Do not ride the space elevator

Published on May 04, 2018

Do not ride the space elevator

    Reading articles about the space elevator, I never cease to be surprised at how much attention they pay to the potentially solvable problem of rope strength, and how little attention is paid to problems that cannot be solved in any way ...

    Space elevator in NASA fantasy

    And so, let's assume that we have a fibrous material with a tensile strength of about 100 GPa (10 000 kgf / mm ^ 2) with a density of 1.5 kg / dm ^ 3. With such material we can build a space elevator. All you need to do is to launch into the geostationary orbit 72,000 km of cable from such material and start unwinding it there in two directions at once: towards the Earth and from it. At some point, one of the ends of the cable will reach the surface, and we will only have to fix it, but go up and down it. What problems?..

    Let's start with the "little things" - the mass of the cable. The optimal cable will be in the middle (near the geostationary orbit) 2-3 times thicker than at the surface of the Earth. But I will conditionally consider its diameter everywhere equal to 1 cm, since I do not set the task to get the exact numbers, but only to estimate the order Why exactly 1 cm, and not 1 mm or 1 m? Because the cable with a diameter of 1 mm will withstand only 7.85 tons of load on the gap. Considering that, at best, 90% of the strength of the cable will be “spent” to maintain its own weight, we find that such a cable will not sustain the weight of a modern large satellite, not to mention spacecraft and, moreover, orbital stations. Well, 1 m is just a bust.

    And so, we have 72,000 km of cable with a diameter of 1 cm and a density of 1.5. The mass of this cable is approximately 8500 tons ... To deliver such a mass to the geostationary orbit more than a thousand launches of heavy launch vehicles will be required! Instead of building an elevator, they could provide for all the needs of mankind in launching spacecraft into orbit for decades to come. And this is if we assume that the cable delivered in parts, already in orbit, can be assembled into a single whole of the necessary strength ...

    But the most interesting begins further. According to various estimates, only in low near-earth orbits (altitude from 200 to 2000 km) there are from 200,000 to 300,000 relatively large objects - more than 1 cm in size. Of these, more than 90% are not more than 10 cm in size, and from that are too small for tracking radar.

    Despite the huge number of relatively large objects in orbit, collisions between them are still very, very rare. Firstly, even the ISS is small by space standards, and all the rest - even more so. So for a collision, the trajectories of two objects must pass very, very close to each other, which is unlikely in itself. But in addition to this, two objects should be at the intersection of the trajectories at the same time! This makes the collision a very rare event, in the entire history of astronautics, they can be counted on the fingers.

    But what will happen in the case of a fixed cable of enormous length? .. On average once an hour, each of these objects crosses the equator. Those. at least 200,000 equator crossings per hour. If we take the equatorial area of ​​the low orbits, 200-2000 km, it will be 85,500,000 km ^ 2. The cross-sectional area of ​​1 cm of cable at a height of 200-2000 km is 0.018 km ^ 2 or 0.2 billionth of the equatorial plane area. Mizer? But we have 200,000 equator crossings per hour! It is not difficult to calculate that on average once every 23,500 hours a fragment of space debris with a size larger than the diameter of the cable will fall into the cable. Those. will be guaranteed to destroy it! If anything, 23,500 hours is 2 years and 8 months. And this is an estimate from above, since this calculation is valid only for a zero size of space debris, and the debris of more than 1 cm across is actually taken into account, which greatly increases the probability of a collision ... In reality, the life of a cable is about a year or even less. Moreover, the reduction of the cable section almost did not extend this period, since space junk will not become smaller. An increase in the cross section also will not do anything: yes, a meter cable will not be able to kill far every fragment of garbage, but they will get into it a hundred times more often, so for the same year they will weaken enough to break under their own weight.

    Total we have: we need to put into the geostationary orbit with classical rockets as much cargo as we have in the whole history have not managed to withdraw there, so that later in the year, until the cable kills space debris, it is very cheap to put cargo into orbit ... which will cause a falling cable, especially if it is killed not near the Earth, but somewhere closer to the geostationary orbit.

    PS If anything, I passionately dream of large-scale space exploration. But in order for my dream to become a reality, money and efforts must be directed to those projects that, at least in the long term, can have an effect. And the space elevator, alas, does not belong to such projects: large-scale space exploration ensures that there will only be more space debris, and for the safety of the cable it should be ten times smaller, i.e. one excludes the other.