Gliese 876 dynamics

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ajtribick
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Gliese 876 dynamics

Post #1by ajtribick » 05.02.2010, 19:41

In our solar system the planetary orbits change relatively slowly with time. However in some extrasolar systems the evolution of the orbits is more rapid, particularly where orbital resonances are involved.

The first planetary system discovered around a red dwarf is an example of this latter category: Gliese 876 has two gas giants in a 2:1 resonance (periods of 30 and 60 days). Through the use of radial velocity and astrometric measurements it is possible to deduce the full 3D orientation of the orbits, a feat not possible for the vast majority of known exoplanetary systems. This add-on shows an example of the orbital evolution of the system over a 10 year period from 2002-2012. Outside this 10-year period, the representation returns to Keplerian ellipses. This was generated with a 4-body Runge-Kutta integration (star + 3 planets) with a timestep of 0.01 days.

One of the best ways of seeing what is going on is to go to the start of the integration and turn on Celestia's partial trajectories option and watch the system evolve.

(add-on removed: updated version coming soon!)

Paper reference:
Bean & Seifahrt (2009), Astronomy and Astrophysics 496, 249-257 "The architecture of the GJ 876 planetary system. Masses and orbital coplanarity for planets b and c".
Last edited by ajtribick on 30.07.2010, 19:48, edited 3 times in total.

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Cham M
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Re: Gliese 876 dynamics

Post #2by Cham » 06.02.2010, 04:35

...and here's a small CELX script to place the user directly in front of this exoplanets system (handy, since it's hard to remember to which star is associated this addon, out of several hundreds of exoplanets systems !) :

Code: Select all

-- Title: A visit to the Gliese 876 system...

   Gliese876 = celestia:find("Gliese 876")

   celestia:settimescale(1)
   celestia:select(Gliese876)
   Gliese876Date = celestia:utctotdb(2002, 8, 3, 11, 58, 48)
   celestia:settime(Gliese876Date)
   User = celestia:getobserver()
   User:gotodistance(Gliese876, 2E8, 4)
   wait(4)
   obs:gotolonglat(Gliese876, math.rad(-10), math.rad(40), 1.2E8, 4)  -- Coordinates to change...
   celestia:setrenderflags { markers = false, orbits = true }
   celestia:setlabelflags{ planets = true }
   celestia:print(" Insert some comments here !", 4)


However, I'm unable to place the observer exactly in front of the system's orbital plane.
Someone has an idea about the proper coordinates to use, so the script places the observer above the orbital plane ?

RA: 343.32°, DEC: -14.26° are the equatorial coordinates of Gliese 876...
"Well! I've often seen a cat without a grin", thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!"

Topic author
ajtribick
Posts: 1780
Joined: 11.08.2003
With us: 15 years 11 months
Location: Switzerland

Re: Gliese 876 dynamics

Post #3by ajtribick » 07.02.2010, 13:04

Well the system's angular momentum about the centre-of-mass is oriented along the vector (-0.704752, 0.232534, 0.670263) in skyplane coordinates. Provided I have figured out the transformation correctly, this corresponds to (-0.721822 0.215178 -0.657778) in ecliptic coordinates. So to go to a vantage point above the system in celx you could try

Code: Select all

--Title: travel to above the Gliese 876 invariable plane

gliese876 = celestia:find("Gliese 876")

-- get a 1 AU length vector... I love microlightyears!
systemNormal = celestia:newvector(-0.721822, 0.215178, -0.657778) * 15.81250741

-- now we need to swap -y and z for some reason...
targetPosition = celestia:newposition(systemNormal.x, systemNormal.z, -systemNormal.y)

eclipticFrame = celestia:newframe("ecliptic", gliese876)

-- this is probably not the most elegant way of travelling but I am not a celx guru
celestia:select(gliese876)
obs = celestia:getobserver()
obs:setframe(eclipticFrame)
obs:goto(targetPosition)
while obs:travelling() do
    wait()
end
obs:center(gliese876);

Topic author
ajtribick
Posts: 1780
Joined: 11.08.2003
With us: 15 years 11 months
Location: Switzerland

Re: Gliese 876 dynamics

Post #4by ajtribick » 30.07.2010, 19:49

I asked for this add-on to be removed from the Celestia Motherlode. A new version with the fourth planet and more care with regard to the orientation of the coordinate system is coming soon...

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John Van Vliet
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Re: Gliese 876 dynamics

Post #5by John Van Vliet » 30.07.2010, 22:20

--- edit ---


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