# Universe Sandbox

Did you speed the simulation up? As you make it go faster and faster, the simulation breaks down and the inner planets tend to leave the solar system. Currently, I’ve got the solar system running along at the default speed (time step = one day) and things are fine in 2055.

Yes, I sped it up to some insane speed just to see what would happen to our solar system. Any idea why faster speeds means way less accuracy?

What the simulation does is solve a bunch of ordinary differential equations using numerical methods. In effect, the simulation calculates the movement of the bodies in discrete time steps, basically moving each body in a straight line for each time step. These straight lines are only an approximation, so a bit of error accumulates during each step. When the time steps are short compared to the speed of the object, the errors are very small. As you increase the time step (speed things up), this approximation become less accurate because you’re moving the body much farther in a straight line before the next time step (larger error). So the faster you go, the larger the error, causing the faster moving planets to start wildly diverging from their orbits and slingshotting out of the solar system.

You can see this if you pay close attention to the trails as you speed things up. At relatively slow speeds, the trails appear to curve smoothly. The faster you go, the trails become more obviously made up of lots of straight lines. At a certain point, you can make the orbits look like polygons (I think I had the moon orbiting the earth in a square) before things fall apart.

I hope this makes sense.

Tiohn has it, but it’s also the first question on the Universe Sandbox FAQ:

Why does Mercury get thrown out of the Solar System when I turn up the time step?

As you turn up the time step you lower the accuracy of the simulation. If the accuracy is too low bodies will get thrown out of the system.

The numbers: Mercury takes about 88 days to make a single orbit around the sun. A time step of 22 days would only be calculating a new position for Mercury 4 times in that period. This isn’t enough accuracy to maintain a stable orbit. The Earth is further out and takes 365 days to orbit the sun. This same time step of 22 days results in about 16 position calculations for the Earth which is enough to maintain an orbit.

``-Tom``

Damn it. I knew that was somewhere and looked everywhere except the faq.

I also made this picture to illustrate:

Awesome… I was under the assumption that Betelgeuze was about as big as they get, but seeing the Cephei stars is just… wow.

Thanks, Tom. Obviously I need to learn how to read.

Seriously. Mind boggling. Our universe is so damn huge.

Doesn’t “huge” imply that it has a beginning and an end?

Anyway, this game finally made the big time, took 2yrs but it’s now on the Steam. I heard them talking about it on the Bombcast, sounds fascinating!

I’m loving it but they’re missing the key scenario, a working model of the solar system including moons, comets, asteroid fields, and space probes. They have scenarios piece meal with these elements but not one system.

My last sandbox I managed to get a star moving at 450km/s which had an extremely elongated asteroid field that would could and slide by just on the leading edge of the star. The planets including Jupiter and Saturn did the same thing, though they had long ago lost their moons and rings.

I highly recommend the powers of 10 scenario.

Edit: I highly recommend a look in the forums, more than a few tools and methods are discussed there that I never really knew about.

Sequel early access launch: http://store.steampowered.com/app/230290/

I hate to necro things but I picked this up on sale, partly because of a course I am teaching in the fall and partly because I like space toys like this. I have to say, it’s pretty darn slick.