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Asteroids (Read 146768 times)
frankuitaalst
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Asteroids
03/28/07 at 13:19:12
 
Asteroids are something very interesting to simulate with GS , therefore this new topic .  
Hereunder a link to the asteroid 2004GU9.  
http://neo.jpl.nasa.gov/cgi-bin/db_shm?sstr=2004GU9&group=all
This one has an orbit which comes close to the earth . Special about it is the revolution period which seems to be 1.001 years . This means it must be strongly under influence of the earth . Its rather big . Diameter is estimated to be 170 - 380 m  
Running the sim I created an .xls file and represented the distance to earth and the evolution of the SMA as a function of time . Result hereunder ...
The SMA varies a lot and seems to have a cycle of about 70 years . The minima and maxima correspond to the closest approaches to earth . The closest approaches have a period of about 35 years .  
There must be a connection between the closest approaches cycles and the SMA .  
I just don't feel by intuition or by maths why the period of the SMA is just the double of the period of closest approaches ... Someone does ?
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Ast2004GU9.jpg
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Tony
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Re: Asteroids
Reply #1 - 03/28/07 at 20:03:16
 
Your intuition is right.  They are definately related to each other.
 
This asteroid has a facinating orbit.  Thanks for bringing it to our attention.  I've wondered if any asteroids could exist in such orbits.  I guess they can.  I just grabbed its data and simulated it.  Appearently, it is trapped in a quasi-orbit around Earth.  This is similar to 2004AA29, which is featured on the Simulations link:  http://www.orbitsimulator.com/gravity/articles/2002aa29.html .  But unlike 2004AA29, this asteroid spends a lot more time in the quasi state.
 
Because of 2004GU9's eccentricity, it traces an oval around its average position in the rotating frame.  And this oval encompases the oval traced by Earth in the rotating frame.  Earth's eccentricity is less, so it traces a smaller oval, as it doesn't venture as far from its average position.
 
This asteroid's semi-major axis is currently slightly greater than Earth's.  This means its period is slightly greater as well.  Orbit after orbit, the trailing edge of its oval approaches Earth.  Earth's gravity pulls it on it in a retrograde direction.  This causes its orbit to shrink a little.  As its semi-major axis decreases, its period decreases as well.  Eventually, its period exactly matches that of Earth's.  Earth's gravity continues to pull, lowering the asteroid's semi-major axis and period to less than Earth's.  This causes 2004GU9's oval to reverse direction in the rotating frame, as it is now travelling around the Sun faster than Earth.  It continues heading in this direction until the new trailing edge approaches Earth.  The opposite now happens.  Earth pulls it in a prograde direction, expanding its semi-major axis and its period until its period is once again greater than Earth's, causing it to once again reverse direction in the rotating frame.
 
Here's my simulation.  Rotating frame is turned on, and set to Earth's period.
http://orbitsimulator.com/gravity/simulations/2004GU9.gsim
 
Here's an animated GIF of~70 simulated years.

 
I re-made your graphs to seperate them, and expand them horizontally to zoom in a bit.  Keep in mind, the period of closest approach is not 35 years.  It is 1 year.  Every year, the asteroid makes a close approach to Earth.  But each year, the close approach distance varies, from a minimum to a maximum.  This is what has a 35 year period.  The zoomed-in graph makes this a little clearer.
 
This graph shows you the state of the system at various points on the graph.

 
I also Google'd it and found that Astronomy.com has a nice article on this asteroid:  http://www.astronomy.com/asy/default.aspx?c=a&id=2060
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frankuitaalst
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Re: Asteroids
Reply #2 - 03/29/07 at 08:37:54
 
Looking at the picture in the moving frame I thought , "waw we discovered earths second moon ".  Smiley
Quite an amazing orbit !  
Googling I found out that NASA already discovered this feature ..., but only 9 months ago ...
See the nice link http://science.nasa.gov/headlines/y2006/09jun_moonlets.htm .  
According to NASA it has been there for at least 500 years in this orbit .  
I'll try a high precision simulation run back in time and see what happened ....
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frankuitaalst
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Re: Asteroids
Reply #3 - 03/29/07 at 13:05:12
 
Nasa is right ...  
Asteroid 2004GU9 was in our neighbourhood for the past 500 years , but where was it before ??
I don't know ....yet  
Herunder the result of the simulation "at high definition" of the ast.  
The figure shows the SMA of the ast and the diastance to earth .as a function of time ( time in yrs)  
It is clear that about 500 years ago , something happened . The ast was not as closely bound to earth as it is now .  
The Dist to earth  goes up tu around 3.0 E11 m ie twice the SMA of earth .  
Does it originate from the asteroids belt and was it captured around  1500 AC ? Probably not , as the SMA changes , but stays close to the SMA of earth , meaning that the ast was more or less in the same orbit , but not "bound" to earth at it is now....  
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Past_of_2004GU9.jpg
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Tony
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Re: Asteroids
Reply #4 - 03/29/07 at 14:20:19
 
After escaping, it should be in a horseshoe orbit.  Examine it in the rotating frame and see.
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Re: Asteroids
Reply #5 - 03/30/07 at 01:21:03
 
Simulating forward, I find that it leaves its semi-quasi state in the year 2605.  And it does indeed enter a horseshoe orbit after escaping.
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frankuitaalst
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Re: Asteroids
Reply #6 - 03/30/07 at 08:38:25
 
Simulating forwards and backwards for in total about 4000 years it seems that the asteroid indeed comes from and goes to an horseshoe orbit . Right now it is almost at it closed binding with earth . The relationship to earth lasts for about 1000 years as can be seen in the picture herunder ...
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Ast_2004GU9.jpg
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frankuitaalst
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Re: Asteroids
Reply #7 - 03/31/07 at 02:54:07
 
Here's another interesting one ...2001GO2...
Data were taken from the nasa site hereunder .  
http://neo.jpl.nasa.gov/cgi-bin/db_shm?sstr=2001GO2&group=all
Simulating forwards and backwards from 01/02/2007 on shows that the asteroid is in an horseshoe-orbit around the earth , but will become bound to earth in about 200 years , staying for about 50 years and then going into horseshoe again . Remarkable is the fact that not so long ago it was bound to earth also , after having been in a horseshoe .  
There seems to be some pattern in it .  
I wonder what's causing this transition from horseshoe to bound orbit . Is it simple a question of earths gravity , or is it the interaction of venus , or mars or maybe the mighty jupiter ? I think jupiter is strongly involved as due to his enormous mass the force on the asteroid exceeds the forces of the  other planets ( not considering the grav filed of the sun ) .
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2001GO2jpg.jpg
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Tony
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Re: Asteroids
Reply #8 - 03/31/07 at 03:19:17
 
You can always delete Venus and Jupiter and try again  Wink  My guess is that they're not major influences.
 
But don't delete the Sun  Smiley.  Trust me, it's needed or Earth and the asteroid will depart ways forever.
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frankuitaalst
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Re: Asteroids
Reply #9 - 03/31/07 at 03:39:45
 
Quote from Tony on 03/31/07 at 03:19:17:
You can always delete Venus and Jupiter and try again  Wink  My guess is that they're not major influences.

But don't delete the Sun  Smiley.  Trust me, it's needed or Earth and the asteroid will depart ways forever.

Just guess whats running now on my computer ? Smiley
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frankuitaalst
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Re: Asteroids
Reply #10 - 03/31/07 at 08:22:19
 
You're right Tony , neither Jupiter nor Venus can declare the jumps between horseshoe orbit and  bound orbit ...
Herunder the screenhot .  
Blue represents the real SMA of the asteroid .  
The pink one is simulated forewards , but with Jupiter deleted from now on .  
The yellow one is simulated backwards with Venus deleted .  
Jupiter seems to have an influence on the orbit after a couple of hundred years , but does not influence the transition ...Question remains unsolved ....
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2001GOwithout.jpg
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frankuitaalst
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Re: Asteroids
Reply #11 - 03/31/07 at 10:21:46
 
2003YN107.... Asteroid , maybe the last one with interesting changing orbit ...
For reference Nasa has a nice site about it : http://science.nasa.gov/headlines/y2006/09jun_moonlets.htm
This small moonlet was for about 7 years our companion and left the orbit around earth last year . Since then it is in a horseshoe orbit . It will come back in about 60 years , but this time it won't stay ...
Herunder a screenshot of the simulation for 2000 years , zoomed into our lifetime .  
The rest of the simulation indicates that this asteroid is not bound closely to earth but prefers its horseshoe ...
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2003YN107jpg.jpg
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frankuitaalst
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Re: Asteroids
Reply #12 - 04/01/07 at 04:11:44
 
May Earth get a new Trojan ?  
Probably not , but it could haven been ... even not on first of april
 
Our sister planet Venus has a real Trojan , Asteroid 2002VE68 , discoverd recently (2002) . It's not really big , but has an unusual orbit which takes it close to the orbit of mercury and earth .  
Data can be taken from the site http://neo.jpl.nasa.gov/cgi-bin/db?name=2002+VE68 .  
Running a simulation with this data for about 2500 years the following screen shots were generated in excel :
Like other Trojans or Coorbitals the orbit seems not really stable ( see second image : variation of the SMA of the asteroid )  
The upper image makes clear that , although the asteroid is a Trojan of Venus , it spents some time closer to earth than to venus ! .  It even came inside the orbit of the moon !  
The SMA tends to increase with time . That should bring it closer to earth .
I wondered how big is the influence of earth on the asteroid .  
Just adding numerically (not vector)  the forces of earth and venus on the asteroid , and take the ratio Fearth/(Fvenus+Fearth), gives the yellow scattered line . It varies between 0.0.. and almost 1.  
This means that Earth really has a big influence on the asteroid .  
The moving average of this ratio ( red line ) makes clear that the ratio really can exceed 0.5 , meaning Earth has a stronger influence than venus .  
At the end of the sim it seems that 2002 VE68 has settled itself on a ratio slightly under 0.5 .  
The pictures may seem fluffy due to downscaling in order to get under the 250k limit .
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2002VE68jpg.jpg
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EDG
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Re: Asteroids
Reply #13 - 04/01/07 at 10:52:28
 
Do you guys have gravsim render farms or something? How the heck churning out these sims so quickly?!
 
I have to marvel at the structure of the graphs here too, so regular!
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Re: Asteroids
Reply #14 - 04/01/07 at 11:31:35
 
Some of us do, currently overhauling parts of my system to try to increase performance again.  I'm Really hoping to get one of the new Quad AMD systems  Wink Tongue Grinhoping Tony recompiles and converts to VB.net, and compiles a multi-processor version Smiley
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