Actually less than that, as orbits with more decay time have more vertical space.

This is most obvious with geostationary orbit. Over a single year you could have say 10,000 satellites in geostationary orbit with essentially zero risk of collision, but without station keeping risk continues to grow every year those 10,000 satellites drift around.

It looks like inactive geostationary satellites will drift to the same longitudes, and tilt their axis away from the pole. If you have a set of geostationary satellites in that situation, the risk of collision is still quadratic in growth.

The risk is the sum of the pairwise probabilities of collision. So the only way you get super quadratic is if incrementally added satellites have increased pairwise risk with other satellites. It is possible that could be the case, because if you have to pack satellites more tightly, then maybe each satellite has higher pairwise risk with its direct neighbors.

That would still be sub-exponential, unless the collision risk between two satellites got exponentially higher as they get more closely packed. For example, suppose you have a ring of satellites, and you double the number. Then immediately neighboring satellites are twice as close. By basic inequalities you can show that considering the non-neighbor pairs of satellites, they have less than quadrupled the total risk of a collision. So by the master theorem we know the risk of collision would only grow exponentially if there were an exponentially higher risk of collision between two neighboring satellites in terms of the reciprocal of their distance. But that is not the case, is it? You’d expect it to be polynomial. Fewer orbits before the satellite drifts past its neighbor, a smaller expected distance to the neighbor as it drifts past… as with most physics problems these are linear components, multiplied together.

15k satellites per year with a 5 year lifespan and a 1-year decay means you'll be stable at 75k satellites. 5 year lifespan with a 3-year decay means you'll eventually be stable at over 100k satellites in orbit with 30,000 of them 'dead' and decaying. That's a massive difference in collision risk.

Is it? It's a big difference in absolute numbers but that doesn't mean it's a meaningful difference in Risk.

If both numbers are quite small relative to the level of concern, the difference can still be irrelevant.

My point is that it takes more than just looking at the number of satilites to understand risk. You need to do the work to show how the collision chance compares to what an acceptable limit might be. Both cases could be very acceptable (or both cases could be unacceptable).

If something was going to deorbit within 1 minute, or was going to deorbit within 4 years, 6 months... It doesn't matter to the creator, because they don't have to change their design at all to meet the rules.

If something was going to deorbit within 8 years (because they previously had a 25 year allowed limit), they now have to rework the design.

There's plenty of room for debate about if 5 years is adequate, but as it stands, _most_ things (under 500km) will naturally deorbit within the legal time frame anyway even without special consideration.

If deorbiting in years is sufficient, the difference in 1 minute vs 4 years is NOT relevant -> to a satellite builder worried about the law.

If everything deorbits within 5 years, the only way for more things to accumulate is to launch things faster. But that's a separate discussion. If everything launched today is deorbited within 5 years, then in 5 years, all satellites will be new satellites launched after today. If everything launched today is deorbited within 5 months, then in 5 years, all satellites will be new satellites launched after today. Deorbit speed under a threshold has no bearing on accumulation beyond that threshold.

If SpaceX launches a trillion Starlink satellites, and they all deorbit within a year, then yes. it's going to be a very crowded year, and we'll have to drastically rethink how much stuff we have in LEO, but at the same time SpaceX would not be in violation of the 5 year deorbit window, so the issue is about how much stuff we're sending up, and not how fast it de-orbits.

"Amount of junk below 450km, total" and "Amount of junk below 450km, that hasn't deorbited after 5 years" are very different things. You're making points about total, while the original point was about deorbit speed.

One time is 10^12 times longer, but the difference does not matter to me. My emails are still sent and received faster than I can possibly perceived.

    population = arrival rate X duration of visit

I am worried though, do we really build satellites that are expected to only work for 5 years? Are we disincentivizing people from building 20 year satellites this way?

"Gabbard Diagram for Low Earth Orbit 1959-2021"

See how the stuff in the lower left corner speeds up towards the lower left corner? That's low flying debris falling out of space.

- Most debris deorbits naturally in a few years. Any debris causing events or accumulation naturally clears out in a reasonable time frame. It's not like debris at 800-2000km which is the real "Kessler Syndrome" concern where it takes decades or centuries.

- Debris mitigation efforts that are already in place are effective. Limiting debris release during launch and deployments has had a huge positive impact over the last few decades.

- "Traffic control" is a lot easier at these altitudes and debris in this range is well tracked. Obviously this doesn't extend to small stuff (<5cm), but due to active mitigation and natural decay this is less of an issue. Also ground radars are getting better and can actually see a lot of these objects now.