The planetary motion equations are written in the ellipse equation format, i.e. $$x^2/a + y^2/b = 1.$$
Can anyone please tell me where I can find the list of all the planetary motion equations, (Mercury, Venus, Mars, Earth, and so on) in the form of $$(x(t)-c)^2/a + (y(t)-d)^2/b = 1~?$$ (Both $x$ and $y$ are functions of $t$.)
Best Answer
Orbits are pretty complicated. Most texts on this deal in terms of predicting positions at a specific time rather than just a simple ellipse, because that model while correct is too basic. As others mentioned position estimation makes it more complex because there are more parameters involved. I'll just pull some stuff for you on the basics. For standard Keplerian orbits you'll need the orbital elements:
This image is Earth-centric like for a satellite, but it illustrates the basics.
Here is an overview and data from JPL good to 2050ad:
The method is a bit long to duplicate here. So I'll link to JPL's illustration on how to compute the planet's position based on the date and the orbital elements.
And for more reading about orbits you might like this article.