Undergrad Does all orbiting space debris eventually fall and why?

[Jonathan212]

Just read somewhere that we have left some 500,000 pieces of debris orbiting around earth. Some probably are near enough to touch a little atmosphere so it is reasonable to expect they will fall eventually. But what about the ones a little further? Will they never return to earth?

 

[RPinPA]

The main cause of the orbital decay is atmospheric drag. Even the tiny bit of atmosphere in low Earth orbit, which I believe is better than any vacuum we can produce on Earth [I'm sure somebody will ding me on that; meanwhile I'll try to track down some numbers for comparison] is enough to cause significant drag at orbital speeds.

So the lifetime increases with altitude as the atmospheric density decreases. I found one estimate of lifetimes here:
https://www.spaceacademy.net.au/watch/debris/orblife.htm

$\begin{array}{|l|l|} \hline \text{Satellite Altitude} & \text{Lifetime} \\ \hline \text{200 km} & \text{ 1 day} \\ \hline \text{300 km} & \text{ 1 month } \\ \hline \text{400 km} & \text{ 1 year } \\ \hline \text{500 km } & \text{ 10 years } \\ \hline \text{700 km } & \text{100 years } \\ \hline \text{900 km } & \text{1000 years } \\ \hline \end{array}$

Is 1000 years long enough to consider "forever"? Notice that we're only at 900 km in this table, and geosynchronous altitude is 36000 km, so I think it's safe to say that geosynchronous satellites are not in danger of falling.

 

[RPinPA]

Trying to answer the question I raised above (how does "vacuum" in orbit compare to "vacuum" on earth?) led me first to this page:
https://web.archive.org/web/20060513193723/http://modelweb.gsfc.nasa.gov/atmos/jacchia.html

That's an archived version of the official NASA atmosphere model that was used for shuttle missions. Didn't find any data though.
Here's another paper, dated 1982, that has some charts. https://spaceweather.usu.edu/files/chapters_1_3.pdf
According to Figure 3, p. 20, the mass density at 300 km is $10^{-10}$ to $10^{-11}$ kg/m$^3$ while at 900 km it's $10^{-13}$ to $10^{-15}$ kg/m$^3$

The best artificial vacuum on this chart appears to be the Molecular Beam Epitaxy at $10^5$ to $10^7$ molecules per cm$^3$. Using 29 gm as the average molecular weight of air I get $10^5$ molecules = about $5 \times 10^{-15}$ kg/m$^3$ so actually the very best vacuums these days are comparable to the 900 km atmosphere. (If I did the calculation right). Pretty good.

 

[Jonathan212]

at 900 km it's 10^-13 to 10^-15 kg/m3

The Avogadro number comes to mind. As in, how many molecules per m3 at moon distance.

 

[Tom.G]

Even the tiny bit of atmosphere in low Earth orbit, which I believe is better than any vacuum we can produce on Earth [I'm sure somebody will ding me on that;

Well, if you insist.

It looks like instellar medium is about 10^-10mbar and the Large Hadron Collider (LHC) at CERN betters it by a factor of ten at 10^-11mbar. But they work REALLY hard at it!

https://home.cern/science/engineering/vacuum-empty-interstellar-space

 

[LURCH]

Notice that we're only at 900 km in this table, and geosynchronous altitude is 36000 km, so I think it's safe to say that geosynchronous satellites are not in danger of falling.

Plus the fact that I don’t think geosynchronous satellites would experience any overal “drag” from what little atmosphere they encounter.

There are, of course, some schemes in development to bring down space junk in a controlled way. Every one of those that I’ve seen looks enormously expensive, complicated, and likely to fail. I’ve always thought that the best approach would be to simply give “atmospheric drag” a helping hand. Put a small pocket of atmosphere in the satellite’s path, and make it lose some orbital velocity.