Is it realistic to see satellites moving across the sky centuries after humans stopped space activity?
After an age of highly developed technology, including many different satellites in various Earth orbits, humanity loses the technology needed to control those satellites. After many centuries, how realistic is it that you can still occasionally see a satellite moving across the sky (say, at least one every few days)? And if so, how bright would they probably be, and how fast would they be seen moving across the sky?
I'm sure the low-orbit satellites would be long gone because there's still air drag. But I have no idea on how high you have to go to have a satellite survive on its orbit for hundreds of years without active orbit corrections. Also, I guess you'd also have to avoid a Kessler syndrome, as that would effectively remove the satellites as individual bright spots in the sky.
1 answer
Satellites will still be visible.
A couple of characteristics make human satellites easy to see. They are fast and bright. Slow objects are difficult to pick out from the background star field. Faint objects don't emit enough light to be seen by the human eye.
Fast
Let's see how orbital period compares with orbital decay.
| Satellite Altitude | Lifetime | Orbital Period (hh:mm:ss) |
|---|---|---|
| 200 km | 1 day | 01:28:29.65 |
| 300 km | 1 month | 01:30:31.18 |
| 400 km | 1 year | 01:32:33.63 |
| 500 km | 10 years | 01:34:36.98 |
| 700 km | 100 years | 01:38:46.38 |
| 900 km | 1000 years | 01:42:59.33 |
| 5000 km | -- | 03:21:18.64 |
| 10,000 km | -- | 05:47:39.69 |
| 20,000 km | -- | 11:50:36.07 |
| 30,000 km | -- | 19:10:51.27 |
| 36,000 km | -- | 24:07:00.8 |
Decay Source Orbital Period Source The difference in orbital periods between 200km and 900km is only 15%. These speeds should be easy to pick out against the background star field. If humans have regressed to where light pollution isn't a problem anymore, then it should be even easier.
Bright
Brightness will depend on the satellite's inclination toward the viewer, altitude, physical size and orbital position. The larger and lower it is, the brighter it will be.
Lumosity is calculated by $I = C / d^2$ source where I is lumosity, C is the source brightness and d is the distance. For our purposes, we only care about the effects of d.
At 200km, the lumosity of the satellite is reduced by a factor of 40000. At 900km, it's reduced by a factor of 810000 or 20x dimmer than a satellite at 200km.
The Sweet Spot
Satellites between 500km and 900km seem to have the best chance. Their orbital decay is measured in hundreds or thousands of years. They are also low enough that brightness shouldn't be too dim because of distance.
There's plenty of wiggle room on the brightness calculations to plausibly assert that there are lots of visible satellites or only a few.
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