## Thursday, March 18, 2010

### Rocket Science and Orbital Mechanics

Having determined that I want the game to happen in and around the solar system, I've got to determine the contours of a board. The major features are pretty obvious; the planets. Let's take a look at some relevant data:

Mercury:
Semimajor axis (Mega km) 57.91 0.387
Sidereal orbit period (days) 87.969 0.241

Venus:
Semimajor axis (Mega km) 108.21 0.723
Sidereal orbit period (days) 224.701 0.615

Earth:
Semimajor axis (Mega km) 149.60
Sidereal orbit period (days) 365.256

Mars:
Semimajor axis (Mega km) 227.92 1.524
Sidereal orbit period (days) 686.980 1.881

Jupiter:
Semimajor axis (Mega km) 778.57 5.204
Sidereal orbit period (days) 4,332.589 11.862

The second column indicates the ratio of that planet's stats to Earth's. The site also lists a number of Asteroids and so forth, which I'll deal with elsewhere.

So let's take a look at that. Mercury, being the closest to the sun, is about .4 AU out. Venus is about .7 AU out from the sun. That gives us a minimum spacing of .3 AU. Jupiter is 5.2 AU out. If Jupiter and Mars are on opposite ends of the sun then we've got a maximum distance of about 6.7 AU. Dividing by .3 we get about 22 spaces distance between planets. 22 spaces isn't a terrible distance; I'm pretty sure I've run RISK rampages that last longer than that.

If you'll notice, the above paragraph assumes the planets might be in different positions around the sun. I've been wanting to build a game where the planets actually rotate ever since I first saw the mechanic in Buck Rodgers: the Board Game (check your local thrift store. Every turn you'd advance your planets one space around the sun, and since the different planets moved around different orbits the relative distance between them would change. When you're plotting the movement of pieces from one world to the next then the varying distances make the calculations more interesting.

On the other hand, I really don't know that I want to do it entirely that way. I mean, I still want the planets to orbit, but I'm wondering if I can't figure out a better way for spaceships to move in space. Y'see, the thing is that motion in space isn't the same as it is on Earth, there's no such thing as a top speed (barring relativity). So what if the spaceships of the day are all torch ships? A Torch Ship is one that accelerates and decelerates all the way from one destination to another. The difference is that the speed builds up, and the ship going from Mars to Jupiter would get there a lot sooner than the ship going from Venus to Mercury and back 22 times. I haven't yet run the calculations to see if it's feasible to work it that way, but my gut says it'd be cooler if we did.

There's also the possibilities of Hohmann Transfers. Named after the guy who figured it out, it's the minimum energy required to go from one orbiting body to another. You accelerate exactly once at takeoff, and decelerate exactly once at your destination, and you sit in space and wait for the rest of the time. Trouble is, it takes on the order of years to get from Earth to Mars in a proper Hohmann transfer, and you can only leave Earth (or Mars) every so often. It'd be cool to do things that way, but I don't want to get into that sort of time scale.

You'll also note that the table has orbit periods. (I wish I could say I remembered the precise definition of Sidereal.) That should allow me to calculate the distances a planet moves along it's orbit every turn. For example, if the minimum space was .3 AU as I figured above, and Earth moves at 1 orbit per year, then Earth will have about 20 spaces to move around it's orbit. (Recall from Geometry that the circumference is two pi times the radius).

So how am I going to eventually work it? I don't know; I'm going to actually have to run the math before I make any decisions. I'll keep you posted