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    Basic Orbit Mechanics & Space Debris
    By Project Calliope | May 29th 2012 10:31 AM | 1 comment | Print | E-mail | Track Comments
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    Alex "Sandy" Antunes is the mastermind behind 'Project Calliope', a pico-satellite funded by Science 2.0 and being launched in 2011 by a mad scientist...

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    Today's primer: orbital mechanics, or how we have to manuever to catch debris.  There's a lot of debris in low earth orbit, ranging from paint chips and spare bolts to a heavy toolbox up through entirely dead satellites.  It's tracked, it's plentiful, it was even featured in Wall-E.  How is it a satellite in orbit runs into debris?
    NASA visualization of orbital debris
    Put simply, for a given orbit, everything moves at the same speed regardless of mass.  If you have the ISS, VelcroSat, and a cloud of debris in the exact same orbit, they'd all move at the same speed but never intercept each other.

    Also, if you speed up in an orbit, you also change your orbital path to a higher one (because your centripedal force outwards is greater so you're overcoming more of gravity's downward pull).  If you slow down in an orbit, you are giving in to gravity and your orbit decays.

    To make it weirder, the speed you need to have in an orbit is lower the higher up you are-- because again, you are fighting less gravity higher up, so you need a lower speed.

    How can this be-- first I say "if you slow down, you go down" then I say "if you are higher up, your orbital velocity is slower".  These seem contradictory, but they actually are two different problems.

    Each orbit is like a rigid track-- if you have a specific orbital radius, you have a fixed velocity for that orbit.  And the higher the 'track', the slower the velocity you need to stay there.  The track is a perfect balance of centripetal force and gravity.

    However, to TRANSFER to a different orbit, you have to jump up (or drop down)-- briefly.  You have to either give yourself a kick to jump higher, or let gravity briefly take over.  That extra kick up (extra energy) gets 'used up' in moving you higher.  Similarly, that loss of velocity (and thus loss of kinetic energy) lets gravity take over and drop you down.

    So you spend energy to move up to a higher orbit but, once you get there, the total kinetic energy you need to stay there is lower than before.

    What this means in terms of intercept manuevering is we cannot just fire a rocket to fly faster and hope to catch debris that's ahead-- because that would also change our orbit.  It also means, in general, we can't say we'll fly 'faster' than the stuff in our orbit and sweep stuff up.  Instead, any change in speed also changes our orbit's altitude and/or shape (eccentricity).

    Since we can't just be like a pool net, sweeping out an orbit, how do we intercept debris?  What makes this solvable is primarily that orbits aren't circular-- especially for debris.  The eccentric (squished circle) orbits therefore intersect in different ways, creating the debris problem.

    In an elliptical (not circular) orbit, you move faster when you're closer to the Earth, and slower when you're further out.  It's a stable orbit, but the speed varies.  Also,  how it's aligned to the Earth varies.

    Ergo, a debris-catcher can, via timing, work to intercept debris that is in a different orbit that has a brief overlap with the VelcroSat orbit.

    This is also why debris collisions occur-- items in orbits of different eccentricity and  orientation collide.

    Prof. Walters at Capitol College found an awesome movie about this, which I put up in at http://ghostlibrary.com/VelcroSat/

    Until next time,
    http://projectCalliope.com, ionosphere->music


    From the time of Sputnik:
       Twinkle twinkle satellite,
       Flying onwards through the night.
       Up above the world you spin,
       Like a council refuse bin.

    Seriously though, reading this makes me want to pop over to our library, and look again at the chapter on orbits in Analytical Mechanics by Grant R. Fowles.
    “Now children, for tonight’s homework I want you all to work out a solution to Kepler’s equation.”

    Robert H. Olley / Quondam Physics Department / University of Reading / England