Starship Asterisk*

NoelC wrote: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.

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

Chris Peterson wrote:

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.

fugfar wrote: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.

Star*Hopper wrote: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

Pete wrote: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.]

neufer wrote: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!

(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

neufer wrote: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.

(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
-------------------------------------------------

neufer wrote: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).

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

neufer wrote: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 [...]

Pete wrote: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.

Pete wrote:

neufer wrote: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?

Pete wrote:

neufer wrote: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.

Pete wrote:

neufer wrote: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 wrote: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?

neufer wrote: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.

neufer wrote: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.

Pete wrote:

neufer wrote: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)?

mark swain wrote: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

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

emc wrote:

mark swain wrote: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.

grump wrote: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 wrote:

grump wrote: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.

a dictionary author wrote: 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.

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

Storm_norm wrote: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.