So what if instead of launching a chemical rocket to the top, your object could go up on a cable reaching far into space? That’s what will happen with the space elevator.
Basic knowledge of space elevator
Let’s say you build a giant tower 400 km high. You can take the elevator to the top and then you’ll be in space. Simple, right? No, it’s not really.
First, you can’t easily build a structure like this out of steel; weight will likely compress and collapse the lower parts of the tower. In addition, it will require a large amount of material.
But that’s not the biggest problem – there are still problems with speed. (Remember, you need to move really fast to get into orbit.) If you were standing at the top of a 400-kilometer tower with the base somewhere above the Earth’s equator, you would actually be moving. moving, because the planet is spinning — this is like the motion of a person on the outside of a spinning ferris wheel. Since the Earth rotates about once per day (is there a difference between sub-rotations and synonymous rotations), it has an angular velocity of 7.29 x 10-5 radians per second.
Angular velocity is different from linear velocity. It’s a measure of rotational speed rather than what we normally think of as velocity – motion in a straight line. (Radians are a unit of measurement to use with rotations, rather than degrees.)
If two people are standing on a ferris wheel as it rotates, both will have the same angular velocity. (Assume it is 1 radian per second.) However, the person farther from the center of rotation will move faster. Suppose one person is 1 meter from the center and the other is 3 meters from the center. Their speeds will be 1 m/s and 3 m/s, respectively. The same thing works with the rotating Earth. Can go far enough that Earth’s rotation gives you the orbital velocity needed to stay in orbit around the planet.
So let’s go back to our example of a person standing on top of a 400 km tall tower. Are they far enough from Earth that they can stay in orbit? For one complete rotation of the Earth, their angular velocity would be 2π radians per day. That may not seem very fast, but at the equator this rotation gives you 465 meters per second. That’s more than 1,000 miles an hour. However, it is still not enough. Orbital velocity (the velocity required to stay in orbit) at that altitude is 7.7 km/s, or more than 17,000 mph.
In fact, there’s another factor: As you increase your distance from Earth, the orbital velocity also decreases. If you go from 400 to 800 km above the Earth’s surface, the orbital speed drops from 7.7 km/s to 7.5 km/s. That doesn’t seem like a huge difference, but remember, the orbital radius really matters, not just the height above the Earth’s surface. Theoretically, you could build a magic tower high enough that you could step out of it and into orbit — but it would have to be 36,000 kilometers tall. That won’t happen.
