# Simple Orbital transfer and intercept equation

I'm working on a game which has a game board made up of objects orbiting the center of the board. You can think of it as our solar system, but greatly simplified in terms of physics. All objects have a mass and gravity of 1.0. Their orbital speeds are simply a linear function of their radius from the center (Sun).

The player has a base, which in terms of our solar system would be Earth. The player needs to send a spaceship to another planet in a different orbit. The spaceship has a constant acceleration (or deceleration), and unlimited fuel.

I need to figure out an equation to get this spaceship going towards one of the planets and intercept it. I've looked at some orbital mechanics web pages, but this is a little beyond my math skills and I think too complex for what I'm trying to achieve. Any help would be much appreciated.

NOTE: If this is better suited for SE.Mathmatica, please feel free to move.

• How realistic do these transfers need to be? Will a plausible-looking arc suffice, or do we need to accurately handle moving gravity wells etc? – DMGregory Dec 12 '19 at 22:58
• Just a plausible arc will do. No gravity wells, swing-bys, etc. – bazcat Dec 12 '19 at 23:50
• Just to make it clear, you realize that you cant plot an orbital transfer at any time to any planet you choose, right? For example your target may be behind the sun when you want reacht its orbit. – PSquall Dec 13 '19 at 10:15