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Comment by gamegoblin | Hacker News Reader

On most days there are up to 20,000 airplanes (which are 100-1000x larger than satellites) in the sky. And the satellites, being at 100x higher altitude, are 100x more spread out than the airplanes.

So just from a "unusable space" point of view, it's on the order of 10000x less of a problem than airplanes. The caveats here are the satellites are moving much, much faster than airplanes, and they stay in the sky much, much longer.

But it's not really a huge problem unless stuff goes wrong and you get Kessler Syndrome. This is more of a risk with the higher constellations like Amazon's and OneWeb's than it is with SpaceX Starlink (which is in a low enough orbit to de-orbit all debris within a few years, rather than centuries).

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> And the satellites, being at 100x higher altitude, are 100x more spread out than the airplanes.

This doesn't feel right. Shouldn't the right frame of reference be the distance to the center of the earth, not the sea level? Then it is not a 100x difference, but more like a 10% one.

Agreed rough math there doesn't seem right. Also, I wonder if there's an added benefit from the inverse square law here: https://en.wikipedia.org/wiki/Inverse-square_law

Here's the actual correct math:

---

Area of sphere: 4πr^2

Airplane cruising height: ~10km

Satellite orbit height: ~550km

Radius of earth: 6371km

thus, relative increase: (6371+550)/(6371+10) = 1.084 = 8.4% increase

Squared (because of first formula) that corresponds with a 1.084^2 = 1.175 = 17.5% increase in area.

---

Still, a few caveats:

1. Earth is huge. 510.1 million km² is a lot of space (+20% at 550km altitude). We could have a million sats with each having more than 1km^2 to themselves.

2. Satellites orbit at different heights. Amazon's and SpaceX's satellites will not be on the same orbit.

3. Starlink satellites are at a sufficiently low altitude that Kessler Syndrom is not a problem; even if they all simultaneously turned into millions of pieces of dead debris at the same time, the atmospheric drag would make them lower their orbits and burn up in just a few months.

If we were also launching from the center of the earth I would agree, but as we are launching from sea level, I think the general idea still holds.

Thought experiment:

You are standing in a field.

There is a 10x10 meter plate hovering 10 meters above you. There is a 1 square meter target on it. You fire a gun upwards at a random location on the plate. There is a 1 in 100 probability you hit the target.

Now imagine there is a 20x20 meter plate hovering 20 meters above you. It is perfectly occluded by the original 10x10 meter plate. It also has a 1 square meter target on it. When you fire at a random location on the original plate, the bullet passes through it and continues on to the higher plate. What is the probability you hit the target on the higher plate? I believe it is 1 in 400.

From this thought experiment it seems that altitude from launch point is what counts.

Except you can't generalize a square plate to a spherical shell...

Can you explain why?

If I am launching a rocket, and there is a 1x1 meter satellite orbiting 1000km above me. What is the probability that my rocket hits that satellite compared to an identical satellite at 2000km above me? The area of the angular sector of the sky that the 2000km altitude satellite is 1/4 of the 1000km altitude satellite.

The orbital launch will follow a curved path through succesive spherical shells. The percentage of the spherical shell occupied by the 1000km satellite is not 4x larger than the percentage of the spherical shell occupied by the 2000km satellite.

This is the wrong mental model entirely unless your rocket launch is directly vertical and instantaneous.

(10x10):(20x20) sounds like 1:4 to me, instead of 1:400, no?

It's not 1:400 -- it's 100:400 which is equal to the 1:4 you mention.

That is, you 2x the height of the target which results in the probability of hitting being 4x less.

Now expand your thought experiment to 4 people, standing in a 10 meter square from each other. They each have their own 10x10 and 20x20 plates, and their own targets.

Clearly the 10x10 plates are lining up (modulo curvature). But the 20x20 plates are not, they're overlapping. So when I shoot through a random location of my own 10x10 plate, there's a chance that I'll hit a target from somebody else's 20x20 plate. Sum up those additional chances, and they'll cancel out the 4x difference you found.

This feels like it would make a nice puzzle, your phrasing makes for a great misdirect / sleight of hand.

I totally agree with you and the other commenters that the total area of the spherical shell is only increasing by a few %, but I still think for the purposes of "escaping earth" as the top level comment was talking about, all that matters is how spread out things are directly above you.

When talking about the area of the spherical shells, it conflates what is above me as equally relevant to things that are on the other side of the planet from me.

That is, satellite X and Y may be over me at 500km and 1000km distance, respectively. Later, they may be directly through the earth from me at distance 13200km and 13700km distance.

In the first case, if I shine a laser straight up, my probability of hitting X is 4 times higher than my probability of hitting Y.

In the second case, (if I could somehow shine a laser straight through the earth), the probabilities are nearly equal.

But my intuition is that for the purpose of escaping earth, this second case does not matter, because we are just dealing with what is above us, not the entire spherical shell.

If your original claim were true, then you'd also be saying that there is twice as much area at 2m above sea level as there is 1m above sea level, and infinitely more than at sea level. If you truly believe this, then I will be willing to make you a trade where I give you one tenth floor condo in exchange for 10 first floor condos.

They're at 100x higher altitude relative to the sea level but nearly the same altitude relative to the Earth's center which is what matters here.

But we know where all the planes are, and actively monitor and move them around to avoid collisions. If there are a sufficient large number of satellites would there not be some risk of accidental collision with spacecraft taking off?

> But we know where all the planes are, and actively monitor and move them around to avoid collisions.

This is also true for satellites.

A similar monitoring applies to satellites as well. We're not launching spacecrafts and just hope that everything goes well.

We know where all the satellites are and they are actively tracked by both governments and private citizens.

Every satellite is in a very deterministic orbit which requires energy to change (enormous amounts of energy for a significant change) so they don't change their orbit significantly nor often.

Ref: https://sos.noaa.gov/catalog/datasets/space-trash-and-satell...

> But we know where all the planes are, and actively monitor and move them around to avoid collisions.

Do you think they don't know where their satellites are?

NASA & the ESA actively monitors all satellites and actually maintains a database of every little piece of space debris they find (payload fairings, failed satellites, etc). They determine the orbit and track it until it falls back to earth.

This is a fun site for tracking stuff in space:

http://stuffin.space/

> But we know where all the planes are

We really don't. We mostly know for commercial flights, but not so much for general aviation. What aviation does is have zones around airports with restricted airspace that is well-controlled.

But we can ground airplanes in a matter of hours. It doesn't really feel comparable.

* Altitude is essentially the same 6300km vs 6700km, so satellites aren't signficantly more spread out.

* Those 20k planes don't all fly at the same time.

* Retired / Broken planes don't fly, satellites may still be on orbit for decades.

* There are no debris flying in the sky at 11000 km/h

* Planes can adjust their path at will instantly for avoidance.

* Planes can be grounded instantly if we need to.

Orbital space is a limited resource that gets depleted very fast and recovers very slowly. We are talking about launching in the next ten years 5x the total number of satellites that were ever launched so far. I am sure humans in 50 years would still be able to launch a thing or two in space as well.

This is an actual problem, and unlike for planes, once the problem is apparent, you can't just take some of them out of the sky while you figure out a solution.

> Those 20k planes don't all fly at the same time.

They absolutely do. Check out https://www.flightradar24.com, there are currently 15,673 planes in the air worldwide at the moment I am typing this comment.

Fair point, but does that really change the conclusion?

Broken planes fall down, while satellites create space debris.

Dead sats in LEO fall.

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