The numbers assume 70% uptake among these customers -- which may or may not be pessimistic.
The numbers also assume 0% uptake among anyone near these people that are not one of these customers. This is probably a little optimistic from a capacity planning perspective.
> just as some North American customers receive service before global coverage was available.
This was a feature of where initial ground stations were located, not of orbital dynamics. A given high inclination short-orbit-period satellite serves all longitudes equally, and the distribution of latitudes it serves is purely a function of its inclination.
Their are several ways to can synchronize the latitudes and longitudes such that you get a repeating pattern. This lets you cover the continental US without having global coverage.
> Their are several ways to can synchronize the latitudes and longitudes such that you get a repeating pattern. This lets you cover the continental US without having global coverage.
This is seriously confused. The Earth turns under that repeating pattern, and the turning of the Earth is asynchronous unless the period of rotation is an integer multiple of the orbital period (which it isn't).
We're in the peak hour right now. This is Starlink. There's no magical favoring of North America (well, except we have a non-operational "train" of new launches overhead). https://imgur.com/a/h94WRsQ
The only thing you can really do is pick your inclination wisely.
Using integer multiples are the obvious, but not only choice. If you look at this visualization you see a higher density coverage over Europe and parts of North America. That’s what let’s them roll out early as the gaps at the equator eventually get filled in. http://www.circleid.com/images/uploads/12233d.jpg
It’s also a significant cost saving measure, though a lot of time is wasted in the band over the Southern Hemisphere it’s still a net win due to global population density from Europe, North America, and Asia. Note, the actual effect is more pronounced as lines of longitude vary their width. But I couldn’t find a better projection.
> If you look at this visualization you see a higher density coverage over Europe and parts of North America. That’s what let’s them roll out early as the gaps at the equator eventually get filled in.
So, you've chosen to just show me an illustration of the sole effect in play, that I've been mentionng to you all day long?
9 hours ago "satellites in highly inclined orbits spend more time around the poles."
5 hours ago "A given high inclination short-orbit-period satellite serves all longitudes equally, and the distribution of latitudes it serves is purely a function of its inclination."
1 hour ago "The only thing you can really do is pick your inclination wisely."
This is not favoring the US. It is favoring things a bit less than 53 degrees North and South (the inclination is 53 degrees). Each satellite spends time up there (down there?) apparently reversing its motion from slightly northwards to slightly southwards, painting a big 'U' in the sky.
And you think this somehow invalidates the data in the study? The study assumed SpaceX's actual constellation dynamics. There's no way to favor North America "more" than the study does.
Edit: Whatever it’s 2:30 am here I am just beating a dead horse.
Not quite I am saying the effect demonstrated is more significant than that was suggesting.
The distance between lines of latitude deceases as you move north. That’s what allows for 24/7/365 coverage in the continental US before the Equator.
Anyway it’s also not just about time spent near though not reaching the poles. The effect is also significant at 30 degrees North vs the Equator and thus the entire continual US benefits.
PS: As to 52 degrees North, much like over the ocean satellites can reach further south than just the area beneath them. Which is why the constitution reaches further north than seems optimal at first glance.
You said "North America" vs. global coverage. I've been mentioning inclination all day long and that yes, inclined orbits spend less time near the equator than at the northern and southern extrema of their orbits. You've insisted that something else in play. Stop trying to save face-- it's OK to not fully understand something.
> PS: As to 52 degrees North, much like over the ocean satellites can reach further south than just the area beneath them. Which is why the constitution reaches further north than seems optimal at first glance.
FFS, broski. Do you read? "It is favoring things a bit less than 53 degrees North and South (the inclination is 53 degrees)"
> The distance between lines of latitude deceases as you move north. That’s what allows for 24/7/365 coverage in the continental US before the Equator.
How does that work? Do you mean longitude? You seemingly use latitude and longitude interchangeably in our conversation. Satellites spend more time at their northern/southern extrema, because ... sine and cosine spend more time near 1 than near 0. And, of course, yes, there's less total land area far north than near the equator.
Your diagram has the actual footprints drawn and they're appropriately elongated when the satellite is north or south. There's no further magical effect based on map projection. The study I cited appropriately adjusts for satellite coverage density but you somehow suggested SpaceX could further concentrate satellites over CONUS beyond the study's analysis, which is how we got onto this entire track. They can't, can they?
I am not making a time argument alone, it’s very important but not the only effect. Lines of longitude converge at the poles. the same effect means lines of latitude get shorter as you move north from 40,000 at the equator, to ever shorter distances moving north until it’s a point at the North Pole.
As the coverage area is a sphere in reality, it should look stretched east/west on a https://en.wikipedia.org/wiki/Mercator_projection as you move north. That pushes full 24/7 coverage slightly south on a 400 satellite constellation. But still enough to cover the continental US at 400 satellite while having gaps at the equator. This is intended behavior as it increases redundancy over the US and population density and incomes are lower at the equator.
As to the US vs North America again I was trying to say different things. The equator pass through South America therefore all of North America benefits. However, only the continental US benefits enough for a 400 satellite network vs 1200 to provide 24/7 coverage.
You mean a circle projected onto a sphere. Or the intersection of a cone with a sphere's surface. Or I don't even know what you mean.
Latitude and longitude are just a crummy coordinate system.
The reason why a given point has more satellite coverage is simply because the circles are on the northern and southern extents of the satellite's movement more of the time. It really is that simple. You're scrunching yourself all up with map projections, etc. If you want, we can go all the way through the spherical trig and derive the exact distribution.
Jeez dude. Just no. Yes, it would be sqooshed on e.g. an equirectangular projection, but not a Mercator. You linked the Wikipedia article. It's right there at the top of the page.
"As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other. In accomplishing this, the unavoidable east–west stretching of the map, which increases as distance away from the equator increases, is accompanied in the Mercator projection by a corresponding north–south stretching, so that at every point location the east–west scale is the same as the north–south scale, making it a conformal map projection."
That's why the satellite footprints on the Mercator projection map that you shared are (correctly) drawn as circles that are getting bigger in apparent size, instead of ellipses.
At the school that I now teach at part-time, we explain this in 5th grade.
> As to the US vs North America again I was trying to say different things. The equator pass through South America therefore all of North America benefits. However, only the continental US benefits enough for a 400 satellite network vs 1200 to provide 24/7 coverage.
OK, which is already modelled in the study that you were responding to. But you implied that Starlink could further move satellites towards CONUS beyond what's modelled. And now you're handwaving about orbital dynamics when I've been mentioning that inclination improves coverage at the northern and southern extremes since the beginning of our conversation. What are you looking to accomplish, exactly? At some point you're just embarrassing yourself.
I was part of a team retained by Starlink doing early feasibility study of optical satellite to satellite links, deriving control system pointing requirements based on relative movement between SV's in various choices of inclined orbit. It's somewhat cringe that you keep trying to explain (wrongly) to me how this works.
P.S. There's one minor effect we've not discussed. It doesn't increase coverage, but it makes individual satellite passes longer. The Earth rotates in the same direction as the satellite is apparently moving near its northern/southern extremes, which lengthens satellite pass times.
The numbers also assume 0% uptake among anyone near these people that are not one of these customers. This is probably a little optimistic from a capacity planning perspective.
> just as some North American customers receive service before global coverage was available.
This was a feature of where initial ground stations were located, not of orbital dynamics. A given high inclination short-orbit-period satellite serves all longitudes equally, and the distribution of latitudes it serves is purely a function of its inclination.