## 2007-02-03

### Application of Sun Zi (i): China's anti-satellite test, and the non-issue of space trash

The Economist disappointed me greatly in its recent analysis of China's anti-satellite missile test recently.

It blindly followed the unsubstantiated claim that the debris of blowing up a low orbit satellite will endanger the space for ages, by claiming,
• "What irony if China, which takes pride in its own recent manned space flights, were to find its ambitions to put a man on the moon and eventually to build a space station set back someday by the still ricocheting rubble from its own irresponsible action".
I am willing to bet half of my wealth against this Economist editor that it won't happen.

The simple fact is, not only the threat is tiny - consider breaking a television and throw scatter it across the Pacific Ocean, what is the chance of a swimmer finding a piece of the TV - it is also against the Newton's law of physics that any high schooler who has done physics would understand.

Let me explain this with a few facts here
1. Unpowered object surrounding the earth can only stay on the orbit when the potential (gravitational) energy (determined by altitude) equals the kinetic energy (determined by speed). Therefore, there is only one solution for altitude, the geosynchronous altitude
2. Therefore, any debris from blowing up a satellite will end up in 3 places: a) spiral down to earth and vaporize when it enters the atmosphere (low energy debris); b) spiral out to outer space and leave the earth's gravitational field for good (high energy debris); c) ends up at the synbronous orbit (just the right energy)
3. The % of debris that ends up in the geosynchronous orbit is extremely small. An analogy would be to thrown a handful of sand and count the numbers of sand that falls exactly on a very thin line 10 meters away
This is the basic physics that the Economist editor could have tried to understand, or ask a high school teacher, before writing that article. (I still have great respect for the Economist as we are all human, who makes mistakes)

----

The Newsweek has provided very good background information of this test. But it made the same wrong claim about debris as the Economist. Furthermore, it made two seriously flawed arguments.
• 1) It claimed that China's test will provide the space-hawks in US with an excuse for an arms race in space. Well, the simple fact is, for all these years, they have been racing against themselves, and it is not China's responsibility or China's business to change the mind of the US. The people in the US should be responsible for the behaviors of US hawks.
• So far the US people have been complacent on Bush's belligerent behaviors toward the rest of the world, and Bush got re-elected in 2004. Al Qaeda's claim that American people are collectively responsible for what its government does does have a point. This is like saying that if the Chinese people "behaves" then the Chinese government will give them democracy.
• Therefore, any argument that whatever China does would affect the minds or impacts of the US hawks are purely bullshits.

• 2) The second mistake in Newsweek's conclusion is that,
• "Some pundits have argued that the test was meant merely to pressure the United States into finally agreeing to a treaty to limit space weapons. But this argument doesn't hold water. For one thing, by obliterating one of its old orbiting weather sensors, China also managed to destroy an informal two-decade-old moratorium on such tests. This would be a strange way to promote arms control, as would recent Chinese moves to develop lasers that could disable American satellites."
• I entirely disagree.
1. Firstly, this is a very valid way to begin a negotiation to limit space weapon. As so far nothing else suceeded, there could be nothing worse.
2. Secondly, if we look at this from the purely strategic point of view (i.e. disregarding political ideology and the like). The only victim in an arms race in space is US, as no one else has any real strategic in the space that can become target of such an arms race! So from China's perspective it is a great move, even though it might not have been intended as such (more likely a result of uncontrolled vneture from local/divisional commanders, as speculated by Newsweek and others).
3. Thirdly, this signifies a new application of games theory to achieve peace as first theorized by Nobel Laureate Schelling's theory. In the old context of the game theory one talks about mutual destruction. Today the balance of power has been disrupted, as the WPMD (weapon of precise mass destruction) the US is applying to Iraq and Yugoslavia runs in parallel with Hiroshima in 1945. By demonstrating that it is very cheap and easy to disable such WPMD, China has shown the world a way to control this kind of crazy warfare. When winning a war is much less easy, everybody will be more careful before waging a war. The world will be a safer place as a result.
All said, a brilliant demonstration of Sun Zi. Achieving the strategic objective, or alleviating the star war threat, by not waging a war -- in fact, by not even technically conducted a weapon test! Technically this is no different from using dynamite to dismantle an old building.

In the next few days, when I find time, I will write about another brilliant demonstration Sun Zi, by one of the smartest politician on the other side of the strait yesrterday. You probably guess it correctly who I am going to talk about.

Brough said...

While agree with your politics, your physics is a little off. There are plenty of stable orbits besides the geostationary orbit. For example, the moon is in a stable orbit but takes roughly 28 days to complete one orbit of the earth. A geostationary orbit just happens to have a period that exactly matches the rotation period of the earth. There are also lower orbits that are stable. Problems arises when the orbit is low enough to encounter drag from the upper upper atmosphere. Then the speed of the orbiting object slows due to friction and the body eventually falls to earth (usually burning up as it enters the lower,denser parts of the atmosphere).
There is a certain amount of junk in orbit around the earth. The article in Wikipedia,
http://en.wikipedia.org/wiki/Space_debris
is a reasonable presentation of current conditions.
But you are correct, the Chinese destruction of an obsolete satellite is unlikely to have significant repercussions for anyone. Indeed, if they took care to hit it in the direction that also slowed it down (I don't know that they did this), then most of the resulting debris would be guaranteed to burn up.

Brough said...

PS: Thanks for the very interesting coverage!

hoi said...

i am new here. Mr. Sun, your articles are very interesting.

My understanding is the point Economist makes clear is at the start of that paragraph you didn't not quote: "As a purely practical matter, there are better ways of dealing with redundant satellites." i very much agree that the firing at satellite is a gesture to demonstrate power rather than anything.

It follows that "What irony if" which says much about how unlikely such thing happens. Still i agree with you that is an overstatement.

Public Servant said...

brough, the moon is not in a stable orbit, and it's getting away from the earth at the speed of 1 and half inch each year.

the argument of space debris is purely garbage, let's do some calculation here:

The earth's radius is 6335.437 kms, the height of the destoyed satellite was 800 kms, so in the worst case scenario, where the fragments only spread in their own altitude, the area they have to cover is:

4pi * (6335.437 + 800)^2 = 639 million square kilometers

1 square km = 1000 * 1000 = 1 million square meters

Now, say there are 10000 satellites in the height, and say they are as big as 100 square meters, now, they would occupy:

10000 * 100 / (639 * 1 million * 1 million) = 1.56/1 billionth area of the entire orbit. Now, say the destroyed satellites breaks into 1000 pieces, that just increases the probilitiy to 1.56 to 1 million -- you are far more likely to be hit by a car than one of these 10000 satellites being hit by a fragement.

Now, remember the calculation is done in the worst case scenario. Most likely, there aren't 10000 satellites on 800KM orbit, most likely, none of the satellites are as big as 30 meters by 30 meters, most likely, most of the fragments are in different orbits, so the actual probability of any satellite being damaged as most likely orders of magnitude smaller than 1.56 to 1 million. The chance of one of these fragments hitting a missle or spaceship or an astronaut at random is even slimer.

Anonymous said...

China and Russia both tried to get US to join the space peace initiative, but Bush declined, citing the principle of "free action".

So now we are complaining about ASAT test and debris. Let's not forget US did the same test in 1985. Those debris must still be in the space menacing others, no?

-bobby