The timeframe varies widely based on the shape of the object and the altitude. There are something like 5 orders of magnitude pressure difference between an object at 100km and one at 500km which is the difference between deorbiting in days vs years.

There's probably more than 5 orders of magnitude difference between throwing an apple core into the woods and a city's worth of sewage, but both are organic waste. I think the analogy is fairly sound.

While true, there’s also an asymmetry here in that a city can expand their landfill or sewer system capacity- orbital space has a fixed capacity

That's not really true. The "capacity" such as it is is defined by current technological ability to track the assets and respond to changes quickly. There's a whole ton of work to be done there as satellite operators only update their position every few days usually. It should be at least daily and ideally hourly or even by the minute.

WTF? Space is incomprehendibly big. The number of potential landfill locations are very limited.

Isn't this thread discussing a very specific orbital range? The 450k-800k range is big, but I'm not sure I'd classify it as "incomprehensibly big".

Anything orders of magnitude larger than the Pacific Ocean deserves that title IMO.

It’s at least bigger than the surface of the earth :)

Landfills can go underground though! Although I agree that it's unlike we can dig several hundred thousand kilometers :)

Huge constellations with stable orbits under active control are irrelevant. It’s really the a pair of uncontrolled satellites colliding that’s a meaningful risk, and that risk grows exponentially with age. To the point where the difference between 1 day and 1 year is effectively meaningless while the difference between 5 years and 50 years is huge.

The risk grows quadratically in decay time, not exponentially.

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

It seems like it should be quadratic in that double the satellites should get 4x the number of collisions, but satellite orbits don’t start out random. Without stationkeeping initially clear orbits become chaotic in that slight differences in initial position and velocity result in wildly different orbits. That transition results in an exponential increase in risk.

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.

I see your point that it’s not random but an exponential increase wouldn’t result from chaotic changes in orbit. That randomizes, making it quadratic.

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.

Thinking about it more, it could probably be modeled by the intersection of random walks that are initially unable to come into contact. I was thinking that was exponential but it’s presumably some polynomial function with a large exponent that’s eventually bound by a different quadratic function for sufficient values of time.

It would seem to be exponential after the first collision, at least.

If we're launching 15k satellites per year as some people expect, the difference between 1 day deorbit and 5 years deorbit is something like 75,000 satellites.

If the risk of collisions in both scenarios is sub 0.0001%, is it a meaningful difference? Very quickly the risk is dominated by being launched into the wrong orbit.

yes, but if deorbiting in years is sufficient, the difference in time is not relevant.

What? Starlink eventually wants 40,000 satellites - with 5 year lifetimes that'll be 8,000 per year... there are numerous other planned constellations, so figure something like 15,000 LEO per year within a few decades.

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.

>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).

The rule is 5 years. You've given 2 examples under 5 years. If everything is going to re-enter within 5 years without boosting then your point is moot, because even in your "massively more collision risky" example, it still abides by the rules.

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.

Just responding to a comment that said "If deorbiting in years is sufficient, the difference in time is not relevant" where it's obviously relevant.. this doesn't seem remotely controversial.

You're arguing a different thing. The topic was satellite design for satellites under 450km.

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.

Let me put this another way, if I use my computer to send emails, it doesn't matter to me if my ping is 10 milliseconds or 10 femtoseconds.

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.