I live in a dark skies area in the Southwest USA. I frequently see the trains as they are inserted into orbit, but your chance of seeing an individual Starlink satellite is zero. It's like trying to see a single object the size of a picnic table, in the dark, 400km away, going 27,000km/hr.
This is totally incorrect, what do you think you are seeing in the trains? You can easily see each individual satellite. Just after sunset you can see many individual satellites, not just starlink.
They added the sun shields in mid-2020, after several hundred satellites had already been launched. Those remain visible, and make up about 8% of their fleet today.
Kinda makes me wonder what we're going to do about all these satellites in 50-60 years when there's thousands of decommissioned ones floating around.
They deorbit themselves after about 5 years... so if starlink goes tits up, at worst you'll see the satellites for around 5 years. Sooner if they are intentionally deorbited.
Seeing high-albedo LEO satellites in orbit is easy with under a dark sky. I remember seeing individual satellites all the time while camping as a child, I'd see at least 2 per minute, all traveling in the same direction. This was before constellations became a thing.
Let's do a bit of back-of-the-envelope rocket science.
Starlink has satellites in several orbits, but at least one I know they're using is 319mi (they have approval for shells as low as 210mi, but I'm not sure if they're using that yet). A human's central vision is about 60 degrees (NOT the same thing as your full field of view). The radius of the earth ranges between 3950 and 3963 miles. I'll call it 3955 for our purposes.
(3955+319) gives us a radius of 4274 miles. Throw in that 17,000mph (27,000 km/hr) figure, one can determine that a Starlink satellite moves at about 3.78 degrees per minute with respect to the center of Earth.
To make things simpler, (again, back of the envelope), I'm going to calculate this using basic trig. The radius of the earth is much larger than the satellite's orbit, so this shouldn't skew the numbers too much.
Imagine standing on the ground and looking straight upwards into the night sky. At a distance of 319 miles, your 60 degree field of view covers a plane that's 2⋅319⋅tan(30°) = 368 miles wide.
This plane cuts a chord through the satellite's circular orbit. Those two points are 2⋅arcsin(368 / (2⋅4274)) = 4.93 degrees apart.
Knowing both the angle between the two points on the chord and the angular speed of the satellite with respect to Earth, we can determine that the Starlink satellite will spend roughly 1.3 minutes (1 minute and 18 seconds) within your central field of view. So, the satellite is definitely not fast enough for the naked eye to miss it, assuming it's big and/or bright enough.
Normally, you'd be right about a picnic table hundreds of miles away. That's tiny and you'd never see it, no matter what speed it was moving at. However, satellites are highly reflective and because they're sitting high above Earth, they can be hit by sunlight even during the night. Maybe(?) they wouldn't be visible in the problem I just laid out, where you're looking straight up, but turn your head a bit and it becomes feasible.
Throw in the fact that there are thousands of them all marching in a spherical parade around Earth, and it's totally reasonable that they'd be visible from the ground. In fact, there's a whole website dedicated to this very phenomenon: https://findstarlink.com/. If we didn't have so much light pollution on the ground in my neck of the woods, the website indicates that I could see them a couple times a night.
Last summer, maybe two ago, I was camping in the middle of nowhere, laying on a sandy beach after sunset and saw a starlink satellite train go up. It was a truly ethereal experience.
Continuing this "I saw a Starlink train" train, I was in Yosemite doing a stargazing tour (i.e. with a guide using a powerful handheld laser to point out individual stars), and we saw the clean line of "stars" making its way across the sky.
A quick search confirmed for us that it was from a recent Starlink launch, and not aliens.
