Tropical Coverage and Equatorial Populations

The M288 orbit, at a little more than R_E altitude ( 2R_E radius ) would be visible to 60° north and south on a perfectly round planet without an atmosphere. On the earth, with atmosphere, clouds, and terrain, satellites must be at some elevation ( angle above the horizon ) to be visible; at least 5°, preferably 10°, and a lot more in deep valleys with mountains or ridges towards the equator. Most of the world's population is north of the equator, so the following discussion will focus on the tropics and mid latitudes of the Northern Hemisphere.

Directly on the equator, and three degrees north and south, the M288 orbit will form an arc directly overhead, and have maximum visibility. However, that is also inline with communication satellites in geostationary orbit, and chances are those will be assigned the same frequencies as server sky. So although server sky could have the best coverage in that region, it will probably be forbidden to operate there and compete with comsats in those orbital positions. On the other hand, the narrow band from 3°S to 3°N, and the regions in the far north and south, are less populated than 3°N to 50°N. This narrow equatorial strip, along with the regions above 50°N, can relay through Iridium, Globalstar, and GEO satellites, as well as fiber optic landlines.

Perhaps 90% of Server Sky direct customers will be located in the 3°N to 50°N latitude band, with perhaps 10% in the 3°S to 50°S latitude band.

If you live south of the equator, you probably live north of 45°S, so your coverage will be good. Continue reading only out of sympathy to your friends to the far north. If you live on the sunny side of the mountains, you still need to be able to see over the mountains sunwards of you, but you will do better than the folks in the shadow of those mountains.

Elevation and Coverage

For most, the M288 server sky constellation will form an arc across the southern sky, with the peak of the arc due south and the width of the arc becoming smaller the farther north you go. The width of the arc - the azimuth range, and the portion of the entire ring visible - will be 120° of the orbit in daytime near the equator. At night, a 60° slice is eclipsed by the shadow of the earth ( ( 59.8° = 2 asin( 6378/12789) peak at the equinoxes, 54.4° = 2 asin( 6378 cos(23.44°)/12789 ) at the summer and winter solstices ).

We can compute the "coverage" as the angle of server sky visible with an elevation of at least 5° 2 acos( cos( acos(6378/12789) - 5° ) / cos(latitude ) ), with an equatorial maximum of 110.2°. If the argument is greater than one, there is no visibility, spring and fall latitudes above 55.1°N or below 55.1°N. From that, we can subtract the eclipse angle to compute the coverage at midnight. These are shown as the graphs below, overlaid on Bill Rankin's clever population versus latitude graph.

source:pc02.c base picture:population1K.png

In between dawn and dusk, the coverage of the M288 constellation visible will depend on the relative angle of the eclipse shadow; it will start diminishing by 15 degrees per hour between dusk and 10pm, then increase at 15 degrees per hour from 2pm to dawn. This will make the M288 constellation invisible at midnight at higher latitudes, above acos( cos( acos(6378/12789) - 5° ) / cos( 29.9°) ) or 48.7° north. Sorry, Canada, no direct Server Sky at midnight. Sorry, Scotland, Scandinavia, Moscow, Alaska - no direct Server Sky at all. The largest city north of 55.1°N is Moscow (55°45′N) , with a population of 10.5 million.

Equatorial Conflict Band

The largest cities ( population > 1M ) in the ±3° "GEO conflict" band are:

These cities are representative of a large unserved rural population. Finding some way to serve them without interfering with GEO communications is important.

Solutions for the Equator and Far North

When server sky is well populated, some of the arrays may go in larger 5° inclination torus orbits around the central orbit. Constellations of these arrays may communicate "off axis" with these cities, as well as reaching more cities of in Russia, Scotland, and southern Scandinavia.

Equatorial cities can be served by wider phased array antennas with very narrow beams, designed to miss GEO satellites, which are in well defined angular positions at 1° spacings. At 38GHz, the wavelength is 8mm; a 3 meter wide antenna will make a 4 milliradian or 0.2° degree beam. The antenna can be wide (east-west) and relatively short (north-south) - that will give it accurate longitudinal pointing with the same gain as a squarer antenna. (Check these numbers!)

Northern cities can also be reached by M480 orbits. With an orbital radius of 16756km, a city at 60°N will have a daytime coverage of 46.2° and a midnight coverage of 1.5° not much, but better than nothing.

Southern Hemisphere

The southern hemisphere fares better; besides scientific stations in Antarctica, there are no cities or towns below 55.1°S. The only cities below 48.7°S are Punta Arenas, Chile (population 110K), Rio Grande and Ushuaia, Argentina (both population 67K). Stanley, Falklands (population 2100) just because. Melbourne, Australia, is the southernmost large city (population 4.4 million) and at 37.8° south has a daytime coverage of 87.2° and a minimum midnight coverage of 27.4°. All of populated New Zealand (with a population smaller than Melbourne) is north of 47°S, and Christchurch (population 370K, latitude 43.5°S), has a daytime coverage of 75.8° and a midnight coverage of 15.8°. Rimuhosting, the company serving this website, is headquartered in Cambridge, New Zealand, at 37.5°S, with a daytime coverage of 87.7° and a nighttime coverage of 37.7°

When Server Sky is fully deployed, the service to a particular ground spot will be divided among the nearby population. Places like New Zealand, with low population density and surrounded by ocean, will have the best service, even if they are not very close to the equator. Terrestrial optical fiber will still be optimal for large cities and dense apartment zones. Medium and low density regions that cannot afford universal fiber deployment will remain the best communication customers for a long time.

Conclusion

Server sky M288 will be visible all night in the tropics and southern temperate zones. This will cover the majority of the world's population, most especially the underserved people in the developing world. In time, other services can be developed for those in the extreme north and directly on the equator.