I'm happy to read a lecture for dummies but I should say upfront that I have been presuming that an homogenous distribution of sats is neither desirable or technically required. So while I get the notion that 45k sats spread evenly over the earth surface results in about a 100 x 100 km cell area and it has a ~ 16 Gbps bandwidth, I accept that sat coverage overlap can change the bandwidth areal density drastically.
Few things:
--Homogeneous distribution of satellites is impossible
--The limit on data for a single satellite is primarily determined by its beamwidth (there are hundreds if not thousands of "hopping" beams on a starlink), or more precisely the area that beam covers on the ground, and the PFD (power flux density) of that beam. The narrower the beam the better, because you can more or less transmit the same amount of data to fewer users, but the narrower the beam the more complex everything gets (you need more beams which means you need more processing which means you need more power which means your sat is bigger, and so on). PFD is basically a hard limit regulated by the ITU and FCC. You can't go above whatever level you get approved for. The combination of the two makes for an asymptotically more difficult effort to add user density. As
@doghousePVD has indicated, ~hundreds of users per square mile is about the limit of 45k worth of satellites (which, again, will not happen for a decade if ever), and that's basically an order magnitude more rural density than the burbs. So, satellite internet WILL NEVER BE the primary connectivity solution for members of the human race. From a residential perspective anyway, it will be for infrastructurally underserved people that actually have enough money to afford internet in the first place, which, whether we like it or not, is the US and Canada for the foreseeable future. Of course there will be global customer base, but the majority of paying customers will be in North America.
Can you explain why the first ~ 600 or sats provided coverage to Northern USA and Southern Canada ? How wide a west-east swath did it include ?
To add color to what's already been stated, the way orbits work, satellites converge near the top and bottom of their orbits (from a latitude perspective) and are generally farthest apart from their neighbors at the equator, which means any constellation will always have higher satellite density near the high latitudes (plus and minus) and low density near the equator. So even if you don't have enough satellite density to provide meaningful service at the equator you likely have enough sat density at high latitudes to provide, in this case, beta service. These high density bands circle the globe in the high 40's and low 50's equally in the north and south, but Starlink sats also [currently] need to have a ground station in view to provide service. SpaceX wisely decided to put their first ground stations in North America, which is why the beta is in NA. Users in Europe have the same satellite density as an equivalent latitude in NA, its just that there are no (or at least not a useable density) of Starlink ground stations there yet.
Here's a decent animation, but there are plenty out there to study:
I'm not understanding why a ring of reception at ~ 50 degrees lat developed from an orbit inclination of 52 degrees relative to the equator
Those are the latitudes where there is the most satellite density. Users above 53 degrees can see satellites as well, but someone at 55° will see many fewer sats than someone at 51° because of the way the trigonometry works.
I also do not understand the calculation of how much surface area on earth is covered by a single sat (ignoring the fact for a moment that the sat is navigating the globe, just imaging it standing still for a moment.)
The satellite's field of view is a cone, which projects on the ground as a circle (just like a flashlight). The radius of that circle is ~1000km, so each satellite can see ~3M km^2.
The issue is that the satellite cannot provide full service to everyone in that area, so the constellation has a gazillion satellites such that there many many overlapping coverage circles, allowing the constellation to intelligently manage traffic by balancing otherwise over/underused satellites as well as onboard resources like processing power, DC power, thermal, etc.
As to why .8 degrees difference that might be to keep them from having the same clumping all the time?
Depends on how much higher the orbit is, but if they're very close in altitude the inclination offset prevents upstairs neighbors from flying over downstairs neighbors for an extended period of time, instead resulting in more crossing orbits.
