## Help Help, We Are All Going to Die! Oh, Wait, Never Mind

I don't know why I have so much fun fact checking the "science" at green blog "the Thin Green Line," but I do.  Today's exercise:

There are, right now, at least half a million pieces of junk in orbit around our cosmic Pig Pen of a planet. Space junk isn't just an aesthetic problem, either: Even tiny pieces of junk orbit at speeds above 15,000 miles per hour, so even the tiniest bit of debris can cause serious damage to anything it comes into contact with. Space junk threatens satellites, manned space missions and even the International Space Station.

While certainly space junk can be a problem in certain instances, I am constantly left helpless with laughter at the absolute urgency this type of blog approaches every problem.  Here are a couple of things that might help you sleep better at night:

• The speed space junk is traveling is largely irrelevant.  It could be 15,000 mph or 50,000.  The important variable is the closing speed of two objects, not their absolute speed.  And (thanks to our friend Newton) we know that objects in the same stable orbits have to be moving at the same speed.  Now, orbits don't all have to parallel and can cross, yielding real relative velocities, but recognize that since over 95% of these half million objects are less than 4 inches in diameter, its a bit like you and your friends firing guns and having the bullets meet in mid-air.
• The drawing he shows makes the sky seem really cluttered.  But let's just take a small portion of this space.  Let's consider the volume of space between 100 and 500 miles above the Earth's surface.  Using a bit of geometry, this space works out to be 93 trillion cubic miles of volume.  Which means one object, generally less than 4 inches in diameter, in space per every 186,000 cubic miles, which for scale is the equivalent volume to a building 40 stories tall that covers the entire continental United States.

Certainly avoiding these objects is a navigation concern for powered spacecraft, which is why all these pieces of junk are watched in the first place.  But the idea of a space superfund to clean this stuff up is so hilariously expensive (given current tech) and such a staggering waste of resources compared to other uses of those funds that one would only expect to find it on, well, an environmental blog.

1. #### Mike:

I'm no orbital scientist (and enough of a skeptic to find global warming laughable), but space junk is a real problem.
First, satellites are incredibly expensive (and valuable) - some cost billions. Imagine life without GPS, weather satellites, etc.
Second, the problem is real. As space junk proliferates, it collides into other objects and fractures them into more hazardous junk. Because the cost of space junk to other is so large compared to the benefit of your own satellite, it boils down to the classic "tragedy of the commons".
The amount of space junk is increasing exponentially because each collision creates many more pieces of debris. The Chinese made the problem a whole lot worse by testing an antisatellite weapon a few years ago.

----
1) The extreme speeds allow even paint chips to become hazardous.
2) Orbits are somewhat random - high correlation between absolute and relative speed. Not sure if all satellites travel west-east, but they certainly have different north-south paths. Orbits get a lot more random after collisions.
3) These tiny bullets get another shot at destruction many times a day because they orbit so quickly.

The Economist had a series of articles (http://www.economist.com/node/16843825) a few months ago - and they believe the solution is not too costly.

2. #### NormD:

I concur with Mike, but add that we also have and plan to have people in space and a paint chip at 50,000 MPH is deadly. Satellites can and are routinely replaced but a destroyed space hotel would have far reaching effects for the manned use of space.

I wonder if you use similar back-of-the-envelope calcs to show that looking for rogue asteroids is a "waste of resources"?

3. #### Craig:

Typical innumeracy among greenies. It is based on "feelings" which are always right...

4. #### MikeinAppalchia:

The faster, lower- orbiting satellites have speeds of about 15-16,000 mph, speed decreases as orbital altitudes increase. So, even if a paint chip and a satellite were in exact counter-orbits, their closing speed would't be in the 50,000 mph range. If any of the junk had those kind of speeds, would they not have reached escape velocity and no longer be a problem?
Relatively, there are about 20,000 (at least) meteors of paint chip and larger sizes and at much higher speeds decending through all of the orbital planes each year. These do not appear to have been much of a problem, why would the "junk"?

5. #### Mike:

Trust me, even at 15,000 mph, a paint chip will leave a mark. :)

Paint chips (and much bigger objects) have never been a problem for us here because they burn up when they hit the atmosphere (there's a lot of kinetic energy at 15kmph). By the time they land, they're nothing more than dust floating at sub-snowflake speed.

6. #### astonerii:

So, how does the speed of two objects, even if nearly identical not have any bearing on the damage that can result from impact? In school they teach us that the reason that we cannot get beyond the speed of light is that as an object approaches the speed of light it exponentially requires more energy to accelerate and when it reaches the speed of light it effectively has infinite energy.

It is this exponential effect I am looking at. As absolute speed increases, absolute energy increases exponentially, thus the higher the speed, the higher the impact energy from a simple 5 mph collision. If this is really the physics we are taught in school, then absolute velocity does matter.

e=(1/2)mv^2
lets use an object of mass = 1
at 0 and 5 speeds the energy difference is 12.5
at 10 and 15 speeds the energy difference is 62.5
at 100 and 105 speeds the energy difference is 512.5
at 1000 and 1005 speeds the energy difference is 5012.5
at 10000 and 10005 speeds the energy difference is 50012.5

15000mph = 6705.6 m/s the energy difference is 33515.5 a whopping 2681.24 times the energy of a 5 m/s collision at a nominal base speed of 0. This is effectively the energy of being hit with an object going 163.3 mph.

7. #### Scott:

Back in 7th grade, we took a field trip to Gettysburg. One of the few things I remember from that trip is seeing two bullets that had met and fused in mid-air during that battle. Just sayin...

Space debris is a real problem for astronauts and satellites. The ISS frequently has to change course to avoid large objects. But almost all of the space debris is tracked, so with proper data-sharing arrangements, space hotels and other stations won't have a problem avoiding it.

8. #### BCM:

Do these people realize how innefective and how much superfund sites on earth cost? Imagine if there was a superfund site in space? The costs would be out of this world! Pun intended :)