Not the best quality video, but a good explanation of the slingshot effect. Incidentally, Bad astronomer has a blog that's worth reading: http://blogs.discovermagazine.com/badastronomy/
In this lesson, we see why the emphasis on apoapsis and periapsis was so important last lesson, as they are used in Hohmann transfers orbits. Incidentally, Hohmann transfer orbits are used for getting satellites into proper orbits, too.
Something I hadn't realized was that our opportunity to launch to Mars (with the greatest efficiency) comes only once every 25 months. Our next opportunity is March 2014. I've got to say, I'm not hopeful we can make it. unless we use a different launch system, like ion drive--but I'm not sure that's going to be ready by 2014, either. However, here's an interesting look at how it might have worked, based on a 1966 study. http://www.wired.com/wiredscience/2012/04/ernsts-ions-week-concludes-nerva-ion-mars-mission-1966/
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