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Trying to Create A Barycentered Simulation (Read 2412 times)
RedStreak
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Trying to Create A Barycentered Simulation
02/09/08 at 15:39:05
 
Hi, I am trying out this gravity simulator in hopes it might figure out some orbital mechanics for me.
 
What I am trying to figure out is this: will a planet that is 0.61 Earth mass possessing a moon that is 0.094 Earth mass in a 205,000 km orbit have a barycenter, and is the barycenter below or beyond the planet's surface?  The diameter of planet is 11480 km and the moon is 4840 km for added info.  The 205,000 orbital distance would be a surface-to-surface measurement, so a center-to-center measured-orbit would be 213,160 km.
 
This simulation is difficult for a newcomer to figure out hence why I'm posting this question.
 
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guyy
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Re: Trying to Create A Barycentered Simulation
Reply #1 - 02/09/08 at 23:26:04
 
Hm...well, you could set this up in Gravity Simulator pretty easily, but unless I'm missing something (which I probably am Tongue), there isn't a very precise way to find the barycenter's position relative to a planet's surface.
 
But this is really just a center-of-mass problem in disguise, so it's pretty simple to calculate yourself (which might be better, since this sounds like a homework question Wink ) using COM = [(Planet mass)*(Planet position) + (Moon mass)*(Moon position)] / (Total mass of system). So in this case, putting the planet at the origin, the center of mass is [(0.61)*(0) + (0.094)*(213,160 km)] / (0.61 + 0.094) kilometers from the planet's center; if that's bigger than 11480, it's above the surface. (You can add the "Earth Mass" part if you want to, but it just cancels out, so the answer is the same.)
 
If you want to try to simulate that anyway, I should probably let someone who knows what they're doing explain it. Tongue
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Tony
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Re: Trying to Create A Barycentered Simulation
Reply #2 - 02/10/08 at 12:41:29
 
Guyy is right.   213160 * .094 / (.094+.61)=28462 > 11480.  So it's above the surface.  
 
To simulate this is easy:
File > New
Objects > Edit Objects
  Change the name from Object1 to Planet
  Change the mass to 0.61 Earth masses
  Change the diameter to 11480
  Press OK
Objects > Create Objects
  Name: Moon
  Mass: .094 Earth masses
  Size: 4840 km diameter, change +- value from 100 to 0
  Semi-Major Axis: 213160 km
  Leave all other values at their defaults
  Press Create
File > Save As...
  Give it a name
 
Use Screen Width to zoom in until the system fills your screen
On the Graphics Options interface, if the first button says "F", press it and it will change to "A".  This puts you in barycenter mode.
If you do not see the Graphics Options interface, press F8 or F9.
If you're using the Beta version, go to preference and set the graphics update to 100.
You can increase your time step to speed up the simulation.
Play around with Trails.  Press T to toggle between on and off.  With the trails on, you can see that the planet traces a circle around the barycenter.  Trails off is fun to watch too.
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RedStreak
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Re: Trying to Create A Barycentered Simulation
Reply #3 - 02/10/08 at 17:37:29
 
Quote from guyy on 02/09/08 at 23:26:04:
But this is really just a center-of-mass problem in disguise, so it's pretty simple to calculate yourself (which might be better, since this sounds like a homework question Wink ) using COM = [(Planet mass)*(Planet position) + (Moon mass)*(Moon position)] / (Total mass of system). So in this case, putting the planet at the origin, the center of mass is [(0.61)*(0) + (0.094)*(213,160 km)] / (0.61 + 0.094) kilometers from the planet's center; if that's bigger than 11480, it's above the surface. (You can add the "Earth Mass" part if you want to, but it just cancels out, so the answer is the same.)

 
So it would simplify to: [ 0 + 20,037.04 ] / [ 0.704 ] = 28,461.705 km (rounded to thousandth)
 
Assuming that I got that number correct, I would then subtract the radii of the Moon and Planet to get the planet's distance from the center of the system right? (11,480 / 2)+(4840 / 2) = 8160 km  so I presume 28,461.705 - 8160 = 20,301.705 km
 
So the system data would be, assuming all these calculations are correct:
 
surface-to-surface distance: 205,000 km
center-to-center distance: 213, 160 km
planet surface to barycenter: 20,301.705 km
moon surface to barycenter: 184,698.295 km
 
Only element I've neglected to add is orbital period, but I do have equations of that which I'll go over (only because I am unsure if I misplace a zero in the moon's mass before), but previously I got 13.204 Days for the orbital period.
 
Let me know if I got something incorrect in the barycenter/COM equations.  I had a feeling, when I realized the planet was only ~6.5 times heavier than its moon (compared to the Earth that's roughly 81 some-times heavier than our moon) that there was a solid chance it'd be a technical double-planet.
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RedStreak
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Re: Trying to Create A Barycentered Simulation
Reply #4 - 02/10/08 at 17:40:30
 
Quote from Tony on 02/10/08 at 12:41:29:
Guyy is right.   213160 * .094 / (.094+.61)=28462 > 11480.  So it's above the surface.

 
That's a relief I got the numbers right.  So is the barycenter 28,462 km or my 20,301.705 km from the planet's surface?
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Tony
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Re: Trying to Create A Barycentered Simulation
Reply #5 - 02/10/08 at 19:23:49
 
Quote from RedStreak on 02/10/08 at 17:40:30:
Quote from Tony on 02/10/08 at 12:41:29:
Guyy is right.   213160 * .094 / (.094+.61)=28462 > 11480.  So it's above the surface.


That's a relief I got the numbers right.  So is the barycenter 28,462 km or my 20,301.705 km from the planet's surface?

 
If your planet is 11480 km in diameter then the barycenter is 28462 km from the center, or 28462-11480/2 = 22722km from the surface.
 
Your period is 2*pi*sqr(sma3/(G*(Mplanet+Mmoon)))
On this page: http://www.orbitsimulator.com/formulas/ , the 3rd formula computes your period for you, complete with unit conversion.  I get 13.5 days.
 
There's no need to round off to the nearest thousandth.  With your inputs of 0.094 and 0.61, you've restricted your answer to 2 significant digits.  Instead of giving you 28462, I should have rounded my answer to 28000, since the 462 will be lost in the noise created by not knowing if 0.61 actually represents 0.605 or 0.615 or somewhere inbetween.  If you want to specify exactly 0.61, you'd put some zeros after it:  0.610000.
 
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