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I recently made an n-body simulation and thought it would be interesting to try and model it on the interior of our solar system (Sun to Mars), but I cannot find initial conditions for such an undertaking. My biggest problem seems to be that I'm not working with a spherical coordinate system and instead have opted to using the 3D Cartesian system. Does anyone know of any data that gives initial positions and velocities of the Solar System's planets and their moons in 3D Cartesian coordinates, so I can plug this into a system of differential equations as initial conditions?

J. M.'s missing motivation
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InquisitiveInquirer
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  • FWIW, AstronomicalData[] has a nice bounty of information, including orbit paths and eccentricities. See e.g. this question. On the other hand, there's a certain appeal in using numerical integration instead of merely taking coordinates from an ephemeris... – J. M.'s missing motivation May 20 '13 at 19:25
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    Just in case you are interested in accuracy, it might be worth noting that the system of ODEs described in your previous question at http://mathematica.stackexchange.com/questions/25039/3d-orbits-and-inaccuracy-over-time is not what is usually meant by an "n-body simulation," because it does not account for interactions among the bodies: it's just a collection of independent central field solutions. It might be a fine approximation for times close to the initial time but will be observably incorrect. – whuber May 20 '13 at 19:36
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    @J.M.: Yeah, there's something very satisfying about using a system of ODEs to calculate each planet's path, so I'd love to have initial conditions to work with and see how the system evolves :) – InquisitiveInquirer May 20 '13 at 20:08
  • @whuber: Since that post I've changed the system to account for interactions between each body. If you're interested I can copy the code for you, but I must warn you, it won't be pretty haha. – InquisitiveInquirer May 20 '13 at 20:08
  • @SjoerdC.deVries: No that's the same thread that J.M. linked us to previously which doesn't use Newton's Law of Universal Gravitation but instead seems to use Kepler's equations and Mathematica's AstronimcalData – InquisitiveInquirer May 20 '13 at 21:41
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    You were asking for positions and velocities. These can be found using AstronomicalData as demonstrated in that question. – Sjoerd C. de Vries May 20 '13 at 21:44
  • @Sjoerd, not a dupe, I'd say. OP wants to generate positions/velocities at other times by integrating the equations of motion starting from positions/velocities at a certain instant (something like what the JPL does for their ephemerides). – J. M.'s missing motivation May 20 '13 at 23:35
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    Since your question got closed... if you're interested in seeing how JPL does it, you might want to see this. – J. M.'s missing motivation May 21 '13 at 07:44
  • @J.M. I wouldn't object the reopening of the question at all, but I still read the question differently than you seem to do. Does anyone know of any data that gives initial positions and velocities of the Solar System's planets and their moons in 3D Cartesian coordinates is nothing other than about getting said data (a Q which is answered) and is not about integrating motion equations. Where in this question do you read more than this? – Sjoerd C. de Vries May 21 '13 at 16:57
  • @Sjoerd, hmm, on second glance, you're right. – J. M.'s missing motivation May 22 '13 at 00:45
  • Yeah, luckily I have the equations set up and just need correct initial conditions. Thanks guys, I'll take a look at the AstronomicalData and see what I can find. – InquisitiveInquirer May 22 '13 at 06:17
  • I had a look at AstronomicalData and there does not seem to be any property for velocity, only speed. Luckily it gives heliocentric (x,y,z) positions which gives me half of what I need, but I cannot find any (x,y,z) heliocentric velocities. – InquisitiveInquirer May 23 '13 at 22:01

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