The following formulas are used to calculate the position of each planet. Certain assumptions are made and therefore the positions are only approximations.
First the mean anomoly is calculated:
,where M is the mean anomoly and Tp and longitude of perihelion are constants.
Then the heliocentric longitude is calculated:
,where v is the true anomoly. However, by assuming that eccentricity is 0 (the orbit of the planet is a perfect circle), the true anomoly becomes the mean anomoly (M).
So now, since the radius of the orbit of the planets is given, and we also have the heliocentric longitude, we can calculate the coordinate of the planet in the solar system using simple trigonometry:
X coordinate = orbital radius * cos(heliocentric longitude)
Y coordinate = orbital radius * sin(heliocentric longitude)
For more information and to find out how to get a better approximation please refer to the following book:
Practical astronomy with your calculator By Peter Duffett-Smith
This is a 3D solar system simulation application, which gives you the approximate location of the planets in the solar system at different time, and some information about each one of them. This application uses HTML5 and WebGL.