Wednesday, March 04, 2009

Satellite Collisions

If something is worth doing its worth overdoing. So rather then continue to explore the massive conspiracy against life that is nuclear weapons I want to look at satellites.

"In an unprecedented space collision, a commercial Iridium communications satellite and a defunct Russian satellite ran into each other Tuesday above northern Siberia, creating a cloud of wreckage, officials said today."

There are all sorts of worries here about the effects of shards of satellite debris hurtling round the earth. Mainly though there are incredibly cool graphics of stuff smashing together.

Now I believe thinking about nuclear submarines as wandering particles (as i did here) makes sense on the grounds they are supposed to act in a random manner. Satellites however are deliberately put into set orbits to exclude collisions. They do change path occasionally though based on fuel leaks, gravity effects or being moved for operational reasons but they do not change path often enough for this model to be anything like a good fit. But if we did think of satellites as particles in a box how often would there be hits? If you are interested in a better back of the envelope there is one here.

"The Iridium satellite spanned about 5 meters across its solar arrays. Strela-2M used gravity gradient stabilization, and probably spanned 17 meters including the gravity boom. When calculating collision probabilities, it's important to remember that booms and antennae mean that many satellites have much larger cross-sections than the size of their main body would imply."

Number of particles=300 satellites
Size of particles= 2 meterish sphere

speed: 8000 mps

size of box= 0.06370550904E+12 cubic kilometers
as in earth Mean radius is 6,371.0 km. So sphere of size (6,371.0 km + 800) - sphere of size (6,371.0 km + 700) is the total area.

total volume of satellite = 600 cubic meters
satellite per unit area= 600/0.06370550904E+12 cubic kilometers

A java program to calculate this is below

class Sat {
public static void main(String[] args) {
int numPart=300;//sat number
int sizePart=2; // sat sizeg.
int speed=8000;//sat speed
Double below=new Double (1d);
below=1.41421356*3.14159265*2;//sqrt(2)*pr*r is part of mean free path sum
Double sizeBox =new Double(63705509040000000000d);//areas sats are in
double totalSat= numPart*sizePart;//total volume of sats
double SatPerUnit=totalSat/sizeBox;//how many sats per unit area?
Double meanFreePath=new Double(1d);
meanFreePath=1/(below*(1/sizeBox));//mean free path calculation
Double often= new Double(1d);
System.out.println("Satelites should hit every
"+often+" years");

Satellites should hit every 1.42E7 years. Which makes me fairly sure I've gotten my zeroes wrong somewhere.

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