Yes, I’ll do this based on the ones people talk about most in my experience. If you want to make your own solar systems, play around with it, do things like adding so much hydrogen to a planet that it turns into a star. Universe Sandbox is the one that you hear most about.
There’s an older version which has a simulation of our solar system without any moons and which you can use for free, it’s just a gravity simulator.
The new version lets you do much more, for instance simulate colliding planets and moons, add water to a planet to create oceans, etc. Here is someone trying it out
Here is someone just having fun with the presets that come with the program - you can for instance collide two Earth’s together, you can keep adding hydrogen to our Earth until it turns into a sun, and so on.
They have a long list of other apps in their FAQ, where you can also read about the approximations they use for their simulation (e.g. they use Newtonian gravity instead of General Relativity - because otherwise it would need a super computer, in our solar system this would only make a noticeable slight difference to the orbital period of Mercury.).
Then there’s Celestia, which is free and open source, often used by astronomers, let’s you explore our solar system and galaxy and add many pre-defined new objects created by users, including spacecraft, stars, planets.
There’s NASA Eyes which is updated with new discoveries as they are made, i s great if you want the orbits of some of the newest objects in our solar system. Explore Pluto’s system of moons for instance. Also to simulate spacecraft missions in detail. Lots of presets. The preview here shows a simulation of the landing of Curiosity on Mars.
Next there’s “Space Engine” which includes large databases of galaxies, stars, planets and minor planets. But it also has numerous procedurally generated stars and planets too. Right out to the edge of the observable universe.
Space Engine - the universe simulator
If you are interested in spacecraft then the Orbiter simulation is rather amazing. This whole video is a simulation, not the real thing, and you can navigate to look at it from all angles when you use the program:
It’s rather geeky because it is so exactly simulated, also interface can be a bit clunky, though with some preset scenarios you can just run. It’s much easier to control with a joystick than with a mouse, so it’s well worth getting a joystick for it, if you don’t have one. Orbiter - Download
For many more apps see the FAQ for Universe Sandbox
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