Golden Anvil

Back at the end of January I mentioned that I was starting work on programming a new game called One Small Step. Well, at last I have some screen shots to show off. Those will be down at the bottom. It's actually taken a huge amount of work to get to this point, and I thought I share some of the details with you (hopefully without boring anyone too much). This might get a little long.

Some of the difficulty has been in determining the equations used to calculate the exact position of a body in orbit at a given point in time. I actually ended up purchasing two text books to help me deal with this issue (although I expect the books to help solve other problems for this and future programs as well).

The first book is Fundamentals of Astrodynamics by Bate, Mueller, and White. It's an introduction to a variety of issues in Astrodynamics. It covers a lot of theory on a variety of topics (even including an interesting chapter on ballistic missiles). I got this because while most of this information is on the internet, it's hard to find stuff that doesn't jump straight from the easy stuff right into the super advanced stuff. This keeps the information at a more consistent level, and while some of the math takes some effort to understand, it's still at least vaguely approachable (though it would be waaaay easier if I hadn't forgotten all my college math).

The second book is Astronomical Algorithms by Meeus. It's a book that covers the practical instead of the theoretical aspects of solving a variety of astronomy related problems. There's great stuff in here that covers everything from calendar conversions (for things like Jewish or Arabic calendars) to a huge variety of other issues related to finding and displaying astronomical entities. It's nice and easy to follow, although doesn't cover anything theory, which means you might have some trouble if you need to expand a situation to be more generic.

Some of the difficulty has been in drawing an exact ellipse. At first I was using the drawing routines from the programming library that I using for my user-interface. Then I discovered that the line for the orbit wasn't exactly on the planet when zoomed in sufficiently far. That led me to discover that they're using an approximation to draw circles and ellipses. It's actually a very good approximation with an error probably on the order of 0.0001%... Normally good enough, but not in my case. Well, getting the ellipse draw was tricky, and required lots and lots of frustrating trial and error, even after I found a good algorithm online.

The end result can be seen in the screenshots below:

Here you can see a shot of the entire system out to Pluto (yes, yes, Pluto isn't a planet). One feature of note here is that the inner solar system and all the various moons exist, but are hidden, since at this zoom level they're too close to the planetary body that they are in orbit around.

Another interesting feature is the button labeled "+7 Days". Every time you click that, time advances 7 days and everything gets updated fairly quickly. For a system containing about 300 bodies, it takes about a third to a half second. As I proceed with the game I'll need to find ways to be tricky and get better performance, but that's good enough for now.

For the shot above, you'll note that I turned off the labels, icons, and orbit paths for Asteroids and Comets. That's because there are 100 randomly generated asteroids in the belt between Mars and Jupiter, and 125 randomly generated asteroids and comets beyond the orbit of Nepture. If I hadn't turned those features off, the display would look a bit... messy.

For this shot I've zoomed in a little bit so that you can see the inner planets, and turned on the icons and orbits for the asteroids and comets.

This is a good time to mention the controls for changing your view. You can use the scroll bars to move the view around, and the one at the top of the window to zoom in and out on the current point in the center of the screen. Or, you can zoom with the mouse wheel and drag the view around by clicking and dragging the mouse. Each time it needs to draw the screen, it takes about 0.1 to 0.2 seconds (or less, depending on the size of the window). While not completely smooth, this is definitely sufficient, and fairly impressive given what's taking place. Again, I may be able to improve performance here in the future.

Finally, I've zoomed in somewhat on Jupiter and its moons. I wasn't able to zoom in enough to allow you to see all the moons, and in fact, the larger, more famous ones are in too close to the center to be visible. Trust me though, they're there.

This brings up another point... I entered in information on all the planets and most of their moons. Each orbit has effectively been rotated so that everything lies in the same plane (everything is 2D, not 3D). Other than that, all of bodies represented should be at the correct locations for the start of year 2000 (a common checkpoint for astronomical data). Orbit shapes should all be accurate. Now, for performance reasons (and because it doesn't matter that much for my purposes), I'm not modeling gravitational peturbations that occur due to the influence of other bodies in the system. That means that accuracy will definitely drift the further you get from the year 2000. Still, it should be sufficiently accurate. Oh, and yes, it did take a while to enter the information, particularly since some of it was not represented in a form that I could use, and I had to manually add together two different numbers in order to get the correct value that I needed.

You'll also notice in the picture that the background is green instead of black. What's happening is that I'm currently drawing a solid green circle around every body to represent the sphere of influence of that body. You can actually see a bit of black in the lower right corner. That's the edge of Jupiter's sphere of influence. Essentially, this is the area within which a body is more influenced by Jupiter's gravity than the sun. Essentially an object isn't going to have a stable orbit around Jupiter unless it's within Jupiter's sphere of influence. This information also gets used with a technique called patched conics for altering the orbit of a body when it passes near to another body. This gives a reasonably accurate means for having objects like comets get their orbit modified if they pass too near Jupiter or something. It's also used when plotting the course a spacecraft takes when traveling between orbits around two different bodies. I haven't yet implemented that stuff yet, but it's coming sometime in the (relatively) near future.

Well, that's probably enough for now. At least there were pretty pictures! Hopefully next time will see the introduction of a way to select and view information about objects, and the implementation of parabolic and hyperbolic orbits. Those types of orbits indicate a body which has reached and surpassed escape velocity of the body around which it orbits. This opens up the possibility of additional asteroids and comets, and... spaceships!

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