Orbital Elevator

ok, here is what i cant understand. where does the energy for the
change in momentum come from.

a spaceplane connects to the lower end. it does not have enough
momentum for orbit.

It then is pulled out (assuming by elevator) to the gateway end. It
is then released with a much higher momentum. It has to take the
momentum from the elevator. But where does the elevator get that
energy from.

--- In spacesettlers@yahoogroups.com, Matt Gallimore
wrote:
>
> Robert,
>
> It was something I read about some time ago. Looking over the
internet, it took a while to find some sites describing it. Because
it didn't seem a popular topic, I assumed there might be a big
technical problem with it.
>
> Anyway, here is one site that describes it better than I did:
>
> http://www.affordablespaceflight.com/howitworks.html
>
> Since the space elevator has many fans, it seems reasonable to
build something first. That would help with discovering some
unforeseen problems. It also would have the possibility of speeding
up the development of the s.e.