Wednesday, May 28, 2008


So when you are bored at work, you end up in weird places. (I know, you are nervous about clicking that link.)

I never appreciated the scale difference between low earth orbit satellites and geostationary ones. I noticed that it seems sort of crowded out there. "How many satellites can actually fit in geostationary orbit?" Well, figuring out that problem seemed much more interesting than examining a huge database of misclassified Accounts Payable.

Here's what I came up with from my searching, rough back of the envelope:

geosynch orbit = 35,600 km
earth width = 12,800 km
circum @ orbit = 263,900 km
+- latitude = 10 dg
+- latitude (tan 10 dg) = 7,400 km
+- altitude = 200 km (higher than that is where sats go to die)
+- positioning of sats = 35 km (margin of error)
min distance between sats = 10 km (made that up)
passing lane east = 35,600 + 35 + 10 + 5 = 35,650-35,800 km
passing lane west = 35,600 - 35 - 10 - 5 = 35,400-35,550 km
# of belts of satellites = 2 (also made up)

Total # of satellite slots @ geostationary orbit = (7400*2/45)*(263,900/45)*2 = 3.86MM.

I'm sure there are more limitations--like it is too expensive to keep satellites in a precise orbit, so most wobble in altitude and latitude. Also, if 70% of the earth is water, you have a lot of coverage where you don't need it. The point is, we can fit a lot more.


Tom said...

Was it you with whom I calculated the number of rolls of paper towels that could fit in a semi trailer, to determine how efficient it was to truck them across the country?

Kaahl said...

No, I don't recall doing that, but it sounds interesting.

Over dinner last night, I ran the problem over with some colleagues (one of which former cal tech astro-physicist) and we were batting around different ways to calculate it. I told them that I tried one approach in particular that just made me feel really dumb--calculating how many 40 km spheres would fit in a sphere circumscribed by the outer geostationary limit and subtracting the number of spheres that would fit in a sphere of the inner geostationary limit. Anyway, even though it was an incorrect approach, I puzzled over it for a bit, and gave up.

Then over dinner, cal tech dude says sphere packing has no closed form solution. Phew.