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(Jon sez:)

Your Writer: Jon Kilgannon I promised a small lesson on the difficulties of arranging for spaceships to meet across planetary distances, and here it is. Please thank William Hess, David Ralston, Nathaniel K, Jamin, Grey Wolf, Amanda Babcock, Heidi Petersen, Ben Loukota, and Ian Auger-Juul for emailing and encouraging me to post this. All of these people have cooler names than I, although some are pseudonyms. (Then again, it is an open secret that "Mark Sachs" is a pseudonym for either Adam Warren or Hayao Miyazaki, so it's all cool.)

First, think about the scale of the Solar System. (As Douglas Adams wrote, "Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is.") The orbit of Pluto is a little less than a light-day across its diameter. Traveling at a blazingly fast (by our twenty-first century standards) velocity of 1/1000th of light-speed, a ship would require about three years to cross the Solar System. And this doesn't include the time required to accelerate to that velocity, nor the time required to stop again at the end of your trip.

Second, realize that the planets are moving. In fact, because the orbits of the planets are ellipses rather than circles the planets are constantly accelerating and decelerating in their orbits, their speeds changing over the course of a local planetary year, a concept which is called Kepler's Second Law. More important than speed (which is a scalar - in this case a measure of velocity without a direction) is the planet's velocity vector, which we can think of as its speed in a direction. The planet's velocity vector changes at all times as the world circles the Sun.

So. We have large distances, so large that light takes noticeable time to span them. And we have the planets, moving targets which are relatively small within this huge volume of space. Into this we drop our two spacecraft, which we hope to make meet up as they pass by a planet.

Suppose our first ship, whose name we shall pull out of a hat and call Enterprise, is at Jupiter a few weeks after perihelion (the moment when Jupiter is closest to the Sun). It leaves Jovian orbit for Mars at noon on Thursday. And suppose our second ship, which we shall randomly name Millennium Falcon, leaves Jovian orbit for Mars at noon on Friday. Only 24 hours have passed between the departure of Enterprise and the departure of Millennium Falcon, yet Jupiter has moved more than a million kilometers along its orbit in that short time. Because Jupiter is leaving perihelion, the planet's orbital speed has decreased over that 24 hours due to Kepler's Second Law. So Enterprise left Jupiter with a little more speed than did Millennium Falcon, and Enterprise also has a day's lead time.

Mars is also moving in its orbit. And, since it's closer to the Sun than is Jupiter, Mars is moving even faster than Jupiter. Also, because the planets don't orbit in neat little rows, Mars is almost certainly in some part of its orbit far around the Sun from Jupiter. So Mars will be zipping along in its orbit and Enterprise needs to calculate an orbit from Jupiter which will intercept Mars, as does Millennium Falcon. And Enterprise still has that lead and that initial speed advantage.

No problem, you're probably thinking. Millennium Falcon can just push down the GO button on the engines a little harder, pour on the antimatter, and catch up to Enterprise, right?

If we have a prodigious amount of energy to waste, the Millennium Falcon can indeed pile on the thrust and arrive at Mars whenever its captain wishes within reason. However, in the real world, we don't have huge amounts of energy on our spacecraft. A spacecraft has to haul its fuel (unless you're using a solar sail or other such oddball propulsion method), and in order to haul fuel you have to expend more fuel to move the fuel...and you need to burn fuel to haul the fuel which hauls the fuel... It all devolves into some really annoying calculus equations which spacecraft engineers learn to hate and which are a big part of the reason we use multistage rockets.

In order to save on fuel, we can use Walter Hohmann's clever Hohmann transfer orbit, in which our ship spends most of its time in an unpowered orbit between our launch planet and our target planet. The Hohmann trajectory has a couple of major shortcomings, however: it takes a very long time to travel this way, and the transfer orbit can only be used within certain rather thin launch windows. Most damningly, from our point of view, if two spacecraft leave on Hohmann transfer orbits 24 hours apart, they will arrive at their destination at least several hours apart - and then will whip by their destination planet without ever meeting.

You can, in fact, get two spaceships which leave on Hohmann orbits a day apart to arrive at their target planet at the same moment, but it requires a perfect alignment of planetary positions and velocities which I am not certain will ever exist between Jupiter and Mars. Also, that perfect alignment would only happen very, very rarely and would happen on a date and at a time which we cannot control, only predict. If you feel like crunching the numbers to find out the answer to this, I'd be interested in hearing the solution.

I'd write even more, but I promised this would be a short column on orbital mechanics, and I can already see some of you falling asleep at your keyboards.

Hey! Wake up!

(Mark sez:)

Your Artist: Mark Sachs Benjamin and Caprice are carelessly throwing around the term "perversion attack" to refer to the network subversion of the other five spaceships' computer systems. This term was of course invented by Vernor Vinge in his novel A Fire upon the Deep to refer to all manner of harmful and overbearing computer programs, such as the Code Red virus or ICQ 2000, that deliberately take over systems and force them to do their author's bidding.

On another topic, the ominous arrival of the Solar Navy destroyer Gorbachev from offstage left can mean only one thing...


A Miracle of Science: promises made, promises kept.