Yesterday evening a good friend of mine*, who happens to run probably the single best astrogation/3D star mapping site on the Internet, sent me email asking for help with a problem. It seems that he's working with a game designer to develop an updated version of "Rocket Flight," one of the most astoundingly accurate games of space travel and trade in the Solar System that I've ever seen. Since the game is still in beta, I can't talk much about it (in fact, I don't know much the new version). As part of the game, my friend was asked to figure out the time of flight between any two planets for any given orbit. As he put it, "I'm not a scientist, I just play one on the Internet," so he came to me for help.
Now, it's been about fifteen years since I was an orbital mechanics engineer for NASA. I worked mostly on the shuttle program, but also worked on the navigation and pointing software for some of the "Great Observatory" orbiting telescopes. But it's been a loooong time since I've sat down and tried to do a problem like this. I'm pretty pleased that it all came back to me fairly readily. At the end of the day, I had come up with a formulation of the problem that would let you input any one of the following and get out the rest: time of flight, delta-v (energy change) needed for the departure and arrival burns, the intercept point with the destination planet, or the shape of the orbit itself. Pretty darn cool, if I do say so myself. The equations that I ended up with are fairly easy to use -- certainly no problem for a spreadsheet or computer program.
I'll be able to make good use of this with my current story, since it involves hauling ore from Mercury to Mars and back. It's important that I be able to figure out the travel time for different fuel burns and ore loads, since this details are discussed by the characters. In particular, the protagonist is going to go from a mid-teen to a late teen/young adult over the course of the voyage, so I need to make sure the trip takes enough time for that to happen. This is just one example of how knowing science is important to writing science fiction. Even if you don't have the background yourself, odds are you know someone who does!
*Interestingly, he and I have never met face-to-face, yet I I've known him for years and consider him to be a great friend. And who says the Internet will make everyone anti-social?
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