Space Elevators

You certainly can change the eccentricity without changing the
energy. But you also change the eccentricity if you keep the
angular momentum fixed and change the energy, as when you exert
force upward at a point other than apogee or perigee. If you keep
both fixed, you're keeping the same shape orbit and just changing
other parameters like inclination.

It doesn't matter (at this level of analysis) whether you're doing
*much* work, as long as you're doing some work even in the idealized
case of no friction and so on. And if you're exerting more force
over the same distance when you reel in against the tides than what
you're having act on you when letting out horizontally, then you're
doing some work.

--- In spacesettlers@yahoogroups.com, Ian Woollard
wrote:
>
> On 08/02/06, Dan Wylie-Sears wrote:
> > Understanding that might be a good exercise for back-of-the-
envelope
> > bull-session discussion. (I haven't read Forward's description,
so
> > this is just me trying to understand it.) If you reel in when
the
> > tether is vertical near perigee, and reel out when the tether is
> > vertical neer apogee, you've worked against the tides when it's
hard
> > and had the tides assist you when they're weaker. You've done
work,
>
> Actually, I don't think you've done work. In principle changing the
> eccentricity (i.e. changing apogee and perigee) of an orbit takes
no
> energy. In practice there's friction in the mechanism; but IRC the
> energy in an orbit is independent of the eccentricity, only
depending
> on the angular momentum around the Earth (which hasn't changed);
and
> that means the net energy of the reeling and unreeling is zero.
>
> > so you've increased the energy of something; all the forces are
> > radial, both for the rotation and for the orbit, so no angular
> > momentum has changed.
>
> Yeah, exactly.
>
> Although, incidentally, after staring at it for ages several years
> ago, I think you can exchange orbital momentum with the rotation of
> the tether. In other words, you can make your tether spin around
and
> around and gain you/lose you a very small amount of extra altitude.
> But the effect is tiny, your tether would explode long before you
got
> anywhere useful using it (although throwing stuff off your tether
as