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"Just how many satellites can we fill space with" That's the (honest) question I have. Articles like this pop up from time to time on HN, but it's hard to tell

"Just how many satellites can we fill space with" That's the (honest) question I have. Articles like this pop up from time to time on HN, but it's hard to tell how big a problem this is. What's the reasonable upper bounds for LEO satellites? How do we determine what is reasonable? Who gets to decide and enforce that?

epicureanideal 5y ago
We can probably do a back of the napkin estimate on this. The radius of the earth is 6563 km, and LEO is 2,000 km or less. If we use 2,000 km for LEO and round the radius of the earth to 6,500 km, the "radius of LEO" is 8,500km. Surface area is 4 pi r^2... so that's a surface area of about 908 million square kilometers. There's a couple ways we could try to guesstimate the upper limit of satellites. How many satellites per square kilometer? Maybe 1? If so, that means 908 million satellites, which is far more than the 114,000 the Canadian company wants to launch. But if we start seeing many deployments in the millions of satellites... that starts to add up pretty quickly. Given the speed of the satellites, is there a certain amount of distance travelled per second that we need to ensure is kept between them, or significant gaps to leave windows for other launches to pass through safely? LEO velocity is about 25,000km/hr, so about 7km/second. If we want a gap of 1 second between satellites (I am not sure if that's excessive or insufficient, just a ballpark) but assuming the orbits are mostly "aligned" so we can keep 1km distance in one axis and 7km distance in the other axis, we can round that to about 1 satellite per 10 square kilometers, so 90.8 million satellites as an upper bound. On the other hand, maybe clusters of launches can be handled more easily by launch planning software by treating them as a group instead of an individual object to be tracked, and maybe for some reason that makes the process easier. Also, the above estimates are probably wild underestimates, because these are based on the surface area of a spherical shell, disregarding all the shells are different altitudes of the sphere... for example, LEO was taken to be 2,000km, but there are nearly equivalent shells at 1,999km, 1,9998km, etc. Even if we assume 10km between shells for our back of the napkin estimate, if we say anything from 1,500km to 2,000km is basically equivalent, we have 50x more capacity than estimated above. Going in the reverse direction, if we assume that for some unknown reason these estimates are off by 2 orders of magnitude, 100x, after accounting for all the equivalent "shells", we're back at roughly the original capacity estimate of 90-900 million satellites.
- whatshisface 5y ago
  I don't think you can use surface area because satellites orbit in great circles, not lines of latitude.
  - epicureanideal 5y ago
    Good point! So we would want to calculate the surface area excluding the poles? We could calculate it more accurately, but the surface area excluding the poles is definitely more than 50%, probably closer to 60-80% of the total surface area, right? So the estimate is still mostly reasonable.
    - tejtm 5y ago
      I think each great circle has its own poles orthogonal to its inclination and earth's poles has naught to do with it. Without station keeping, LEO orbits (thankfully) degrade so the outter shells will be gradually bleeding into the lower shells as well.
    - vkou 5y ago
      You want to calculate the number of orbital intersections, and space them out to avoid collisions.
  - deleted 5y ago
    [deleted]
- manbart 5y ago
  Another big factor to consider is how obsolete satellites are de-commissioned. Can they be made to re-enter the atmosphere when no longer needed, or is a permanent piece of debris at that point?
  - legerdemain 5y ago
    I think at some point Steve Wozniak comes along and picks them up.
choeger 5y ago
Space is big. Any orbital plane has a diameter of, roughly, 13000km. That gives a sphere with a surface area of about 5.3 * 10^8 square kilometers. We could give every satellite in a single plane 100 square kilometers and still put millions of satellites in it. From the perspective of a rocket launch through a plane that's pretty safe. But orbital mechanics dictate that satellites on different orbits have their orbits intersect in two points, obviously. So we need to coordinate Management of orbital planes such that the satellites' orbits in a single plane don't intersect with each other. That means, inside a plane we would have to create "subplanes", instead of a plane one would assign a shell. Capacity then depends a lot on how much space we want to leave. Say we want 1km "vertically" and 10km "horizontally" and a shell has a thickness of 10km. Then you can still put about 4000 satellites on the same orbit and have 40000 satellites in that shell at most. So there is a lot of space in space. But coordination will be crucial.
- skeeter2020 5y ago
  When you look at WHERE everyone wants to put those orbits it does shrink dramatically though (hint: central lattitudes)
bryanlarsen 5y ago
The big unknown in the back of the envelope calculation is the degree of control over each satellite. What percentage of the satellites are uncontrolled? For instance, of Starlink's 1600 satellites, over 100 of them have become non-functional, most of them the unused v0.9 test satellites. However, most of these failed satellites have been actively de-orbited. A few failures are non-responsive and are de-orbiting naturally, which takes about a year. This factor is much less important at the Starlink of 550km because air pressure deorbits those satellites relatively quickly. If failure rates stay below 0.1% and orbits below 500km and proper international "traffic control" is implemented, billions of satellites would not pose a Kessler risk, IIRC. At higher altitudes that number decreases very rapidly. Sorry I can't find a link to those calculations.
draggnar 5y ago
Also, has anyone studied the debris? If we go to hundreds of millions of little satellites, that is a significant mass. what is that debris made of, is it reactive, what happens to it?
wmf 5y ago
I've seen plans for an orbital shell every 10 km with around 2,000 satellites per shell. Maybe 150 shells total with over 300K satellites.
- teruakohatu 5y ago
  2,000 per shell shoulds like a a very small lower bound. The density would be less than 2,000 humans spread over the entire earth.
gentleman11 5y ago
We may as well get it over with. Our launch strategy as a species is so bad that we will inevitably lose access to our orbital region due to the high velocity garbage eventually. If we get to that stage early on, we can stop pretending that governments and companies are capable of acting like adults /s

epicureanideal 5y ago

We can probably do a back of the napkin estimate on this. The radius of the earth is 6563 km, and LEO is 2,000 km or less. If we use 2,000 km for LEO and round the radius of the earth to 6,500 km, the "radius of LEO" is 8,500km. Surface area is 4 pi r^2... so that's a surface area of about 908 million square kilometers. There's a couple ways we could try to guesstimate the upper limit of satellites. How many satellites per square kilometer? Maybe 1? If so, that means 908 million satellites, which is far more than the 114,000 the Canadian company wants to launch. But if we start seeing many deployments in the millions of satellites... that starts to add up pretty quickly. Given the speed of the satellites, is there a certain amount of distance travelled per second that we need to ensure is kept between them, or significant gaps to leave windows for other launches to pass through safely? LEO velocity is about 25,000km/hr, so about 7km/second. If we want a gap of 1 second between satellites (I am not sure if that's excessive or insufficient, just a ballpark) but assuming the orbits are mostly "aligned" so we can keep 1km distance in one axis and 7km distance in the other axis, we can round that to about 1 satellite per 10 square kilometers, so 90.8 million satellites as an upper bound. On the other hand, maybe clusters of launches can be handled more easily by launch planning software by treating them as a group instead of an individual object to be tracked, and maybe for some reason that makes the process easier. Also, the above estimates are probably wild underestimates, because these are based on the surface area of a spherical shell, disregarding all the shells are different altitudes of the sphere... for example, LEO was taken to be 2,000km, but there are nearly equivalent shells at 1,999km, 1,9998km, etc. Even if we assume 10km between shells for our back of the napkin estimate, if we say anything from 1,500km to 2,000km is basically equivalent, we have 50x more capacity than estimated above. Going in the reverse direction, if we assume that for some unknown reason these estimates are off by 2 orders of magnitude, 100x, after accounting for all the equivalent "shells", we're back at roughly the original capacity estimate of 90-900 million satellites.

whatshisface 5y ago
I don't think you can use surface area because satellites orbit in great circles, not lines of latitude.
- epicureanideal 5y ago
  Good point! So we would want to calculate the surface area excluding the poles? We could calculate it more accurately, but the surface area excluding the poles is definitely more than 50%, probably closer to 60-80% of the total surface area, right? So the estimate is still mostly reasonable.
  - tejtm 5y ago
    I think each great circle has its own poles orthogonal to its inclination and earth's poles has naught to do with it. Without station keeping, LEO orbits (thankfully) degrade so the outter shells will be gradually bleeding into the lower shells as well.
  - vkou 5y ago
    You want to calculate the number of orbital intersections, and space them out to avoid collisions.
- deleted 5y ago
  [deleted]
manbart 5y ago
Another big factor to consider is how obsolete satellites are de-commissioned. Can they be made to re-enter the atmosphere when no longer needed, or is a permanent piece of debris at that point?
- legerdemain 5y ago
  I think at some point Steve Wozniak comes along and picks them up.

choeger 5y ago

Space is big. Any orbital plane has a diameter of, roughly, 13000km. That gives a sphere with a surface area of about 5.3 * 10^8 square kilometers. We could give every satellite in a single plane 100 square kilometers and still put millions of satellites in it. From the perspective of a rocket launch through a plane that's pretty safe. But orbital mechanics dictate that satellites on different orbits have their orbits intersect in two points, obviously. So we need to coordinate Management of orbital planes such that the satellites' orbits in a single plane don't intersect with each other. That means, inside a plane we would have to create "subplanes", instead of a plane one would assign a shell. Capacity then depends a lot on how much space we want to leave. Say we want 1km "vertically" and 10km "horizontally" and a shell has a thickness of 10km. Then you can still put about 4000 satellites on the same orbit and have 40000 satellites in that shell at most. So there is a lot of space in space. But coordination will be crucial.

skeeter2020 5y ago
When you look at WHERE everyone wants to put those orbits it does shrink dramatically though (hint: central lattitudes)

bryanlarsen 5y ago

The big unknown in the back of the envelope calculation is the degree of control over each satellite. What percentage of the satellites are uncontrolled? For instance, of Starlink's 1600 satellites, over 100 of them have become non-functional, most of them the unused v0.9 test satellites. However, most of these failed satellites have been actively de-orbited. A few failures are non-responsive and are de-orbiting naturally, which takes about a year. This factor is much less important at the Starlink of 550km because air pressure deorbits those satellites relatively quickly. If failure rates stay below 0.1% and orbits below 500km and proper international "traffic control" is implemented, billions of satellites would not pose a Kessler risk, IIRC. At higher altitudes that number decreases very rapidly. Sorry I can't find a link to those calculations.

draggnar 5y ago

Also, has anyone studied the debris? If we go to hundreds of millions of little satellites, that is a significant mass. what is that debris made of, is it reactive, what happens to it?

wmf 5y ago

I've seen plans for an orbital shell every 10 km with around 2,000 satellites per shell. Maybe 150 shells total with over 300K satellites.

teruakohatu 5y ago
2,000 per shell shoulds like a a very small lower bound. The density would be less than 2,000 humans spread over the entire earth.

gentleman11 5y ago

We may as well get it over with. Our launch strategy as a species is so bad that we will inevitably lose access to our orbital region due to the high velocity garbage eventually. If we get to that stage early on, we can stop pretending that governments and companies are capable of acting like adults /s