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The animation is accurate. To stay stationary, a satellite has to be 35000km away from the earth, these will be about 500km away. They will move very fast across your line of sight, but have very low latency.

thank you all for clarifying!

Geostationary is around 35,000km, starlink satellites will be around 300-500km, hence the low latency.

They aren't in geostationary, so they won't be stationary (relative to the ground)

It helps with load balancing. Google Bloon planned to automatically geographically appropriate satellite clusters based on real-time demand, so I assume there are similar plans for Star-Link.

Do you mean stationary with respect to the earth, or with respect to each other?

The answer in either case is that they'll be moving, because the low orbits they will be in require it.