The first episode of the Foundation series on Apple TV shows a terrorist trying to destroy the space elevator. It's a good chance to discuss the physics of space elevators and what would happen if one exploded. It wouldn't be good.
It allows us to have weather satellites, a space station, and even the James Webb Space Telescope, because people like to put stuff beyond the Earth's atmosphere. We usually call it a rocket, but right now we only have one option for getting stuff into space.
Don't get me wrong, rockets are cool, but they are also expensive and inefficient. Let's take a look at what it takes to get a small object intoLEO. The International Space Station is about 400 kilometers above the surface of the Earth. You need to accomplish two things in order to get this object into the sky. You have to lift it up to 400 kilometers. It wouldn't be in space for long if you only increased the object's altitude. It would fall to the ground. It has to move fast in order to stay in LEO.
It turns out that the amount of energy we put into a system is equal to the change in energy in that system. There are different types of energy. An object has a certain amount of energy due to its speed. If you increase an object's speed, it will increase in energy. The distance between the object and the Earth affects the potential energy. Increasing an object's altitude increases its potential energy.
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Let's say you want to use a rocket to raise the object to the right altitude and also increase its energy to get it up to speed. Getting into space is more about speed than height. 11 percent of the energy is in the potential energy. The rest would be rapid.
33 million joules is the total amount of energy that would be needed to get that object into the air. If you put a textbook on a table, it will take about 10 joules. It would take a lot of energy to get there.
The problem is more difficult than that. Chemical rockets don't just need energy to get a small object into the sky, they also need to carry their fuel for the journey. They need to launch with even more fuel until they burn this fuel. Up to 85% of the total mass can be fuel in real-life rockets. That is inefficient.
What if your object could ride up on a cable and travel all the way into space? That's what a space elevator would do.
Space elevator basics.
Imagine you built a tower that is 400 kilometers tall. You can ride an elevator up to the top and then be in space. Simple, right? It's not.
The weight of the structure would likely cause the lower parts of the tower to collapse. It would require a lot of material.
There's still an issue with speed. You need to move fast to get into space. If you were standing on the top of a tower with a base on the equator, you would be moving because the planet is rotating. The Earth has an average speed of 7.29 radians per second since it rotates once a day.
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The difference between linear andangular velocity is not the same. It is a measure of speed, not movement in a straight line. The radians are a unit of measurement and not degrees.
If two people are standing on a merry-go-round, they will both have the same speed. Let's say it's 1 radian per second. The person that is farther from the center of rotation will be moving faster. One person is 1 meter from the center and the other person is 3 meters away. Their speeds will be 1 m/s and 3 m/s. This is the same thing that works with a rotating Earth. It's possible to get far enough away that the Earth's rotation will allow you to stay in the correct position around the planet.
A person is standing on the top of a tower. Are they far enough away from Earth to stay in space? The Earth's rotation would cause their radians to be 2 per day. The rotation at the equator gives you a speed of 465 meters per second. It's over 1,000 miles per hour. It's not enough. At that altitude, the orbital velocity is over 17,000 miles per hour.
As you increase your distance from the Earth, the orbital velocity decreases. If you go from an altitude of 400 to 800 kilometers above the surface of the Earth, the speed decreases to 7.5 km/s. It doesn't seem like a big deal, but remember, it's not just the height above the surface of the Earth that matters. You could build a tower that was high enough that you could just step off and be in the air, but it would have to be at least 36,000 kilometers tall. That is not going to happen.
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