Would a space elevator necessarily need to be situated on the equator?

Question

The simplest kind of space elevator would be a large mass somewhat beyond geosynchronous orbit tethered to earths surface such that the tether is always under tension from centrifugal force overpowering gravity, but I feel like the equator would be a problematic place to put it because of satellites and space debris. Is there any reason a space elevator can’t be put at high latitudes while still extending away from the axis of rotation?

Answer 1

The center of mass of your space elevator is going to need to be in the geostationary orbit, no matter where you put the base anchor. As a result, while you can put the foot elsewhere other than the equator, at least at that center-of-mass point, it will be over the equator.

Well, technically, a bit higher than that; the whole point of a Space Elevator is using the tension of having the center of mass above the synchronous orbit to pull up the rest of the structure below it. Either way, though, it's going to have to pass through the equator... because all orbits pass through the equator. And if your space elevator doesn't have a point on it that traces out an ordinary Keplerian orbit where you can put your docking station, warehouses, and so on at (which is typically that geostationary orbit), you've decided not to use the primary utility of building one in the the first place.

And if you're building a space elevator, you're committing to doing something about satellites and debris in orbit around your planet, regardless of where the foot is, so unless there are political, geographical, or logistic reasons preventing you from putting the base on the equator, might as well put it there so you don't have to make it longer than you need to.

Answer 2

The easy answer is "no, it's just a lot simpler and cheaper"

The Earth is spinning and you're taking advantage of that spin to create your elevator. On the equator, the forces along the shaft of the elevator (ignoring things like climate) are perpendicular to the surface of the Earth. When you're lifting, you can take advantage of the maximum centripital force to minimize energy costs. When descending, you can take advantage of maximum gravity force.

At the poles you have a little less efficiency, but still some advantages. The elevator is still perpendicular to the surface of the planet, but you no longer have the advantage of centripital force when you lift the car. We'll ignore the twist to the story due to the rotation of the planet — it's not that big a problem.

But if you put that elevator anywhere else, benefits decrease and problems increase pretty quickly.

let's anchor that sucker on the Tropic of Capricorn

Let's assume that Australia gets its knickers in a twist and decides to throw the proverbial bird at the whole world and build its own elevator — smack dab on the Tropic of Capricorn. Now what happens?

The elevator won't be perpendicular to the surface of the planet because the planet's surface is curved and the force wants to push the elevator straight-out from the axis of spin. That makes it, what, lean more-or-less 45°? This puts uneven stresses on the elevator, exacerbates climate effects, and basically throws half of the benefit of gravity out the window. (You still get centripital force, though!)

But what does all that translate to?

Cost!

In the fight between physics and economics, economics wins more often than you might think

When the Obama Administration pulled the trigger and disallowed manufacture of 60, 75, and 100 watt incandescent bulbs, it caused people to howl! Was it the right choice? From the perspective of forcing people off of the addiction to energy-hogging incandescent light bulbs and forcing them to use energy-efficient LEDs, yes. But from the perspective of forcing people to stop using cheap 50¢ light bulbs in favor of, at that time, still very expensive (\$20-\$50) LED bulbs, no! People on fixed incomes were unimpressed with the argument that LEDs would last longer. They couldn't live without light waiting to save up to buy one.

Cost is a big deal, and the cost of building and maintaining a space elevator at the equator is as cheap as it gets. It doesn't hurt that in many ways the climate effects are also minimized. But build that darn thing anywhere else, and you must be prepared to pay for it.

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Edit

A number of commenters have suggested that centripital force can be ignored. Well... kinda. There's a tether between the top of the elevator and the base. It's not enough to simply get the top of the elevator moving in a valid orbit — you need to keep it there with the drag of that tether due to everything from bad weather conditions to centripital force. Yes, you could use thrusters to do that... at a cost.

Every dollar spent to keep the elevator operating away from the equator is a dollar that didn't need to be spent.

Answer 3

As noted in other answers, while the center of mass of the tether (the core of the space elevator) must be geostationary (hence, above the equator), the anchor point at the surface need not be -- but there's a limitation on how far from the equator it can be: the excess strength of the tether material.

Every degree the foot is moved north or south of the equator, is a degree of off-plumb attachment in the tether, which increases the tether weight (which is one of the limits -- the tether must support its own weight, that of the counterweight, the elevator structure, and any payload on the elevator, plus weather loads -- likely very small relative to static and dynamic loads from normal operation, but need to be considered) and introduces shear loading. Any mechanical or materials engineer will tell you shear loading is bad, when you're operating near the absolute limits of the strength of your material (and you will be). Shear itself is bad enough for a tensile-only material like the carbon nanotubes currently considered the best candidates for tether material, but it introduces a biaxial load (both shear and tension) which unavoidably weakens the material, which is already pretty weak in shear.

While I've read that IFF we can produce carbon nanotubes in lengths of tens of kilometers, defect free, and bond them together into cable without weakening them, we can pretty readily make a space tether, I've also read that there's not a huge safety factor in the strength. If you choose to handwave a super-material (like Niven's scrith or Sinclair monofilament), you make your own rules, but if you're abiding by real world physics, every 95 km (~ one degree) you move your base anchor away from the equator will have a disproportionate effect on the tether's ability to support space elevator operation.

There's one potential practical exception to this: if you mount a large enough solar sail at the top of the "beanstalk" -- well beyond the neutral point, out at the counterweight -- you might be able to continually adjust its angle to provide a reasonably constant force pushing the top end out of an "orbit" and into a powered path in a circle that doesn't cross the equator. How big your solar sail can be, and how much northward or southward force it can produce would determine how far off the equator your anchor can be and still keep the tether locally vertical.

There are other engineering problems to be solved in doing this -- not least that I don't have the math to calculate what it would do the stresses on the tether or the anchor point -- but it's at least not a violation of orbital mechanics; in fact, it's akin to the situation we already have with a beanstalk where we use a counterweight at greater than orbital speed to keep tension on the tether.

Answer 4

If strictly ideal, then yes equatorial.

If it is desirable to have the idealized ladder that has a fixed earth connection, it must be geostationary which requires positioning above/along the equator.

If not touching earth, no.

If it is acceptable to have the earth end mostly in one region with no earth contact. Ie earth end sits at an elevation 10 to 40 Km above earth. Then geosynchronous orbit is a reasonable possibility/option. The high elevation makes a big difference to ease of construction thus cost.

Space hooks could be almost wherever.

If center of mass is not at geostationary level/height. Then it would be more correctly labeled a space hook and a space hooks can be in many more possible orbits. Also a small space hook can be constructed and placed into orbit within five to ten years if any of the major space organizations decided to prioritize it.

Space hooks would only make ground momentarily if they do, majority would have closest approach to earth measured in kilometers. Cost to orbit would be the price of a flight of a high altitude aircraft.

Other satellites, debris is an issue for all.

Answer 5

I am surprised no other answer spoke about that (maybe I read to fast), but in the original designs I read, the best place for the "space port"/anchor on earth (if you choose to have it at "ground" level) is neither on the equator nor any other static place, but a platform in the ocean that can move on the surface of the earth. That way :

• you can move it to avoid debris/satellite in orbit
• more importantly, you can avoid storms. In most designs, the tether is a nanotube fiber, which is, among others, extremely sensible to high temperatures that could be caused by lightnings

For more information about the concrete prospects of these space elevators on earth and why it is supposed to be anchored in the oceans, there is the 2003 Nasa Study (this is an old project) and the last 2021 engineering study from ISEC

Answer 6

Almost all of the answers presume that the elevator has to stay in place. (Thank you, @Carm) This isn't the only answer, it's just the best one.

An alternative answer would be to have the bottom of the platform perform a figure-8 over a set area of land. If a geosynchronous satellite isn't directly over the equator, it will make a loop over an area every 24 hours. This could be used to take advantage of multiple launch points, with a "space hook," or landing platform that would grab the flying craft and drag it upward.

The challenges of this design are that you have to perfectly balance the orbit so that the end of the tether drags through the atmosphere. The size of the loop would be largely limited by atmospheric drag on the tether which, over time, would attempt to drag the counterweight back to earth.

Answer 7

Not necessarily

While it is necessary that a tethered space elevator must stay on equatorial orbit, there is no necessity to attach this elevator at the equator.

@Zeiss Ikon is quite right to point this out, let's me elaborate a little bit more on this.

Think about Tetherball. The ball is attached to the top of a pole, but its plane of rotational does not contain this top - the ball spins somewhere below it. Similarly, it is theoretically possible to design a space elevator which center of mass sits on geostationary equatorial orbit, while its tethering point is located anywhere on Earth's surface. Moreover, our space elevator can have multiple points of attachment, which can be very useful if multiple nations are sharing the same space platform.

What's complicates things though is tether's own mass. Ideally, we should have massive space platform and nearly massless cable, but realistically this is not possible. All space elevator design require massive cable, if this cable is not vertically upright, things get complicated. Now think about tetherball on a massive iron chain. It would still spin, but its behavior would be different. Overall, the requirement to attach the tether not on equator can be a project killer.

Answer 8

space elevators work best at the equator, and at the poles, and everything else is chaos

Considerations about satellites are valid, but once someone is investing in a space elevator they can invest in satellite cleanup or protection.

What you want to consider is the strain caused by the orbit. In an equatorial elevator the strain works in your favor, the constant angular speed at the end of the elevator pulls the whole structure up. The orbit is circular, and in line with your structure. In a polar elevator you have no orbit and so no strain to keep the elevator in place. This isn’t good, but a strong enough elevator can support itself. Further more, the elevator just holds itself upright with very little other strain. In a non-equatorial and non-polar elevator you have a problem. The end and the center of mass have circular orbits, but not in line with the center of mass of the earth. This means that your elevator will strain towards the equator as the elevator tries to follow a normal orbit and has to apply radial force to maintain the different orbit.

This means that the force you have in the each direction is based on the azimuth of the elevator in relation to the earth. The upwards direction is the cos(azimuth)*cos(azimuth) of the azimuth, and the sideways force is the cos(azimuth)*sin(azimuth). So to maximize upward force, azimuth must be 0. To maximize the sideways force, you sit a 45 degrees of the equator, and have half the normal upwards force in the sideways direction, and only an equal half in the upwards direction also. Near the poles at 90 degrees the upwards is zero, but so is the lateral.

Therefore, build at the equator to get to equatorial orbit and for low cost elevators, build at the poles for polar orbits and high strength elevators, and build anywhere else to flex on Kardashev type 1 civilizations.

Answer 9

If you have multiple base stations, the orbiting part of the elevator can be above the equator, with two base stations, both equidistant from the equator at opposite latitudes. It should be simple trigonometry to figure out how far from the equator the stations need to be to make the tethers miss the most debris-filled latitudes. Basically the tethers make a big "A" shape with a ring of debris passing between them.

It could also be possible to move the orbiter by varying the lengths of the cables. Reeling in the cable at the north base and letting out more cable at the south base will move the orbiter north. Reeling in the cable at the south base and letting out cable at the north base will move the orbiter south. If you have 4 ground stations, you can move the orbiter east and west as well.

Answer 10

An elevator cable anchored away from the equator (let's say north) will form a curve asymptotic to the equatorial plane. It will not be straight, because it is not ‘vertical’ with respect to the forces on it; and its top end will be some small but nonzero distance north of the equator, because of the northward component of tension on it, balanced by the southward component of Earth's gravity (which is zero on the equator). Centrifugal force pushes away from Earth's axis, not its center.

There must be a maximum latitude for the anchor, at which the sag makes the cable tangent to the ground. I lack the skill to find what that latitude is; it depends on the amount of taper in the cable.