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Venus at 1 AU (Read 7640 times)
david
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Venus at 1 AU
09/14/07 at 16:56:31
 
Hi All. I am very green with this software and fairly green with astronomy in general. I have a question which motivated me to download the software... I'm sure my curious mind will have others.
 
What would happen if Venus was displaced and its new location was 1 AU from the sun exactly opposite the earth so that the earth and Venus were 2 AU apart and carving out the same or roughly the same 365 day orbit?
 
Would the presence of both planets in the same orbit cause their orbits to decay? Would one planet catch up to the other over time for any reason? If not indefinitley, how long would such a precarious arrangment last?
 
I tried to edit Venus to reflect this position but I have no idea what I am doing.
 
If anyone knows the answers or can design a simulation or help me to do so please msg back.
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Tony
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Re: Venus at 1 AU
Reply #1 - 09/14/07 at 17:38:29
 
Hi, David, Welcome to the forum  Smiley
The point you're describing is Earth's Lagrange 3 point.  It is not stable, so eventually this configuration will fall apart.  However, Earth's L4 and L5 points are stable.  I think there's a thread on this forum with an L4 and L5 simulation.  Regarding your L3 question, I made it for you so you can try:
 
http://orbitsimulator.com/gravity/simulations/venusL3.gsim
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david
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Re: Venus at 1 AU
Reply #2 - 09/14/07 at 23:41:01
 
I see what you mean.
 
Based on that and the other thread, are you saying they would have remained stable if they started out at 60 degrees from each other?
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frankuitaalst
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Re: Venus at 1 AU
Reply #3 - 09/15/07 at 00:42:55
 
The new venus should get into an horseshoe orbit after some time , moving towards earth , getting close and then moving away again ...This goes on and on.  
In the case of an initial offset of 60° the planet should stay there .  
 
Looking at the sim I wondered if it is possible to give Venus a slightly different speed or slightly different position so that it can be captured as a new moon , eventually also reducing its mass. Anybody has an idea ?  
( I tried to give Venus 0.5km/s and 1km/s extra speed in the x-axis , but this doesn't work . Venus comes very close but wasn't captured )
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david
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Re: Venus at 1 AU
Reply #4 - 09/15/07 at 12:10:53
 
Quote from Tony on 09/14/07 at 17:38:29:
Hi, David, Welcome to the forum  Smiley
The point you're describing is Earth's Lagrange 3 point.  It is not stable, so eventually this configuration will fall apart.  However, Earth's L4 and L5 points are stable.  I think there's a thread on this forum with an L4 and L5 simulation.  Regarding your L3 question, I made it for you so you can try:

http://orbitsimulator.com/gravity/simulations/venusL3.gsim

 
Thanks, this is exacly what I was looking for.
 
When I run this at high speed the moon breaks away from earth into its own orbit around the sun, then mercury is catapulted away within 2000 years. I tried to run a sim of the conventional solar system at high speed and Mercury and venus were catapulted away within 3000 years. Am I doing something wrong?
 
If Venus would be stable at 60 degrees from earth in the same orbit, why does it not stabilize when it gets to there?
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shellandtube
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Re: Venus at 1 AU
Reply #5 - 09/16/07 at 03:01:07
 
Quote from david on 09/15/07 at 12:10:53:

When I run this at high speed the moon breaks away from earth into its own orbit around the sun, then mercury is catapulted away within 2000 years. I tried to run a sim of the conventional solar system at high speed and Mercury and venus were catapulted away within 3000 years. Am I doing something wrong?

If Venus would be stable at 60 degrees from earth in the same orbit, why does it not stabilize when it gets to there?

 
David the larger the timestep you use the less accurate the simulation  cry
I think I am right in saying that the program approximates the curved orbits as straight lines the length of which are dependant on the timestep. Small timestep = more, shorter lines and greater accuracy.
Large timestep = less, longer lines and lower accuracy.
Eventually you will reach a limiting case where the accuray is reduced sufficiently to loose the orbit entirely.
The image below conists of a real curve in red and straight line approximations of it. The one that most accurately fits the curve has the most shorter lines. I hope this illustrates the point if i didnt explain it well.
And as for venus not stabilizing when it reaches 60 degs I think thats because it already has additional orbital energy by virtue of the fact that its catching ( or less if its receding) the earth. I think something could be captured into a L4/L5 point but the rate of migration to the point would have to be very low and possibly the ratio of the masses large (i.e trojan asteroids)
 
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The shortest distance between two points is a straight line, or is it?
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Tony
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Re: Venus at 1 AU
Reply #6 - 09/16/07 at 13:03:19
 
Quote from frankuitaalst on 09/15/07 at 00:42:55:
...The new venus should get into an horseshoe orbit after some time...
...Venus comes very close but wasn't captured )  

 
Running the simulation I posted, I get a tadpole orbit that later evolves into a horseshoe orbit.  And the eccentricities of both Earth and Venus grow.  That's probably periodic, and after a certain amount of time, they will reach maximum eccentricity, then their eccentricities will begin to shrink.  Venus never will get captured.
 
 
Quote from david on 09/15/07 at 12:10:53:


...When I run this at high speed the moon breaks away from earth into its own orbit around the sun, then mercury is catapulted away within 2000 years. I tried to run a sim of the conventional solar system at high speed and Mercury and venus were catapulted away within 3000 years. Am I doing something wrong?

You're using too large of a time step.  Shellandtube's explanation is a good one.  Don't go any faster than 4096.  If you want additional speed without degrading the accuracy, download the beta version. ( http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1176774875 )
and set the "Update Graphics Interval" to 500 in the Preferences menu.
 
Quote from david on 09/15/07 at 12:10:53:

If Venus would be stable at 60 degrees from earth in the same orbit, why does it not stabilize when it gets to there?

Nothing actually completely stabalizes at a L4 or L5 point.  Rather, the objects orbit the point in a tadpole orbit.  The slower the object's velocity relative to Earth while at this point, the smaller the orbit around the point.  But as an object passes through this point, there is no mechanism to slow it down, so it simply passes through, rather than stabalizing there.
 
Quote from shellandtube on 09/16/07 at 03:01:07:
...The image below conists of a real curve in red and straight line approximations of it.

Your explanation is good.  But if you think about it, your "real curve" is actually made from straight-line approximations as well since it is made from pixels.  In this case, the straight lines are so small as to deceive your eye into thinking that it is a smooth curve.  This is what Gravity Simulator does too.  That's why you don't see any hexagon-shaped orbits Smiley
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frankuitaalst
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Re: Venus at 1 AU
Reply #7 - 09/16/07 at 13:39:54
 
Heres a picture of the path of Venus in rotating frame ref to Earth with the Picard integrator .  
Earth is the little green line at the left above.  
Venus is here on his way back already . It needed about 130 years to closest approach .  
I don't understand fully why Venus makes such funny loops in its apprach .
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Tony
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Re: Venus at 1 AU
Reply #8 - 09/16/07 at 14:17:32
 
Quote from frankuitaalst on 09/16/07 at 13:39:54:
...I don't understand fully why Venus makes such funny loops in its apprach .

Those loops represent its eccentricity.  In the simulation I posted, Venus had no eccentricity in the beginning, so it approaches without doing the loops.  But after the simulation runs a bit, it gains eccentricity and begins making loops.
 
Keep in mind that Earth's period is also altered by the encounters, so locking Earth still in your rotating frame hides half the story.
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Tony
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Re: Venus at 1 AU
Reply #9 - 09/16/07 at 15:42:46
 
Here's a looped animation of 1 horseshoe cycle.  This was made 300,000 years after the start of the simulation, giving pleanty of time for Venus to develop eccentricity in its orbit.
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shellandtube
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Re: Venus at 1 AU
Reply #10 - 09/17/07 at 11:37:53
 
Quote from Tony on 09/16/07 at 13:03:19:
 But if you think about it, your "real curve" is actually made from straight-line approximations as well since it is made from pixels.  In this case, the straight lines are so small as to deceive your eye into thinking that it is a smooth curve.  This is what Gravity Simulator does too.  That's why you don't see any hexagon-shaped orbits Smiley

 
Yeah I did see but thought it was too much detail to go into. I didn't want to confuse the lad or myself for that matter  Tongue.
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The shortest distance between two points is a straight line, or is it?
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david
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Re: Venus at 1 AU
Reply #11 - 09/17/07 at 14:47:44
 
Thanks again for your helpful responses
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david
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Re: Venus at 1 AU
Reply #12 - 09/17/07 at 15:16:14
 
One last thing.  
Tony, could you make sim with Venus in L4 initial position and we can see if it stays there?
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Tony
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Re: Venus at 1 AU
Reply #13 - 09/17/07 at 17:23:36
 
This uses a rotating frame to keep Earth still.  It's easier that way to determine if Venus is also still relative to Earth.  To turn off the rotating frame, uncheck it in the View menu.
 
http://www.orbitsimulator.com/gravity/simulations/vL4.gsim
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shellandtube
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Re: Venus at 1 AU
Reply #14 - 09/17/07 at 23:05:03
 
Here is a sim of the Earth plus another body (0.25 Earth masses) set 60 degrees behind the Earth. The orbits are highly eccentric (e=0.8). Viewed in a rotating frame locked to the Earth and gives 2 kidney bean orbits 60 degrees apart.
A big thanks to Tony for putting it on the server for me   Smiley.
 
http://orbitsimulator.com/gravity/simulations/users/shellandtube/KidneyBean.gsim
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The shortest distance between two points is a straight line, or is it?
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