http://jupiter.samba.org/jupiter-impact.html

And his name: Anthony Wesley of Murrumbateman, Oz

[neufer]

The increase in collisional cross-section due to the target body's gravity is called gravitational focusing. A back-of-a-piece-of-scrap-paper-while-slacking-off-at-work calculation to go with the diagram in the link:

Picture a spherical target body of mass M and radius R.
Before: a small body approaches at speed v on a trajectory whose closest approach would be b if the target were massless. (b is the so-called impact parameter.)
After: the small body has been deflected by the target's gravity and just grazes the target body surface tangentially at speed v_coll.
Specific (i.e. per unit mass) angular momentum, v dot-product r, is conserved: v b = v_coll R
So is specific energy (until the impact itself of course): v^2/2 - GM/[r_initial ~= infinity] = v_coll^2/2 - GM/R
Rearrange this and use v_esc = sqrt(2GM/R) to get:

v_coll = sqrt(v^2 + v_esc^2) (...Pythagoras? I guess this line follows immediately from simple velocity vector geometry)
b = R sqrt(1 + v_esc^2 / v^2)

The effective cross section that a large spherical body presents to incoming small bodies is larger for slower initial closing speeds and also for larger target mass, which seems intuitive. Doesn't seem to make a HUGE difference in Jupiter's case... Closing speed of v = v_esc ~= 59.5 km/s "only" increases the planet's collisional x-section by a factor of 4.

[EDIT: ...by a factor of 2, not 4! Also, the above doesn't account for the Sun's gravity.]

Nice piece of work, Pete.

We know what the closing speed of a typical Oort cloud comet on Jupiter would be: v ~ 13.07 sqrt(3) km/s
(Jupiter orbital speed = 13.07 km/s).

This gives an increase of Jupiter's cross section by about a factor of 8 => 1000 earth cross sections

However the closing speed of an Oort cloud comet coming up from behind Jupiter is: v ~ 13.07 [sqrt(2)-1] km/s

This gives an increase of Jupiter cross section by about a factor of 122 => 15,000 earth cross sections > the area of the sun!

[neufer]

Nice piece of work, Pete.

We know what the closing speed of a typical Oort cloud comet on Jupiter would be: v ~ 13.07 sqrt(3) km/s
(Jupiter orbital speed = 13.07 km/s).

This gives an increase of Jupiter's cross section by about a factor of 8 => 1000 earth cross sections

However the closing speed of an Oort cloud comet coming up from behind Jupiter is: v ~ 13.07 [sqrt(2)-1] km/s

This gives an increase of Jupiter cross section by about a factor of 122 => 15,000 earth cross sections > the area of the sun!

I did a more careful analysis using Pete's formula with backside impinging angles > 0º .

The amazing thing is that the surface escape velocity is 10 times the relative comet velocity (v) and
one must go out to ~ 100 Jupiter radii for the escape velocity to be comparable to the relative comet velocity
[a roughly sufficient condition to inject the comet into an (e)lliptical (o)rbit... one that returns to
impinge precisely on Jupiter's orbit for many other shots at Jupiter's solar sized collisional cross section].

Hence, the collisional cross section (initial & return) is comparable to the area of the sun while
the initial elliptical orbit insertion cross section is comparable to 100 times the area of the sun!

Code: Select all

(solar area) sigma        comet impinging
collision   e.o.          angle    speed
----------------------------------
1.0         200            10º	 6.05 km/s
0.26         50            41º   12.1 km/s

Here, Pete's own calculation of an effective doubling of the collisional cross section
for relative comet velocity ~ escape velocity repeats itself but for this time for the
situation where these velocities are actually equivalent ... at ~ 100 Jupiter radii!

Thus the significant elliptical orbit insertion cross section
σ = 2 x (100^2) Jupiter cross sections = 200 solar areas.
-------------------------------------------------
Values used:

Jupiter diameter: 10.86 earth diameters
Sun's diameter: 109 earth diameters

60.5 km/s : escape velocity at Jupiter's surface
13.07 km/s : circular orbital velocity at Jupiter
18.48 km/s : parabolic comet orbit velocity at Jupiter

v = 18.48 - 13.07 = 5.41 km/s for 0º backside impinging angle
v = 6.05 km/s for 10º backside impinging angle
v = 12.1 km/s for 41º backside impinging angle

[neufer]

Hubble Captures Jupiter's New Spot
Source: CBC News 07/27/09 1:00PM



<<This image provided by NASA's Hubble Space Telescope taken with it's Wide Field Camera 3 on Thursday July 23, 2009 shows the sharpest visible-light picture taken of the impact feature (dark spot) and "backsplash" of material from a small object that plunged into Jupiter's atmosphere and disintegrated. This is a natural color image of Jupiter as seen in visible light. The spot is a debris plume associated with turbulence in Jupiter's atmosphere, NASA reported, estimating it was caused by the impact of an object about the size of several football fields.>>

[neufer]

I did a more careful analysis using Pete's formula with backside impinging angles > 0º .

The amazing thing is that the surface escape velocity is 10 times the relative comet velocity (v) and
one must go out to ~ 100 Jupiter radii for the escape velocity to be comparable to the relative comet velocity
[a roughly sufficient condition to inject the comet into an (e)lliptical (o)rbit... one that returns to
impinge precisely on Jupiter's orbit for many other shots at Jupiter's solar sized collisional cross section].

Hence, the collisional cross section (initial & return) is comparable to the area of the sun while
the initial elliptical orbit insertion cross section is comparable to 100 times the area of the sun!

Code: Select all

(solar area) sigma        comet impinging
collision   e.o.          angle    speed
-------------------------------------------------
1.0         200            10º	 6.05 km/s
0.26         50            41º   12.1 km/s
-------------------------------------------------

Here, Pete's own calculation of an effective doubling of the collisional cross section
for relative comet velocity ~ escape velocity repeats itself but for this time for the
situation where these velocities are actually equivalent ... at ~ 100 Jupiter radii!

Thus the significant elliptical orbit insertion cross section
σ = 2 x (100^2) Jupiter cross sections = 200 solar areas.

The backside of Jupiter proved to be such a wonderful "seductive flame" for attracting & killing comets that I thought I would look at the solar system's first line of defense against comets: Neptune. Like Jupiter, Neptune's surface escape velocity is roughly an order of magnitude greater than the velocity of an Oort Cloud comet impinging on the planet's back side. Hence Neptune is simply a miniature version of Jupiter with all cross sections scaled down by a factor of 8 (~ Jupiter's area/Neptune's area):

Code: Select all

(solar area) sigma        comet impinging
collision   e.o.          angle    speed
-------------------------------------------------
0.125        25            06º	 2.35 km/s
0.032         6            37º    4.7 km/s
-------------------------------------------------

Neptune diameter: 3.86 earth diameters
Sun's diameter: 109 earth diameters

23.5 km/s : escape velocity at Neptune's surface
5.43 km/s : circular orbital velocity at Neptune
7.68 km/s : parabolic comet orbit velocity at Neptune

v = 7.68 - 5.43 = 2.25 km/s for 0º backside impinging angle
v = 2.35 km/s for 6º backside impinging angle
v = 4.7 km/s for 37º backside impinging angle

[Pete]

Very cool analyses, neufer.

The elliptical insertion area you compute for Jupiter, 200 solar areas, corresponds to 20 000 Jupiter areas, or about sqrt(2e4 / pi) * 7e7 m / (5.2 AU) = 0.7% of Jupiter's distance from the Sun. For comparison, the radius of Jupiter's Hill sphere (inside of which a body loosely held together will be tidally disrupted) is (1.898e27 kg / 3 / 1.989e30 kg)^(1/3) = 7% of Jupiter's distance from the Sun. It seems from this that any weakly bound object scattered by Jupiter will also be tidally ripped apart.

We know what the closing speed of a typical Oort cloud comet on Jupiter would be: v ~ 13.07 sqrt(3) km/s
(Jupiter orbital speed = 13.07 km/s).

I'm feeling unusually dense... Where does the sqrt(3) factor come from?

However the closing speed of an Oort cloud comet coming up from behind Jupiter is: v ~ 13.07 [sqrt(2)-1] km/s

I understand that sqrt(2) - 1 comes from the fact that the parabolic velocity at Jupiter's distance is just sqrt(2) v_J.

The amazing thing is that the surface escape velocity is 10 times the relative comet velocity (v) and
one must go out to ~ 100 Jupiter radii for the escape velocity to be comparable to the relative comet velocity [a roughly sufficient condition to inject the comet into an (e)lliptical (o)rbit [...]

In the derivation for effective collisional cross-section, the quantity 2GM/R (planet mass and radius) was replaced with v_esc, the *surface* escape velocity. Does the formula still hold if you use *local* v_esc at arbitrary distances from Jupiter? I have trouble understanding how the distance at which local escape speed roughly equals comet speed is an estimate of the e.o. cross section.

[neufer]

Very cool analyses, neufer.

The elliptical insertion area you compute for Jupiter, 200 solar areas, corresponds to 20 000 Jupiter areas, or about sqrt(2e4 / pi) * 7e7 m / (5.2 AU) = 0.7% of Jupiter's distance from the Sun. For comparison, the radius of Jupiter's Hill sphere (inside of which a body loosely held together will be tidally disrupted) is (1.898e27 kg / 3 / 1.989e30 kg)^(1/3) = 7% of Jupiter's distance from the Sun. It seems from this that any weakly bound object scattered by Jupiter will also be tidally ripped apart.

If that were the case then Jupiter's moons are in a lot of trouble

Aren't you really referring to the much smaller Roche limit?

We know what the closing speed of a typical Oort cloud comet on Jupiter would be: v ~ 13.07 sqrt(3) km/s
(Jupiter orbital speed = 13.07 km/s).

I'm feeling unusually dense... Where does the sqrt(3) factor come from?

Jupiter is traveling at 13.07 km/s
The Oort Cloud parabolic comet is traveling at 13.07sqrt(2) km/s

The most common type of collision would have these velocity vectors
roughly perpendicular to each other to form a [1,sqrt(2),sqrt(3)] triangle.

However, for Jupiter & Neptune the cross section for "slow motion" Oort cloud comet rear ends collision is so large that most side & head on collisions can be effectively ignored. (Note that when the deflected comet returns to Jupiter in its elliptical orbit the relative velocities are exactly the same as in the original collision so that the large "slow motion" cross sections are retained even for side collisions. )

However the closing speed of an Oort cloud comet coming up from behind Jupiter is: v ~ 13.07 [sqrt(2)-1] km/s

I understand that sqrt(2) - 1 comes from the fact that the parabolic velocity at Jupiter's distance is just sqrt(2) v_J.

Yes, It's just as if a returning 25,000 mph Apollo capsule had collided with the 18,000 mph Sky Lab.

The amazing thing is that the surface escape velocity is 10 times the relative comet velocity (v) and
one must go out to ~ 100 Jupiter radii for the escape velocity to be comparable to the relative comet velocity [a roughly sufficient condition to inject the comet into an (e)lliptical (o)rbit [...]

In the derivation for effective collisional cross-section, the quantity 2GM/R (planet mass and radius) was replaced with v_esc, the *surface* escape velocity. Does the formula still hold if you use *local* v_esc at arbitrary distances from Jupiter? I have trouble understanding how the distance at which local escape speed roughly equals comet speed is an estimate of the e.o. cross section.

Actually, any deflection at all from a rear end collision will cause the parabolic orbit to pass in front of Jupiter thereby transferring cometary energy to Jupiter energy and inserting the comet into an elliptical orbit around the sun. Hence, one could make the case that the Hill sphere cross section is the relevant value here.

However, my proposed smaller cross section will virtually guarantee an elliptical cometary orbit that returns closely to the "scene of the crime" within a reasonable time frame.

[Pete]

If that were the case then Jupiter's moons are in a lot of trouble

Aren't you really referring to the much smaller Roche limit?

Oops! Yeah, I was confused. Fortunately for the moons, they're within Jupiter's Hill sphere ("sphere of influence").

The most common type of collision would have these velocity vectors
roughly perpendicular to each other to form a [1,sqrt(2),sqrt(3)] triangle.

Thanks.

Actually, any deflection at all from a rear end collision will cause the parabolic orbit to pass in front of Jupiter thereby transferring cometary energy to Jupiter energy and inserting the comet into an elliptical orbit around the sun.

Isn't it also possible for a comet approaching from the rear to gain energy from Jupiter and leave the solar system? (something like this, where the Sun is off the bottom of the diagram)?

[neufer]

Actually, any deflection at all from a rear end collision will cause the parabolic orbit to pass in front of Jupiter thereby transferring cometary energy to Jupiter energy and inserting the comet into an elliptical orbit around the sun.

Isn't it also possible for a comet approaching from the rear to gain energy from Jupiter and leave the solar system? (something like this, where the Sun is off the bottom of the diagram)?

Yes, where the perijovian point is also behind Jupiter then Jupiter slows down and the comet gains energy.

Note, however, that this is more than made up for by the advancement of the perijovian point for the trajectory coming from the other side.

All this probably means is that the elliptical orbit insertion cross section is simply shifted off center from Jupiter based upon the direction of the incoming comet. The off center cross section for an off center incoming trajectory might still be as large or larger as it would be otherwise.

[emc]

emc

Feel the breeze at 100mph on a motor bike?

Now speed your bike up to 65,000mph and feel that breeze... (Just an example ..)

Mark

As a matter of fact, I have felt 100mph+ breeze on a motor bike. Interesting that you should bring it up... more interesting that I am still alive, but that is another story not the least bit astronomical.

I like neufer's and Chris Peterson's comments on the 65k+ mph... I expect hitting a bug would also be somewhat catacylsmic.

[bystander]

I like neufer's and Chris Peterson's comments on the 65k+ mph... I expect hitting a bug would also be somewhat catacylsmic.

Hey, Ed! No worries! They don't have windows on motor bikes.

[grump]

emc

Feel the breeze at 100mph on a motor bike?

Now speed your bike up to 65,000mph and feel that breeze... (Just an example ..)

Mark

As a matter of fact, I have felt 100mph+ breeze on a motor bike. Interesting that you should bring it up... more interesting that I am still alive, but that is another story not the least bit astronomical.

I like neufer's and Chris Peterson's comments on the 65k+ mph... I expect hitting a bug would also be somewhat catacylsmic.

When I rode I wore an open face helmet - hitting a (big) fly at 60mph stung a bit, and was fatal for the fly. What was really interesting was riding through a swarm of bees at that speed.

[apodman]

When I rode I wore an open face helmet - hitting a (big) fly at 60mph stung a bit, and was fatal for the fly. What was really interesting was riding through a swarm of bees at that speed.

Like Ralph Nader's Corvair, bees can be unsafe at any speed. My first bee sting, acquired while riding a bicycle with my mouth open, was on the inside of my upper lip. Very inconvenient. Never rode with my mouth open again.

[rigelan]

I ride my bike with sunglasses at all times for the same reason.

When I rode I wore an open face helmet - hitting a (big) fly at 60mph stung a bit, and was fatal for the fly. What was really interesting was riding through a swarm of bees at that speed.

Like Ralph Nader's Corvair, bees can be unsafe at any speed. My first bee sting, acquired while riding a bicycle with my mouth open, was on the inside of my upper lip. Very inconvenient. Never rode with my mouth open again.

[Storm_norm]

we are calling the black mark on jupiter an "impact scar"

since Jupiter is pretty much composed of gas, what exactly did the comet (or object) impact?

or is "impact" just the generic term in this case?

Does this mean that every tiny spec of dust that encounters our atmosphere get the term "impact" ?

[geckzilla]

You don't have to hit something solid to make an impact, nor does size matter.

im·pact (ĭm'păkt')
n.
1. The striking of one body against another; collision.
2. The force or impetus transmitted by a collision.
3. The effect or impression of one thing on another: still gauging the impact of automation on the lives of factory workers.
4. The power of making a strong, immediate impression: a speech that lacked impact.

[The Code]

neufer

I stand corrected...You are the man to ask...

You very much, do know your stuff.

I am sorry for thinking otherwise.

Quality posts thanks.

Mark

[Storm_norm]

from webster's online dictionary.org.
http://www.websters-online-dictionary.o ... ion/impact

1. A single collision of one mass in motion with a second mass which may be either in motion or at rest. 2. Specifically, the action or event of an object, such as a rocket, striking the surface of a planet or natural satellite, or striking another object; the time of this event, as in from launch to impact. 3. To strike a surface or an object.4. Of a rocket or fallaway section: To collide with a surface or object, as in the rocket impacted 10 minutes after launch

the connotation of the word "impact" is that the comet or object made contact with a surface. I'd like to argue that any object that falls into the depths of the jupiter gases doesn't actually make contact with a surface. instead, jupiter incorporates the comets and other types of space debris into itself.
the scar that was left on jupiter is a blemish in comparison to a real celestial impact like theia impacting the ancient earth. or the Herschel crater on the Saturn moon Mimas.
Jupiter has been swallowing up comets, asteroids and other dust in the solar system for billions of years. its a naturally occuring event that hardly deserves the term "impact."
those comets, those asteroids are just bugs on jupiter's highway to increasing its size and content.

impact ?? nah, not when describing a celestial meeting of comet bugs and Jupiter.
Jupiter eats comets for breakfast. it doesn't impact them.

[Chris Peterson]

from webster's online dictionary.org.
http://www.websters-online-dictionary.o ... ion/impact

1. A single collision of one mass in motion with a second mass which may be either in motion or at rest. 2. Specifically, the action or event of an object, such as a rocket, striking the surface of a planet or natural satellite, or striking another object; the time of this event, as in from launch to impact. 3. To strike a surface or an object.4. Of a rocket or fallaway section: To collide with a surface or object, as in the rocket impacted 10 minutes after launch

the connotation of the word "impact" is that the comet or object made contact with a surface. I'd like to argue that any object that falls into the depths of the jupiter gases doesn't actually make contact with a surface.

You can argue it all you want, but I don't think you're going to convince many people that this wasn't a collision. A comet striking Jupiter certainly meets the very first definition given- one mass in motion striking another. There is no requirement for a "surface". Astronomically, we talk of all sorts of collisions. Star systems form because diffuse clouds of gas and dust collide. This is normal usage of the term.