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barycentre question (Read 2127 times)
EDG
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barycentre question
06/28/07 at 22:30:34
 
On the BAUT forum someone asked what the solar system would be like if Jupiter had been a star to start with. In the process of answering, I figured out that the barycentre of the Sol-Jupiter system (if Jupiter was 0.08 solar masses) would be 0.3855 AU from Sol - that happens to be at pretty much the same orbital distance as Mercury.  
 
Which got me wondering - what would happen to a planet that tried to orbit the same distance as the barycentre? In that scenario Sol could hold onto planets out to 2.12 AU so it's not impossible for there to be a planet orbiting Sol itself at a distance of 0.3855 AU. Or would EVERYTHING have to orbit the barycentre?
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Tony
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Re: barycentre question
Reply #1 - 06/28/07 at 23:07:10
 
Remember that Jupiter tugs Mercury about as hard as it tugs the Sun, cancelling out most of the effect.  A planet that tried to orbit the Sun in at the same distance as the barycenter of the Sun-Jupiter system would often find itself beneath the surface of the Sun.  If Jupiter had 10x mass... I'm not sure.
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Re: barycentre question
Reply #2 - 06/29/07 at 01:01:44
 
Is it something that can be simulated in gravity simulator? Can it handle barycentres yet?
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Re: barycentre question
Reply #3 - 06/29/07 at 11:12:35
 
Quote from Mal on 06/29/07 at 01:01:44:
Is it something that can be simulated in gravity simulator? Can it handle barycentres yet?

Gravity Simulator has always been able to handle barycenters.  They are a natural consequence of n-body simulations.  The default view is to lock an object to the middle of the screen, hiding the barycenter, but on the "Graphics Options" interface is a button "F" which turns into "A" if you press it, and back to "F" if you press it again.  It toggles you between Absolute (default) mode and Floating (barycenter) mode.
 
Check out the animations on these pages.  They're in .avi format, and some browsers have their security settings set to prohibit displaying .avi's so if you can't see them, you'll have to change your security settings to allow them:
http://www.orbitsimulator.com/gravity/articles/plutosystem.html
http://www.orbitsimulator.com/gravity/articles/barycenter.html
 
Here's an image I made of the path of the Sun around our solar system's barycenter.  This represents about 100 years.  To make this, I edited the Sun's size to 0 so it would trace a thin path.  Then I set it to floating mode and zoomed in.  Then I photoshopped a circle the size of the Sun into the image for comparison.  As you can see, the barycenter of the solar system is often beneath the surface of the Sun, but the Sun often ventures beyond the barycenter.  In any case, the barycenter of the solar system is never external to the solar corona.

 
To make an object orbit the Sun at the distance of the barycenter of a Sun / 10xJupiter system:
 
Create the system:  
 File > New
 Objects > Create Objects
 sma = 5 AU
 mass = 10 Jupiter masses
 Leave all other values at their default
 
Compute the barycenter:
 Mass of Sun = 1.989e30 kg, Mass of Jupiter = 1.8786e27 kg, Mass of 10xJupiter = 1.8786e28 kg
 d=Sun Jupiter distance = 5AU
 distance from Sun to barycenter = d-(d*Sun mass/(Sun mass + 10xJupitermass)) = 5AU - (5AU * 1.989e30/(1.989e30kg+1.8786e28kg)) = 0.4678 AU
 
Create test particle at this distance from the Sun:
 Objects > Create Objects
 sma = 0.4678 AU
 Leave all other values at their default
 
Choose floating mode by pressing the "F" button on the Graphics Options interface.
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