Re: wired - What Happens If a Space Elevator Breaks?

On Sun, 23 Jan 2022 13:14:46 -0800, a425couple wrote:

> from
> https://www.wired.com/story/what-happens-if-a-space-elevator-breaks/
> 
> What Happens If a Space Elevator Breaks
> 
> These structures are a sci-fi solution to the problem of getting objects 
> into orbit without a rocket—but you don’t want to be under one if the 
> cable snaps.
> 
> space elevator in foundation
> PHOTOGRAPH: TCD/PROD.DB/APPLE TV+/ALAMY
> 
> IN THE FIRST episode of the Foundation series on Apple TV, we see a 
> terrorist try to destroy the space elevator used by the Galactic Empire. 
> This seems like a great chance to talk about the physics of space 
> elevators and to consider what would happen if one exploded.
> (Hint: It wouldn't be good.)
> 
> People like to put stuff beyond the Earth's atmosphere: It allows us to 
> have weather satellites, a space station, GPS satellites, and even the 
> James Webb Space Telescope. But right now, our only option for getting 
> stuff into space is to strap it to a controlled chemical explosion that 
> we usually call "a rocket."
> 
> Don't get me wrong, rockets are cool, but they are also expensive and 
> inefficient. Let's consider what it takes to get a 1-kilogram object 
> into low Earth orbit (LEO). This is around 400 kilometers above the 
> surface of the Earth, about where the International Space Station is. In 
> order to get this object into orbit, you need to accomplish two things. 
> First, you need to lift it up 400 kilometers. But if you only increased 
> the object’s altitude, it wouldn't be in space for long. It would just 
> fall back to Earth. So, second, in order to keep this thing in LEO, it 
> has to move—really fast.
> 
> Just a quick refresher on energy: It turns out that the amount of energy 
> we put into a system (we call it work) is equal to the change in energy 
> in that system. We can mathematically model different types of energy. 
> Kinetic energy is the energy an object has due to its velocity. So if 
> you increase an object’s velocity, it will increase in kinetic energy. 
> Gravitational potential energy depends on the distance between the 
> object and the Earth. This means that increasing an object’s altitude 
> increases the gravitational potential energy.
> 
> So let's say you want to use a rocket to increase the object’s 
> gravitational potential energy (to raise it to the right altitude) and 
> also increase its kinetic energy (to get it up to speed). Getting into 
> orbit is more about speed than height. Only 11 percent of the energy 
> would be in the gravitational potential energy. The rest would be kinetic.
> 
> The total energy to get just that 1-kilogram object into orbit would be 
> about 33 million joules. For comparison, if you pick up a textbook from 
> the floor and put it on a table, that takes about 10 joules. It would 
> take a lot more energy to get into orbit.
> 
> But the problem is actually even more difficult than that. With chemical 
> rockets, they don't just need energy to get that 1-kilogram object into 
> orbit—the rockets also need to carry their fuel for the journey to LEO. 
> Until they burn this fuel, it's essentially just extra mass for the 
> payload, which means they need to launch with even more fuel. For many 
> real-life rockets, up to 85 percent of the total mass can just be fuel. 
> That's super inefficient.
> 
> So what if, instead of launching atop a chemical rocket, your object 
> could just ride up on a cable that reaches all the way into space? 
> That's what would happen with a space elevator.
> 
> Space Elevator Basics
> 
> Suppose you built a giant tower that is 400 kilometers tall. You could 
> ride an elevator up to the top and then you would be in space. Simple, 
> right? No, actually it's not.
> 
> First, you couldn't easily build a structure like this out of steel; the 
> weight would likely compress and collapse the lower parts of the tower. 
> Also, it would require massive amounts of material.
> 
> But that's not the biggest problem—there's still the issue with speed. 
> (Remember, you need to move really fast to get into orbit.) If you were 
> standing on the top of a 400-kilometer tower with the base somewhere on 
> the Earth's equator, you would indeed be moving, because the planet is 
> rotating—this is just like the motion of a person on the outside of a 
> spinning merry-go-round. Since the Earth rotates about once a day 
> (there's a difference between sidereal and synodic rotations), it has an 
> angular velocity of 7.29 x 10-5 radians per second.
> 
> Angular velocity is different than linear velocity. It’s a measure of 
> rotational speed instead of what we normally think of as 
> velocity—movement in a straight line. (Radians are a unit of measurement 
> to use with rotations, instead of degrees.)
> 
> If two people are standing on a merry-go-round as it spins, they will 
> both have the same angular velocity. (Let's say it's 1 radian per 
> second.) However, the person that is farther from the center of rotation 
> will be moving faster. Let's say one person is 1 meter from the center 
> and the other person is 3 meters from the center. Their speeds will be 1 
> m/s and 3 m/s respectively. This same thing works with a rotating Earth. 
> It's possible to get far enough away such that the Earth's rotation 
> gives you the required orbital velocity to stay in orbit around the planet.
> 
> So let’s go back to our example of a person standing on the top of a 
> 400-kilometer tower. Are they far enough away 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 might not seem very fast, but 
> at the equator this rotation gives you a speed of 465 meters per second. 
> That's over 1,000 miles per hour. However, it's still not enough. The 
> orbital velocity (the velocity needed to stay in orbit) at that altitude 
> is 7.7 kilometers per second, or over 17,000 miles per hour.
> 
> Actually, there's another factor: As you increase your distance from the 
> Earth, the orbital velocity also decreases. If you go from an altitude 
> of 400 to 800 kilometers above the surface of the Earth, the orbital 
> speed decreases from 7.7 km/s to 7.5 km/s. That doesn't seem like a 
> large difference, but remember, it's really the orbital radius that 
> matters and not just the height above the surface of the Earth. 
> Theoretically, you could build a magical tower that was high enough that 
> you could just step off of it and be in orbit—but it would have to be 
> 36,000 kilometers tall. That’s not going to happen.
> 
> 
> Here is something that's very cool and more practical: An orbit at the 
> altitude of 36,000 kilometers has a special name. It's called a 
> geosynchronous orbit, meaning that the time it takes an object to 
> complete one orbit is exactly the same time it takes the Earth to 
> rotate. If you put this object in an orbit directly over the equator, it 
> will appear in the same location in the sky relative to the surface of 
> the Earth. (Then it's called a geostationary orbit.) That's useful, 
> because you know exactly where to find it. A geostationary orbit makes 
> it easier to communicate with objects like TV or weather satellites, or 
> for satellite cameras that need to stay focused on the same part of the 
> Earth.
> 
> OK, back to the space elevator. If we can’t build a tower from the 
> ground up, we can hang a 36,000-kilometer cable from an object that’s in 
> a geostationary orbit. Boom: That's the space elevator.
> 
> To get this to work, you would need a large mass in orbit—either a space 
> station or a small asteroid. The mass has to be large so that it doesn't 
> get pulled out of orbit every time something climbs up the cable.
> 
> But perhaps now you can see the problem with a space elevator. Who wants 
> to make a 36,000-kilometer-long cable? For a cable that long, even the 
> strongest material, like kevlar, would have to be super thick to prevent 
> it from breaking. Of course, thicker cables means more weight hanging 
> down below, and that means the higher parts of the cable have to be even 
> thicker to support the cable below. It's a compounding problem that 
> seems essentially impossible. The only hope for the future of space 
> elevator construction is to figure out how to use some super strong and 
> lightweight material like carbon nanotubes. Perhaps we will make this 
> work someday, but that day is not today.
> 
> What About a Falling Elevator Cable?
> In the first episode of Foundation, some people decide to set off 
> explosives that separate the space elevator’s top station from the rest 
> of the cable. The cable falls to the surface of the planet and does some 
> real damage down there.
> 
> What would a falling space elevator cable look like in real life? It's 
> not that simple to model, but we can make a rough guess. Let's model the 
> cable as being made up of 100 individual pieces. Each piece starts in a 
> motion around the Earth, but with the same angular velocity as the 
> Earth. (So, not in orbit.) In an actual space elevator cable, there 
> would be some tension forces between pieces. But just for simplicity, in 
> the model each piece will only have the gravitational force from the 
> interaction with the Earth. Now I can just model the motion of these 
> individual 100 parts of the cable to see what happens. (It's actually 
> not too difficult to do this with some code in Python—but I'll skip all 
> of that.)
> 
> Here's what it would look like:
> 
> PLAY/PAUSE BUTTON
> VIDEO: RHETT ALLAIN
> 
> So, what's going on? Notice that the lower part of the cable just falls 
> to Earth and probably causes some severe destruction. In this model, it 
> wraps about a third of the way around the equator, even though its full 
> length would almost make it all the way around the Earth, which has a 
> circumference of 40,000 kilometers.
> 
> But some of the parts of the cable might not even hit the surface. If 
> the pieces start high enough, their velocity will increase as they get 
> closer to the surface. It's possible that the pieces will speed up 
> enough to put them in a non-circular orbit around the Earth. If you are 
> living on the equator, that's a good thing. Better to have that debris 
> in space than falling on your head, right?
> 
> Of course, if the cable is still intact, then each piece would be 
> pulling on other nearby pieces. This would cause more of the cable to 
> crash into Earth. But at some point, the forces in the cable would 
> become so strong that it would just break apart. You would still end up 
> with space debris.
> 
> So not only is building a space elevator very difficult, but you really 
> don’t want the cable to snap and fall. Maybe it’s a good thing that we 
> are still in the rocket phase of space exploration.
> 
> 
> Rhett Allain is an associate professor of physics at Southeastern 
> Louisiana University. He enjoys teaching and talking about physics. 
> Sometimes he takes things apart and can't put them back together.
> CONTRIBUTOR

An interesting video

https://www.youtube.com/watch?v=DZdjjbULyrY