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I was thinking of making a simple 2D model of the solar system, with planets moving along ellipses like

$$x(t) = k_x \sin(t + k_t) (\sin(k_\phi) + \cos(k_\phi))$$

$$y(t) = k_y \cos(t + k_t) (cos(k_\phi) - \sin(k_\phi))$$

and, for earth at least, a angle that some longitude (say the Greenwich Meridian) is facing in the $xy$ plane:

$$d(t) = k_dt+k_e$$

or something equally minimal.

Two questions:

  • Where can I find the appropriate constants in the most cut-and-paste-able form?
  • How long will this kind of model be accurate for? (If I want to use it to vaguely look in the right part of the sky for a particular planet)
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Search for the word "planetarium". There exist computer models as well as real world analogues. You have to realize that when more than two bodies are involved in a gravitational solution it is only numerical approximations that can work, for a while. For the solar system I do not think your model will be true for long. You would be better served to use a free planetarium on the web. –  anna v Mar 9 '12 at 15:55
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Well that's no fun ;) –  Lucas Mar 9 '12 at 17:00
    
Your ellipses have the sun at the center, and not at the foci. You should at least use equations that put the sun at a focus of the ellipse and get the angular velocity correct. –  Peter Shor Mar 9 '12 at 22:40
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