First of all, what is a space elevator? Well, as the name suggests, it’s an elevator-like structure that extends from the surface of the Earth up into space. Oh, one thing I forgot to mention…it doesn’t actually physically exist just yet. Clearly, it would be totally awesome to be able to take a cute, little elevator ride straight up into the heavens, but…easier said than done. – At this point that is.
Even though the idea has been around since the late 1800s, there are still many obstacles that make its practical realization nearly impossible. The first ideas started out as simple towers built so high so as to enter the geostationary Earth orbit (GEO). Once there, it would orbit the Earth with an equal orbiting period, causing it to remain stationary relative to Earth.
The problem with this model is that it would be a compression structure, with the primary forces being compression. A tower can only go so high before it will buckle under its own weight. There is simply no material known to man that is both strong and light enough to withstand the compression forces the weight-force of a 35,000 kilometer-high tower (the approximate altitude of the geostationary orbit) will exert along its height.
The other option, and the one that is currently considered “viable”, is a model that utilizes tension as opposed to compression. The way this would (theoretically) work is by launching repeated (thousands actually) space shuttles loaded with materials into the geostationary orbit, from where they would begin lowering cable toward the Earth’s surface. By gradually connecting additional segments, the cable should eventually reach Earth, where it will be anchored.
So is it possible to build a space elevator? Well, I sure hope so…However, hope may not be enough at this point. The rest of the article covers various physics-related aspects of a space elevator as well as the limitations scientists and engineers face in making it a reality. Note that research on a space elevator is ongoing, and as such, certain aspects are subject to change as new technology emerges.
Physics of the Space Elevator
There are two primary forces at work concerning the statics of a space elevator – the force of gravity or centripetal force, and the Earth’s centrifugal force. The Earth exerts a gravitational force on an object, the strength of which varies depending on the object’s altitude. The further it is from the Earth’s surface – or its core, depending on how you look at it – the weaker the force of gravity. The force of gravity can be calculated by the following equation:
where gh is the gravitational acceleration at height h above sea level, re is the Earth’s mean radius (6,371 km), and go is the standard gravitational acceleration on the Earth’s surface (9.806 m/s2). Using this formula, the gravitational force at the geostationary orbit would be about 0.2 m/s2.
A centrifugal force is one that is directed away from the center of a given object, and is used in relation to spinning or rotating objects and the phenomenon of things seemingly flying outward from a spinning object. A ride in a merry-go-round is an example of a centrifugal force pulling you away from the axis of rotation.
But the fact of the matter – and here is where it gets a little tricky – is that this force only exists so long as the opposing centripetal force exists. It’s really no more than the “sensation” of being pulled outward from the center of the spinning mass.
In reality, if the centrifugal force overpowers the centripetal force, it will cause the object to fly tangent to the point on the orbital path that it occurred – not outward from the center of the spinning mass. A yo-yo being spun like a sling-shot is a good example that illustrates this principle. The yo-yo is kept in orbit by these 2 forces, the centripetal and centrifugal forces.
The string that keeps the yo-yo from flying away is continually pulling it toward the center of the spinning mass – your hand – as it spins. This force that tries to pull it in is the centripetal force, and the opposing force that keeps the string taut, is the centrifugal force. However, if you were to let the yo-yo go, releasing it into the air, in which direction would it fly? Yes, tangent to the orbital path!
If you were to take several photos in continuous shooting mode of the yo-yo “in action” within split-seconds of each other, you would no doubt witness this phenomenon first-hand. If you want the yo-yo to fly up vertically upon release, you’d have to release it when the string connecting the yo-yo to your hand forms a horizontal line, with the direction of angular motion being upward.
So, relating this to the space elevator, the force of gravity equals the centripetal force, the yo-yo string if you will. The centrifugal force would counter the force of gravity, keeping the cable taut in tension, and is what would prevent the whole structure from crashing down to Earth. In order for the centrifugal force to be strong enough however, the entire system’s center of mass would have to be above the geostationary orbit.
To achieve this feasibly, a large counterweight would have to be installed some 144,000 kilometers above Earth – almost half the distance to the moon. This counterweight would be slowly extended into space to match the gravitational pull (centripetal force) of the lowering cable to Earth as it is constructed. An alternative would be to simply extend the cable (instead of the counterweight) to the needed distance to achieve equilibrium.
The Coriolis Effect and How it Will Affect a Space Elevator
Imagine you and a friend on opposite sides of a carousel tossing a ball back and forth to each other. As it spins, the rotation will cause the ball being thrown to seemingly assume a slightly curved path. If the carousel spins clockwise viewed from above, the curve will be to the left from the thrower’s perspective, and to the right from the receiver’s.
The Coriolis effect only manifests itself in a rotating reference frame, or non-inertial frame of reference. A non-inertial frame of reference can be described as a point of observation where you, the observer, are experiencing continuous changes in velocity. A rotating object is just such a situation, where even though the rate of rotation may be constant, the direction of movement is continually changing.
Let’s say there was a tall tree that hung over the carousel in the above example, and you climbed up and observed 2 kids throwing the ball back and forth while spinning. From your vantage point up in the tree, now an inertial frame of reference in relation to the carousel, the ball will no longer seem to curve, but will fly straight. The difference lies simply in the observer’s frame of reference.
Well, we all know that the Earth rotates as it orbits the Sun, right? So doesn’t that mean we should see the Coriolis effect even if we’re not on a carousel? The answer is yes. However, because the Earth rotates at only 1 revolution per day, the effect is so small that it’s not detectable unless an object is in flight for a fairly long time.
But let’s say we succeed in building a space elevator…will the Coriolis effect have to be taken into consideration? Yes, it will! As a climber ascends up the cable vertically, it must accelerate not only in the vertical direction, but in the horizontal as well. Because the Earth is spinning and the cable is spinning with it, the ascending climber must also achieve the equivalent angular velocity as it climbs.
The good news is that even though the Coriolis effect will cause the climber to pull the cable slightly backward as it ascends, the centrifugal force will always bring it back to the vertical position due to it being the natural energy-favorable position. By the time a climber gets to geostationary orbit, it will have reached an orbital velocity of roughly 3 kilometers per second.
Here’s an animated video clip on the Coriolis effect and centrifugal force for those who are interested.
The primary snag in the development of a space elevator is the lack of a material that is both strong and light enough to support the enormous tensile load of the cable. Various calculations put the required tensile strength of the cable between 130 giga-pascals and 300 giga-pascals (Gpa). As a comparison, structural steel has a tensile strength of about 250 mega-pascals (Mpa) – about 1000 times weaker than required.
The closest known material to being a viable candidate is carbon nanotube. It has a measured tensile strength of 63 Gpa, but a theoretical tensile strength of 300 Gpa. However, at this point, carbon nanotube can only be produced in very small quantities – in the tens of centimeters. So to think of making a 100,000+ kilometer cable out of carbon nanotube is simply unrealistic at this point.