19 February 2009

You may have heard of the recent fender bender in outer space between an Iridium satellite and a “defunct” Russian satellite:

Satellite collision could pose space threat – Crash creates debris; slight risk to space station, minor impact on Iridium

MSNBC.com
12 Feb 2009

Russian and U.S. experts say the first-ever collision between two satellites has created clouds of debris that could threaten other unmanned spacecraft.

Russia’s Mission Control spokesman Valery Lyndin says there is little risk to the international space station with three crew members aboard.

Lyndin said Thursday that officials would monitor the debris from Tuesday’s collision to make sure no fragments get near the station. He said the station’s orbit was adjusted in the past to avoid debris.

Other Russian and U.S. officials warn that satellites in nearby orbits could be damaged.

The smashup occured over Siberia when a derelict Russian military communications satellite crossed paths with a U.S. Iridium satellite.

The two big communications satellites collided in the first-ever crash of two intact spacecraft in orbit, shooting out a pair of massive debris clouds and posing a slight risk to the international space station.

NASA said it will take weeks to determine the full magnitude of the crash, which occurred nearly 500 miles (800 kilometers) over Siberia on Tuesday.

Okay, so let’s think about this, because I don’t buy it. Why not?

Earth is big. In fact, according to Google, the radius of earth is 6,378.1 kilometers. The collision occurred 800km over the surface of the earth. That gives a sphere with a radius of 7,178.1 km. The equation to compute the surface area of a sphere is as follows:

Sphere Surface Area = 4 * π * r²

“r” is the radius of the sphere. So, in the case of the imaginary sphere around the earth that would contain the satellite collision, its surface area is about 647,483,749 square kilometers.

Now, according to SpaceFlightNow.com:

U.S. STRATCOM routinely tracks about 18,000 objects in space, including satellites and debris, that are 3.9 inches across or larger.

That’s all objects in space 3.9 inches across or larger, including all satellites. 18,000 objects. So, if we perform some simple mathematics and divide the total surface area of our “satellite sphere” by the number of objects that U.S. STRATCOM claims are up there in space around the planet, we get:

647,483,749 km² / 18,000 objects = 35,971 km² per object (roughly)

Now let’s check Wikipedia.org for some surface area numbers:

1290 km²    = Los Angeles, California, USA
10,991 km²  = Jamaica
301,230 km² = Italy

Well, isn’t that a daisy? Each of the 18,000 objects in space – many of which are teeny-tiny – have a sizable chunk of space: almost 28 times the size of LA, over three times the area of Jamaica, or about 12% of the area of Italy.

You might think to yourself that this isn’t a terribly large amount of space. After all, Italy isn’t very big, right?

Not all the objects floating around in space are on the same “surface”. They are at many different altitudes above the earth. In addition, the biggest objects, satellites, have very different altitudes and orbits. That greatly reduces the chances that any two objects will collide with one another.

And if that isn’t good enough for you, others have done some even more impressive calculations with the information available:

U.S. STRATCOM routinely tracks about 18,000 objects in space, including satellites and debris, that are 3.9 inches across or larger.

From this quotation, I conclude there is a database containing information about position, velocity and direction of the motion of all such objects. As I could further read:

Tracking priority and ‘conjunction analysis’ – identifying which objects may pose a threat to manned spacecraft – is the first priority.

Other priority, as I suspect, is avoiding collisions by expensive orbital installations, like satellites.

Considering facts that:

satellites are guidable, at least those which are functional, there are available sufficient computing potential in order that US STRATCOM tracked any collision possibilities at least few days ahead, estimated maximum chance of collision of two satellites moving with speed 0,51 km per second making one turn around globe per day on a random, variable but perpendicular orbits between 450 and 850 km above Earth is like once in 483 mln years (I assumed satellite to be cubes with an edge of 10 meters). There no possibility for an accidental collision.
We can conclude then, there is a false information in cited article that is quite probable when contrasted with the calculated propability of an accidental collision.

The chances of two satellites with varying orbits between 450 and 850 kilometers above earth is about 1 in 483,000,000 years.

Now, I’m no physicist or mathematician. But I also wasn’t born yesterday.

It seems highly unlikely that the story we’re being told is true. So, what really happened up there between the US and Russian satellites? Who knows!

So why do I care? It’s the principle of the thing. If I’m told that a Mac computer with a G5 processor is X number of times faster than a Pentium 4, and I know that’s not true because I understand a thing or two about processor architecture, then somebody is lying and that makes me mad.

Similarly, if somebody tries to blow smoke up my bum about an “accidental satellite collision” when it seems highly unlikely because I know a thing or two about satellites and mathematics, well, that makes me mad, too.

And it should make you mad, as well. After all, your tax dollars are paying for it. Are you happy when you take your PC in for service and pay the guy behind the counter a bunch of money, and he lies to you and tells you its hopelessly broken and you need to buy a new one?

But hey, if you enjoy paying people to lie to you, knock yourself out! You’ll be doing the rest of us a big favor.

Satellite Fender Bender: I don’t think so
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