Can I accurately plot the orbits of our solar system's planets using equations?

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Equations exist to graph the orbits of the solar system's planets, allowing for the creation of a static model that simulates their positions over time. The user seeks a method to plot these planetary bodies on a grid based on a specific date and time, without delving into complex physics. The goal is to develop a program that calculates distances between any two orbital bodies, potentially for use in a game. A resource from the Jet Propulsion Laboratory provides approximations for planetary positions from 3000 BC to 3000 AD. Accurate plotting can facilitate educational models and simulations of the solar system.
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I have been searching the internet for the last few days with no luck, due probably to the improper phrasing of my searches, for what I think is a fairly straight forward set of answers.

Basic Question: "Are there equations to graph the orbits of our solar system's planetary bodies on to a graph?"

Expanded: Assuming a static model of our solar system (one in which simulated for millions of years outward would show no deviation in the orbits), Is the a set of equations to plot the stellar bodies onto a grid based on a date/time given for earth?

I would like to be able to create essentially a solar system model in a computer than is bothering with Newtonian physics or whether planet a will crash into planet b. Basically, I want to write a program (possibly later incorporate it into a game) that will give me a distance from any two orbital bodies given a date/time. This would be somewhat the equivalent to solar system models made for elementary science fairs.
 
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