Barry Gershenfeld wrote:
>
> >From: "Matthew Mucker" <mmucker@AIRMAIL.NET>
> >> Actually, I think this is backwards.  I'm no expert, but after
> >> reading Gene Krantz' autobiography, I reacll that NASA had
> >> lots of problems with stuff like this until they realized
> >> that at a lower orbit, a body must revolve around the earch
> >> much faster to keep it in orbit.  Any experts out there who
> >> can clarify?
>
> >Object of mass m rotating around a gravitation field of strength 'mu'
> >so-called Earth:
> >Centigugal force = m * V * V / R                (V is velocity and R the
> >radius)
> >Weight = mu * m / ( R * R )
>  (snip)
> >Jeszs Gonzalo
>
> In english:  At a higher orbit you are traveling faster.  As in,
> if you were standing still and watched it go by.  (So-called,
> linear velocity).  But at the same time, it takes longer to
> complete an orbit, so it "goes around" slower (so-called,
> angular velocity).

Actually, higher circular orbits have a slower tangential velocity than
lower circular oribits.
Vcirc = sqrt(GM/r) where G is the gravitational constant, M is the mass
of the orbited body and r is the radius of the orbit.

Incidentally the mu referred to above is mu=GM, the gravtiational
paramenter for the body in question. In general the constant isn't
specifically tied to Earth, it can be computed for any mass.

AIAA (www.aiaa.org) has a very good book written by Chobotov on this
subject. If I had it with me I could give you the complete reference. I
think it was simply called "Orbital Mechanics".

> This is a favorite story of mine, because the best and brightest
> missed the point the first time.  Not that I knew anything, I
> read about it in the paper back then, and I hope I remember
> it right.
>
> On one of the early Gemini flights they did a rendezvous experiment.
> As I recall, a lot of the Gemini program was aimed towards working
> out all the particulars about rendezvous-and-docking for the
> subsequent Apollo (moon shot) program.  This flight predated
> the later docking with other capsules, adapters, Russian
> ships, etc.  What they did was to put lights on the booster
> stage which remained in orbit (or near-orbit) along with the
> flight capsule.  Early in the mission they practised the
> rendezvous maneuver with this booster.  It didn't work.
> Basically the complaint was "the more I tried to catch
> up with it, the farther away it got".  So they went home
> and did some head scratching, and presumably looked at
> those formulas again, and said, "Oh...now we get it".
>
> Essentially you slow down, drop to a lower orbit, which
> lets you swing ahead of the thing you want to catch up with.

Hill's equations weren't widely known at the time, and less widely
understood. Hence the initial problems.

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