Nice, erm... altitudes, let's see what we can do there :P
but argle blargle! another person who doesn't understand geostationary/micrastationary orbits apparently :P
geostationary orbits can only be stationary above points on the equator, if you put it 60°N;-140°W (also, isn't -140°W==140°E) and push it at the required speed to orbit it (obviously you don't just place satellites and push them, but you know what i mean) after 12 hours it would be at -60°N;-140°W (60°S,140°E) 12 hours and it would be back at 60°N,-140°W(60°N,140°E) 12 hours at it would be back at -60°N,-140°W(60°S,140°E) see the pattern? hmm, if you want something over 60°N;-140°W all the time though, you have to have a degree of "not-nearness" you're willing to cope with :P
(you also need more satellites)
Basically, space the satellites around so that as one heads from 60°N to -60°N(60°S), another is coming up. how many satellites are you willing to afford?
2 satellites:
put 1 up at 60°N,140°E and push at T-0hours, then 12 hours later put one at 60°N,140°E and push.
Maximum distance of nearest satellite from 60°N: 60° (they will be at 0°N,140°E when they meet and swap priority (unless you want to do whatever you want to do when they're below the equator too, energy harvesting sounds like something that can be done wherever you are, which actually might mean it would make more sense to just put 1 satellite in micrastationary orbit over the equator :P)
I shall continue as if it is necessary to have a satellite over 60°N,140°E which it may well be, sounds pretty classified...
3 satellites:
put #1 at 60°N,140°E at T-0hours, #2 at 60°N,140°E at T+8hours, #3 at 60°N,140°E at T+16hours
Maximum distance of nearest sattelite from 60°N: hmm... this is a more conplex calculation... (as they will sweep faster over the latitude lines as they get nearer to the equator... I might be able to guestimate using a sine wave :P)
*does some calculations*
T=24/S
degrees away = cos(((T/2)/360)*24)*60 = cos((((24/S)/2)/360)*24)*60 = cos(288/(360S))*60 = cos(4/(5S))*60
I think this should be quite accurate but i wouldn't say 100%
3 satellites would mean the maximum distance to the nearest one would be... fuck these calculations are wrong apparently.... oop, yeah i see, stupid mistake
T=24/S
degrees away from equator = cos(((T/2)/24)*360)*60 = cos((((24/S)/2)/24)*360)*60 = cos(180/S)*60
degrees away = (1-cos(180/S))*60
ok, the maximum distance to nearest satellite with 3 satellites would be: 30°
maximum distance to nearest satellite with 4 satellites: 17.57359°
maximum distance to nearest satellite with 5 satellites: 11.45898°
6 satellites: 8.03848°
7 satellites: 5.94187°
8 satellites: 4.56723°
9 satellites: 3.61844°
10 satellites: 2.93661°
15 satellites: 1.31114°
20 satellites: 0.73869°
25 satellites: 0.47312°
30 satellites: 0.32869°
40 satellites: 0.18496°
50 satellites: 0.11840°
75 satellites: 0.05263°
100 satellites: 0.02961°
also, handily as micras is a totally perfect sphere *glares at anyone who disagrees and threatens to go back to
this model* this means that the angle to the nearest satellite will be the angle on that list from straight up.
*draws a picture*
so if you wanted to be able to look down an take arial photographs at all times of day and night, you would want a shallow angle, 5degrees or so...
ok, for the other 2 of those 3 satellites i have to change 60degrees to 40 and 50 respectively...
I'll make a speadsheet
gah, openoffice calc works in radians
Where the highest latitude is 60°:
Maximum angle to nearest satellite with 1 satellite: 120°
Maximum angle to nearest satellite with 2 satellites: 60°
3 satellites: 30°
4 satellites: 17.5735931288071°
5 satellites: 11.4589803375032°
6 satellites: 8.03847577293368°
7 satellites: 5.94186792585485°
8 satellites: 4.5672280493228°
9 satellites: 3.61844275284549°
10 satellites: 2.93660902229079°
15 satellites: 1.31114395597166°
20 satellites: 0.738699564291734°
25 satellites: 0.473117921131327°
30 satellites: 0.328686277903603°
40 satellites: 0.184959976012322°
50 satellites: 0.118396294303706°
75 satellites: 0.052630194068497°
100 satellites: 0.029606378056104°
Where the highest latitude is 50°:
Maximum angle to nearest satellite with 1 satellite: 100°
Maximum angle to nearest satellite with 2 satellites: 50°
3 satellites: 25°
4 satellites: 14.6446609406726°
5 satellites: 9.54915028125263°
6 satellites: 6.69872981077806°
7 satellites: 4.95155660487904°
8 satellites: 3.80602337443566°
9 satellites: 3.01536896070458°
10 satellites: 2.44717418524232°
15 satellites: 1.09261996330972°
20 satellites: 0.615582970243112°
25 satellites: 0.394264934276106°
30 satellites: 0.273905231586335°
40 satellites: 0.154133313343602°
50 satellites: 0.0986635785864221°
75 satellites: 0.0438584950570808°
100 satellites: 0.02467198171342°
Where the highest latitude is 40°:
Maximum angle to nearest satellite with 1 satellite: 80°
Maximum angle to nearest satellite with 2 satellites: 40°
3 satellites: 20°
4 satellites: 11.7157287525381°
5 satellites: 7.6393202250021°
6 satellites: 5.35898384862245°
7 satellites: 3.96124528390323°
8 satellites: 3.04481869954853°
9 satellites: 2.41229516856366°
10 satellites: 1.95773934819386°
15 satellites: 0.874095970647772°
20 satellites: 0.492466376194489°
25 satellites: 0.315411947420885°
30 satellites: 0.219124185269068°
40 satellites: 0.123306650674881°
50 satellites: 0.0789308628691376°
75 satellites: 0.0350867960456647°
100 satellites: 0.019737585370736°
It's hardly rocket science :P
I'm not 100% certain they're correct to over 9000 decimal places, but they're damn close. (this is simply a disclaimer in case bill comes here, he will find a minor error in my calculations :P)
