This page shows how a space elevator could exist off the equatorial plane.
It shows a string in equilibrium between 3 forces: gravitation, centrifugal
force and tension from the anchor point on the ground. Since creating this
page I have written a paper on the subject that has a lot more detail. You
can find the paper
{{[jump="../../publications/NonEquatorialUniformStressSpaceElevators.pdf"]here}},
or my slides from the third annual space elevator conference
{{[jump="../3rd-conference-notes/OffEquator-Talk.pdf"]here}}.
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In this figure, the green circle is the Earth, the red circle shows
geosynchronous altitude, the pink line is the equatorial plane, and the
blue curve is the space elevator. Please ignore the numbers on the graph, I
did not bother with the actual physical constants; however, the general
shape of the elevator is correct. Moreover, the string that I used here is
uniform, it does not get thicker when the tension increases. That would
also change the shape of a real elevator slightly. Just like an equatorial
elevator, this elevator could be shortened by using a counter-weight. In
that case, the shape of the elevator would change slightly, though.
As you can see, the elevator is entirely above the equatorial plane. The
y-axis component of gravitation tries to pull the whole elevator
towards the equator. The force excerted by the anchor point is the only
thing preventing the elevator from "falling" towards the equatorial plane.
The configuration that is shown is static. The elevator doesn't swing
around above and below the equatorial plane. Note that the center of gravity
of the elevator is not in geosynchronous orbit. There are two reasons why
this is not a problem. First, the earth is exerting a force on the
elevator, so the elevator is not an isolated object in orbit. Second, but
less important in this instance, the
elevator is not infinitesimal compared to the gravity field in which it is
orbiting. Therefore, it shouldn't be expected to exactly follow the simple
orbital rules that apply to point objects.
In my opinion, the main drawback with the off-center elevator is that there
is a huge tension on the anchor point. This means that the cable will
have to be heavier. Also, it means that a way has to be found to get the
anchor setup. When building an equatorial elevator, there is no need for
a force from the anchor point, so the elevator can simply be extended up
and down until it reaches the ground. The off-equator elevator needs a
force from the ground to stay off equator, so that strategy won't work. The
only idea I can think of is to make an equatorial elevator, and then move
the anchor point to the desired position.
I am not sure how hard pulling the elevator into place would be, because I
did not do the simulation with real numbers.
If you put a higher tension on the elevator from the anchor point, other
neat configurations are possible. For example, with just the right tension
from the anchor, a single strand can join two points that are at opposite
lattitudes.
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If the tension increases even further, the elevator crosses the equatorial
plane at a lower altitude, and then does some really strange things. Such
an elevator would have to be infinitely long to remain in place, so it is
just a concept.
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By cutting the elevator off at the equator and joining it
with another branch that comes from the opposite latitude, and connecting
that to an equatorial elevator, you get the forked elevators that are
described in science fiction (for example in Kim Stanely Robinson's Mars
trilogy). But since the tension at the ground is even greater than it would
have been with the simple off-equator elevator, I don't really get the
point.