What would happen if the space elevator broke


So what if your object wasn’t launched on a chemical rocket, but rather rode on a cable that stretched all the way into space? That’s what happens in a space elevator.

Space Elevator Basics

Suppose you build a giant tower 400 kilometers high. You can take the elevator to the top and you’ll be in space. Simple, right? No, not actually.

First, you can’t easily build such a structure out of steel; the weight could compress and collapse the lower part of the tower. Also, this will require a lot of material.

But that’s not the biggest problem – the speed issue remains. (Remember, you need to move very fast to get into orbit.) If you’re standing on top of a 400-kilometer tower with its base somewhere on the Earth’s equator, you’re really moving because the Earth is spinning – this Like the movement of a person outside a spinning carousel. Since the Earth rotates about once a day (Difference Between Stellar Rotation and Weather Rotation), which 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, not what we usually think of as speed – linear motion. (Radians are the unit of measurement used for rotation, not degrees.)

If two people are standing on a spinning carousel, their angular velocity will be the same. (Let’s say it’s 1 radian per second.) However, the farther from the center of rotation, the faster the person moves. Suppose one person is 1 meter away from the center and the other person is 3 meters away from the center. Their velocities will be 1 m/s and 3 m/s respectively. The same applies to the spinning earth. It’s possible to get far enough away that the Earth’s rotation gives you the orbital speed you need to stay in orbit around the Earth.

So let’s go back to our example of a person standing on top of a 400km tower. Are they far enough from Earth to stay in orbit? For one full circle of the Earth, their angular velocity would be 2π radians per day. This may not seem fast, but at the equator, this rotation gives you 465 meters per second. That’s over 1,000 miles per hour. However, this is still not enough. The orbital speed at that altitude (the speed required to stay in orbit) is 7.7 kilometers per second, or over 17,000 miles per hour.

Actually, there’s another factor: as your distance from Earth increases, so does the orbital velocity. From an altitude of 400 km to 800 km above the Earth’s surface, the orbital velocity decreases from 7.7 km/s to 7.5 km/s. This may not seem like a big difference, but keep in mind that it’s the orbital radius that matters, not just the altitude above the Earth’s surface. In theory, you could build a magic tower high enough that you could walk down from it and into orbit—but it would have to be 36,000 kilometers high. This is not going to happen.



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