question on orbits and boosting

From: Darwin Teague (
Date: Sun Nov 23 2008 - 14:18:24 UTC

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    I was trying to explain to a friend why they boost the ISS.'s orbit and 
    discovered a flaw in my explanation. Here is the gist of it.
    The lower the orbit, the faster a sat has to go to counteract gravity.
    Even at 220 miles up, there is enough atmosphere to gradually slow the ISS. 
    Therefore it needs to boost itself into a higher orbit periodically.
    Am I right so far?
    If so, why does slowing it down make it go down and not up?
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