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Jupiter, Earth's savior? (Read 15388 times)
shellandtube
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Jupiter, Earth's savior?
09/15/07 at 03:52:09
 
I remember seeing a program that suggested that the Earth was protected from asteroid collisions due to the gas giants. I decided to test this theory by creating a slightly scaled down version of the solar system with 2 earthlike planets in close orbit to a 0.1 solar mass star and 2 jupiterlike planets further out. I then created 100 asteroids with eccentric orbits such that very few (approx 5) were "earth crossing". I then ran the simulation with a 512 timestep and found that after 200 years 2 were captured by the GG's, 9 had been ejected and the majority of the remaining asteroids where now in orbits that where highly eccentric and very short period. That is to say the were earth crossing and no longer crossed the orbits of the gas giants. From looking at the masses of the planets and the sun it would appear that the vast majority of the collisions were from asteroids impacting the sun. This would obviously mean that they crossed the orbit of the earthlike planets. This would suggest that they increase the chances of earth impacts? Over a longer period of time those asteroids that haven't impacted the sun and no longer are significantly affected by the GG's are now fair game for the earth! So what I have found is the idea of protection is false. Or is my simulation too innacurate/unreliable?
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frankuitaalst
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Re: Jupiter, Earth's savior?
Reply #1 - 09/15/07 at 07:05:40
 
I recently saw an article about this item , here's a link .  
http://space.newscientist.com/article.ns?id=dn12532
Jupiter may indeed have a negative influence upon the Earth treads
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Re: Jupiter, Earth's savior?
Reply #2 - 09/15/07 at 10:41:34
 
Cheers frank. I reran the simulation paying attention to what was happening. The interactions with the GG's caused the asteroids to loose momentum and therefore peturbed the orbits such that they headed for the dominant mass of the system ie the sun. Depending on how much momentum they lost they either entered into small period orbits or collided with the sun. Under certain conditions they were captured by the larger of the GG's but quite often they were later ejected from the solar system. Due to interactions with the other gas giant working on a similar principle as above.  The outer GG (lowest mass) slowed them down allowing them to become more eccentric with respect to the larger inner GG and were then ejected.
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Re: Jupiter, Earth's savior?
Reply #3 - 09/26/07 at 11:34:33
 
Does Jupiter protect us against collision from asteroids ?  
I came up with the following sim , not giving an answer to the question above , but resulting in nice images ...
Supose the solar system is surrounded by a ring of asteroids , lets say 360 , one asteroid every degrees .  
Position them at 32 AU from the sun ( about the orbit of Pluto ) .  
As they are in rest initially they will be pulled inwards by the sun , accelerating and will cross Neptune , Uranus ; Saturn , Jupiter , Mars ...to reach Earth .  
Will they hit Earth ? What's the influence of Jupiter ?  
The sim in annex shows the end phase of the simulation as the asteroids have come close to Earth after a journey of several years having crossed the outer planets ...
Ill post an animated gif of this sim .
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Re: Jupiter, Earth's savior?
Reply #4 - 09/26/07 at 11:41:12
 
Heres the animated frame of the above simulation , covering the period before close approach to Earth .  
Screenshots were made initially every 120 days .  
As the asteroids come closer the screenshot rate as well as the zooming was increased . May be somewhat confusing . Sad  
Interesting is the following : watch how the asteroids are initially close to Neptune ( at 9 o clock ) . Does Neptune influences their motion ? Seems not to be , but watch till the end...
Also Jupiter seems to influence the orbits .
I'll post the end of the simulation .
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Re: Jupiter, Earth's savior?
Reply #5 - 09/26/07 at 11:57:42
 
The picture herenunder represents the end of the simulation , starting at the end of the previous picture .  
The initial circular confuguration of the bodies is now heavily disturbed at 9 'o clock (Neptune ) and at 6 'o clock ( Jupiter ) .  
All the asteroids are now heading towards the sun ( I don't think one has collided with the outer planets , no does one collide with Earth á) .  
The picture hereunder gives only an impression of the movement . Running the sim makes much more fun.  
It is really amazing to see how the asts are "sucked in" by the sun , one after another like a chain .  
Only 5 of the original 360 bodies survive .
It seems to be so that the asteroids that survive are those which were disturbed ...They stay alive and stay as a threat .
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Re: Jupiter, Earth's savior?
Reply #6 - 09/27/07 at 10:48:18
 
Another way to get an idea about Jupiters influence on asteroid orbits ...
In the sim hereunder 500 small objects were created in a circular path around the sun within Jupiters orbit +/- 1% . So they appear as a circle . Jupiter is somewhere in the middle of them , originally at about 12 'o clock .  
Will Jupiter catch them ? Will they be ejected or bound as a moon to Jupiter ?  
The picture herunder gives the first thirty years of the life of this asteroids .  
 
It's remarkable that Jupiter creates very quicly a "gap" in the ring , some asteroids are pulled outwards , others are driven inwards , others tend to orbit Jupiter .  
I guess that after longer átime Jupiter will be able to create Trojans or will be puliling the asteroids into horseshoe orbits .
The asterods driven inwards yet remain at a safe distance from the inner planets .  
( Question : is it possible here to post 2 files ie. also the .gsim file ? ) á
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« Last Edit: 09/27/07 at 14:49:14 by frankuitaalst »  

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Re: Jupiter, Earth's savior?
Reply #7 - 09/27/07 at 23:06:44
 
In the following sim it is clear how Jupiter whipes out the nearby asteroids .  
360 asteroids are initially orbiting at Jupiters orbit +/- 2% .  
The simulation covers a little bit more than 12 years corresponding plusminus to one Jovian year .  
Jupiter is shown as the pink dot at 5 'o clock in this rotating frame.  
It's amazing how quickly Jupiter clears the gap .
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Re: Jupiter, Earth's savior?
Reply #8 - 09/28/07 at 08:07:11
 
Just out of curiosity, does anything change if you remove Saturn from the system? I know that there are resonances with Saturn (nu1, I think) that serve to define inclination/eccentricity limits in the main belt, but I don't know if those apply in the situation you've set up here.
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Re: Jupiter, Earth's savior?
Reply #9 - 09/28/07 at 09:35:02
 
Heres the same system , but run for 170 years . A screenshot corresponds with 1 year .  
It's remarkable how Jupiter pulls the asteroids from the outside and drives them away to the inside .  
There also seem ,on average , to be more asteroids leading Jupiter then there are trailing .  
The system seems to behave somewhat chaotically but NO asteroid was lost in this period although they all have a diameter of 10 km .
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Re: Jupiter, Earth's savior?
Reply #10 - 09/30/07 at 06:55:48
 
I don't think Saturn plays a big role in this sim , but I'll give it a trail .  
Wondering if asteroids may behave differently dependent upon their initial orbit I created three orbits : yellow = AU Jup ; green = AUJup-3% and blue = AUJup+3% .  
Total of bodies is 360.  
The sim herunder uses three screenshots per year and covers 40 years of simulation .  
It's nice to see how the different families of asteroids "round the corner" in a different way . There's also a difference in the leading and trailing part of the ring .
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Re: Jupiter, Earth's savior?
Reply #11 - 09/30/07 at 13:17:56
 
How far does Jupiters influence on asteroids extends ?  
Its influence is amazing as can be seen in the following pictures ..
240 low mass asteroids were positionned  at 4AU ( 600 mio  km ) ie more than 1AU from Jupiter .  
Jupiter is situated at the bottom of the frame ( not always visible ) .  
Its hard to believe how Jupiter modifies the initial circular orbits of the asteroids ...
(positionning the asteroids at 650 mio km gives even more dramatic pictures )  Huh.  
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Re: Jupiter, Earth's savior?
Reply #12 - 10/01/07 at 13:02:05
 
Frankuitaalst. If you look at the numbers its not that difficult to imagine why.
Jupiter is approx 1E-3 (9.5E-4 really) solar masses and in your sim its 4 times closer 1au vs 4 au. So considering the point when they are perfectly aligned, jupiter asteroid sun. The force in the jupiter direction is a significant % of the solar direction. (Fj/Fs)=1E-3/(1/16) or 1.6E-2 which is 1.6%.
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Re: Jupiter, Earth's savior?
Reply #13 - 10/01/07 at 22:30:47
 
your calculation is right .  The 1.6% may seem small , and in fact it is , but this gives the asteroid a direction to Jupiter . The net force grows as distance decreases , so that this crazy figures may arise .
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Re: Jupiter, Earth's savior?
Reply #14 - 10/02/07 at 10:06:43
 
The influence of Jupiter also works of course when the asteroids orbit at the outside .  
Hereunder a simulation running for 100 years .  
The asteroids are in a 3:2 resonance to Jupiter  (AU : 6.817 to 5.203 Jup).  
The influence of Jupiter is small in the beginning but due to the resonance some knots are build after several years.  
After more years it seems that 3 knots are build .
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Re: Jupiter, Earth's savior?
Reply #15 - 10/03/07 at 23:12:23
 
The picture hereunder gives the same simulation as above (3:2 resonance with Jupiter ) . Sim was run for 125 years .  
In order to get an impression how the particles behave the orbit was created by 4 circle segments of 90░ each of a different color .  
After some time 3 knots are created which wind up and unwind as they orbit. By chance 2 knots are positionned at the intersection of 2 different colors . Following the simulation on screen it's nice to see how the particles do not mix up .  
The winding up is really that big that nearly a full quarter segment lies in one knot  Roll Eyes.
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Re: Jupiter, Earth's savior?
Reply #16 - 10/06/07 at 19:28:13
 
Asteroids on a 2:1 resonance to Jupiter are shown here ...
Their orbit comes close to Saturn ( yellow dot )in this rotating frame to Jupiter ( pink dot at 10 'o clock ) .  
The influence of Saturn is really big . In this timeframe of 50 years Saturn strips away a lot of asteroids , creating a gap . Creation of the gap is a matter of just a couple of years .
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Re: Jupiter, Earth's savior?
Reply #17 - 10/06/07 at 19:36:02
 
That last one was quite interesting.  You might want to set the rotating frame period to Saturn's orbital period and try it again.  It looks like the particles trailing Saturn after the gap are in L4 tadpole orbits or perhaps horseshoe orbits.
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Re: Jupiter, Earth's savior?
Reply #18 - 10/07/07 at 03:20:32
 
Good idea ...  
Heres a gif for the fisrt 75 years in Rotating frame to Saturn ( yellow dot at the right ) .  
Saturn steals two times material from the ring in this timeframe. Its action on the ring is rather violent as the material is ejected far away .  
Interesting is to follow the "tail" of the gap going upwards  after the fisrt encounter .  
The tail seems to sweep several times ...as if the animal was wounded.  
I'll post the second part of the sim , also 75 years .  Some horseshoe structure is visible there .
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Re: Jupiter, Earth's savior?
Reply #19 - 10/07/07 at 03:30:38
 
Heres the second part of the simulation , also covering 75 years .  
I can't detect yet any horseshoe orbits to Saturn .  
But interesting is the cloud of objects which release at the top just after the beginning .  
They "lift off" and start to move anti-clockwise , accelerating and decelerating .  
Looks as if they are in a horseshoe orbit around Jupiter . Do they ?  
Would be funny : Jupiter gets horseshoe asteroids with the help  of Saturn .
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Re: Jupiter, Earth's savior?
Reply #20 - 10/07/07 at 05:11:29
 
Nopes ... no trojans for Jupiter either . I ran the sim for more than 250 years . Although Jupiter has a big influence there s no building of trojans. I think the original distance from the ring ( and thus also the momentum ) is just to big . Same may be true for Saturn . What do you guys think ?  
Heres the .gsim file .  
I ran it at 32000 sec , reducing speed to 8000 for a while when saturn was close
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Re: Jupiter, Earth's savior?
Reply #21 - 10/07/07 at 05:46:11
 
Frankuitaalst, I am running a similar sim but with the asteroids in a slightly elliptical orbit (SMA 7AU and e=0.18). Just set it running, if i see anything of interest i will post about it. The eccentricity will alter the relative velocity of the asteroids and the gas giants and i expect it to provide slightly different results.
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Re: Jupiter, Earth's savior?
Reply #22 - 10/07/07 at 06:44:07
 
Here is a screenshot from the sim i mentioned above. Its in a rotating frame locked to saturn. I am not quite sure how to interpret it. Any help guys?
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Re: Jupiter, Earth's savior?
Reply #23 - 10/07/07 at 11:43:40
 
You have the Trails on ? What you see is normal I think . What timestep do you use ? I didn't go further than 32000 ( in order not to throw out any objects )
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Re: Jupiter, Earth's savior?
Reply #24 - 10/08/07 at 12:44:40
 
about 8100 for the timestep and yes the trails are on. i changed the doEvents interval and Plot count to make it run quicker i think it was every 150 itererations. I expected to see the loops but some of them were strange. There was 1 that looped around a point at least twice and then moved off. It's not in this pic though. Could it have been a temporary trojan? The point it was circling seemed to be a little more than 60 degrees ahead and on its second loop the loop was larger and more elliptical. After that it moved away and i lost it in bulk. I looked for the position of jupiter just after i lost it and think jupiter would have been close by when it destabilized.
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Re: Jupiter, Earth's savior?
Reply #25 - 10/08/07 at 13:35:02
 
It may be possible that you had a temporary trojan . Trojans are however hard to get out of a bunch of "random" bodies . If the velocities and positions don't match ...theres little chanche to get a stable trojan . I whished I knew how to create one .
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Reply #26 - 10/08/07 at 15:11:47
 
I only noticed it when I turned the trails on, it only made 2 loops then dissapeared. How long it had been there I couldn't say. My thinking is when jupiter passed it destabilized it so it may well be possible that a previous passage of jupiter caused it to become a trojan. The page on wikipedia about trojans is useful.
http://en.wikipedia.org/wiki/Trojan_asteroid
 
My best guess to create one artificially would be to create a bunch of 50 or so objects such that they where all close to the sma of jupiter say +/- 1% and 60 degs in front (or behind) also +/- a few degrees. If you then run the sim with rotating frame to jupiter you might get lucky. I think a trojan would just orbit around the L4 or L5 point in a rotating frame? I guess you would know more than me. I gather from your posts that you work in some related field. Whereas I am a chemical engineer and this is just a hobby.
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Re: Jupiter, Earth's savior?
Reply #27 - 10/08/07 at 19:46:16
 
So I took my own advice and tried it out. created 50 objects sma 5.204 +/- 1% and spread them out at 60 degrees behind +/- 1.2 degs. I ran the simulation for 300 years. The objects spread out a couple of degrees either side of 60 and pretty much stayed there. The bunch expanded and contracted over 25 years or so but remained in the vicinity of the lagrange point. Does this make them all trojans? From the wikipedia definition in the above link it does.
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Re: Jupiter, Earth's savior?
Reply #28 - 10/08/07 at 22:57:39
 
Sure , this is definitively a way to make trojans, or at least some of them . In a three body system trojans stay at their position . Due to perturbations of other planets trojans tend to make orbits around their stable point . This orbits are dynamically stable , meaming the orbit can change but will not drift off.  
Problem is : how do trojans arrive at their stable point from elsewhere. What orbit should they have so that at some time they are captured as a trojan ?  I was never able to simulate such thing. Anybody does ?  
Creating a ring of bodies as seen in the previous posts hasn't yet created trojans till now.  
To answer your question : I'm not profesionally involved in astronomy or something like that . I'm a mechanical engineer and work in the field of anaerobic digestion . Astronomy is just a strng interest of mine.  
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Re: Jupiter, Earth's savior?
Reply #29 - 10/08/07 at 23:04:31
 
Quote from frankuitaalst on 10/08/07 at 22:57:39:
Due to perturbations of other planets trojans tend to make orbits around their stable point

The other planets have nothing to do with it.  Delete them and you'll see.
 
If you place an object directly on the L4 or L5 in a perfectly circular orbit, it will not drift.  But if you nudge it a little, so its velocity is no longer perfect, it will circle the L point regardless of whether other planets exist or not.
 
Also, if you place an object near an L4 or L5 point, but not directly on it, it will also orbit the L point, regardless of whether other planets exist or not.
 
The perturbations from the other planets will, however, make it impossible to set up the perfect L4 or L5 scenerio.  But even if they don't exist, you can still have objects orbit the L4 and L5 points.
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Re: Jupiter, Earth's savior?
Reply #30 - 10/08/07 at 23:13:17
 
I am involved with the manufacture of nylon polymers. Jupiters trojans could have formed at the same time as the planet and become locked there as it started accumulating gas and became massive. Or they might be the remnants left over from the formation of the inner planets gradually pushed out by the solar wind or who knows?
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Re: Jupiter, Earth's savior?
Reply #31 - 10/09/07 at 01:11:27
 
That's one theory for the trojans of Neptune.  I don't see why it wouldn't apply to Jupiter as well.  They were planetesimals that were co-orbital with the planetesimals that formed Jupiter, but got locked into Jupiter's L4&5 points when Jupiter's mass became significant.
 
I doubt the solar wind is strong enough to push anything more massive than gas and microscopic grains.  Even if it was, the result would not be a wider semi-major axis, but a higher eccentricity.
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Re: Jupiter, Earth's savior?
Reply #32 - 10/09/07 at 08:55:18
 
Quote from Tony on 10/08/07 at 23:04:31:

The perturbations from the other planets will, however, make it impossible to set up the perfect L4 or L5 scenerio. áBut even if they don't exist, you can still have objects orbit the L4 and L5 points.

You're right . I formulated the sentence poorly .  
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Re: Jupiter, Earth's savior?
Reply #33 - 10/09/07 at 09:09:50
 
Heres a simulation of 100 Asteroids in the leading L-point of Jupiter with a tolerance of +/- 1% in both AU and Anomaly . Simulation spans 25 years. Asteroids tend to spread out but look stable .  
BTW : looks as if Mercury resonances to Earth at nearly 1:4 , as the screenshots were made every 90 days.
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Re: Jupiter, Earth's savior?
Reply #34 - 10/09/07 at 11:05:14
 
Thats what I got in my sim. I ran it longer and found that they spread and contracted over time. Mine was also the trailing L point but that shouldnt make any difference.
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Re: Jupiter, Earth's savior?
Reply #35 - 10/09/07 at 13:10:15
 
Wondering if also Saturn can hold Trojans ( according to literature there are no trojans discovered... ) I ran the sim herunder .  
Two times 50 asteroids were located in the L - point . The blue have a spread of1% the orange ones have a spread of 2% . The sim was run for 100 years . It's nice to see how the orange spread more than the blue over time .  
Trojan behaviour seems to be possible over this timescale , but I wonder why the asteroids drift so quick (maybe I didnt give the 2% inclinaton ) .  
Question to Tony : I positioned them to the M Value of Saturn +60 degrees . Was this correct ?
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Re: Jupiter, Earth's savior?
Reply #36 - 10/09/07 at 14:21:39
 
From the first pic it doesnt look like they are 60 degrees behind. They are drifting away from saturn moving towards 60 degs. I run a sim and pause when the planet of interest is either to the left or right of the sun (0 or 180 degs respectively) and then create with a man anomoly +/- 60 from 0 or 180.
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Re: Jupiter, Earth's savior?
Reply #37 - 10/09/07 at 20:06:44
 
Moving off topic for a sec, I was reading about Hill sphere's and Roche limits and came across something interesting. It was suggested that if a body had enough tensile strength to pass beyond the roche limit it would reach a point where objects not bound to the surface would be pulled off by the gravity of the larger body. By considering the gravitational forces I came up with a formula to calculate the SMA of the orbit at which the 2 gravitational forces where equal. This assumes both bodies remain spherical and that the definition of SMA is from the centre of mass of each object.
Putting in the numbers I got a value of 17800km for the earth moon system which is a gap of 9300km from surface of earth to surface of moon!
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Re: Jupiter, Earth's savior?
Reply #38 - 10/10/07 at 04:27:26
 
Yes I noticed also that the 60░ offset wasn't visible on the screen , that's why I ask Tony if I did it right .  
Nevertheless : heres the same sim but run for 500 years in steps of 5 years .  
One can notice that some asteroids drift away.
Look whats happening to the end of the sim : the asteroids come close to Saturn and move back in a different orbit . Seems as a horseshoe path was created .  
I think I didn't get the L-point from the beginning as I took the actual value of the SMA of Saturn instead of the mean SMA.    
I think however Saturn is capable to sustain coorbitals , although none have been found till now.
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Re: Jupiter, Earth's savior?
Reply #39 - 10/10/07 at 11:08:56
 
I think you derived the equation to calculate the distance at which a body feels an equal but opposite attraction from 2 other bodies . This means that in this position the body doesn't feel any external force , so even a droplet of water (if not evaporating ) would remain a droplet .  
A body in this point remains here if both planets also remain at their position .
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« Last Edit: 10/10/07 at 13:58:37 by frankuitaalst »  
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Re: Jupiter, Earth's savior?
Reply #40 - 10/10/07 at 13:22:56
 
Yeah to calculate the point the equation is based on the exact balance of forces and yes exactly at the point there is no net force. I ought to have said anything inside the orbit above or just to go all the way put a "less than" in the equation.
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The shortest distance between two points is a straight line, or is it?
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Re: Jupiter, Earth's savior?
Reply #41 - 11/12/07 at 11:31:49
 
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Re: Jupiter, Earth's savior?
Reply #42 - 11/13/07 at 21:26:22
 
Quote from Tony on 11/12/07 at 11:31:49:
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Huzzah! Good work, Tony! Smiley
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Re: Jupiter, Earth's savior?
Reply #43 - 01/04/08 at 11:47:13
 
By accident I discovered a nice animation about the Trojans orbiting Jupiter .  
Hereunder is a link to the picture.  
http://chemistry.unina.it/~alvitagl/solex/hiltro.gif
Jupiter must be the body on top of the picture , I guess in rotating frame .
The picture was generated with the Solex program .  
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