I have been following the Dawn mission to asteroid Vesta with keen interest. The mission team is relying on simulation data because for various reasons accurate measurements of the probe's position are only available occasionally. The probe is expected to achieve orbital insertion around Vesta today, but without accurate data not available until tomorrow, we can only speculate on whether orbit has been achieved.
For hour-by-hour data, the team relies on the MYSTIC simulator. This gives vital data including Dawn's speed in relation to Vesta, and its range to the asteroid.
I'm no rocket scientist, but I do have basic skills in physics and maths, and a keen interest in space flight. A number of years ago, I worked out my own very basic system for understanding orbital mechanics, including the basic equations for simple orbits, from first principles. I used these, with the simulation data, to show that Dawn appeared to have achieved orbital insertion around Vesta earlier this morning.
I have discussed my calculations with others interested in this mission. It occurs to me that there may be other keen amateurs out there interested in understanding the basics of orbital mechanics. So it is my intention to publish a series of posts on the subject.
It won't be for everyone, by a long way. But if you have a good grasp of high school physics and maths, you should be able to follow along. My own maths ability reached its limit shortly after high school level, so I haven't included anything too demanding! It also won't satisfy real rocket scientists, who use levels of calculus way beyond me and can tell you all the fundamentals I've missed out. However, if my basic version is flawed rather than just simplistic, then I'd really like to be corrected so please do get in touch!
If you're interested, keep an eye out for my following posts which detail my Orbital Mechanics for Dummies...
By the way, the title is not intended to patronize. I consider myself to be a mathematical dummy, at least compared to the abilities of my peers when I was studying. My aim is to use my limited skills to understand how orbits work, and how to work out their parameters. There are plenty of more complete works on the subject, but this is intended to be an easy entry.