Exposing PseudoAstronomy

October 26, 2008

Asteroid Belts – Proximity of Rocks and Why Navigation Is Not Dangerous (Sorry, Han Solo)

Even though a majority of my posts-to-date have been post against religious astronomy arguments to “prove” the Judeo-Christian creation myths, the intent of my blog really is not to “bash” religion, but to explore and explain examples of bad astronomy (or, pseudo-astronomy … sorry Phil).

To that end, I’m going to take a break from AiG and ICR propaganda and talk about a sci-fi ploy that’s often used and yet is very unrealistic:  Asteroid Belts.

I’m certain that 90%+ of people aged 25-50 remember Han Solo zig-zagging around asteroids while the Emperor’s ships tried to follow in pursuit during one of the original three Star Wars movies.  Or, for the Star Trek fans, there are at least two examples of that series using this ploy — one was an episode of The Next Generation and another from Enterprise, the latter showing a highly chaotic belt system with large chunks of rock careening around and changing direction while their shuttle pod tried to maneuver around.

What do these have in common?  They’re not realistic, at least not based on what we know of our own asteroid belt.

A Brief History of the Asteroid Belt

The asteroid belt was first “discovered” in 1801.  I put “discovered” in quotes because it was actually the largest asteroid that was discovered then – 1 Ceres – by Giuseppe Piazzi.  Ceres’ orbit showed it to be between Mars and Jupiter, and it was hailed as a new planet.  But, rather quickly, more objects were discovered in nearly the same region of space as Ceres.  William Herschel, based on this, suggested they be termed “asteroids” as opposed to planets, and that’s what they are called today (though in 2006 the International Astronomical Union re-classified Ceres as a “dwarf planet”).

More and more asteroids were discovered over the years, most of them between Mars and Jupiter, from about 1.8 A.U. to just under 3.3 A.U. where 1 A.U. is the average distance between Earth and the Sun, 149,600,000 km or 93,000,000 miles.  To-date, over 429,000 asteroids have been identified, the majority of them lying in the main belt (data source: ftp://ftp.lowell.edu/pub/elgb/astorb.html ).

How Many Asteroids of What Size?

Now that you know a tiny bit about the history of what we know about the asteroid belt, the next information relevant for this discussion is how many asteroids there are of what sizes.  The first asteroids to be discovered were big, mainly because they’re bright.  “Big” in this case is a few hundred kilometers across, something like the size of the state of Ohio.

Most of the asteroids, however, are much much smaller than that.  In general, the distribution of sizes follows what’s known as a “power law” distribution, where the number of small asteroids grows much more quickly than the reduction in size.  The slope of this power law is generally estimated to be -3.  What that means is that every time you halve the size of an asteroid, you have 8 times as many.  So say there are 100 10-km asteroids.  With a -3 power-law slope, that would mean there are 800 5-km asteroids.  And 6400 2.5-km asteroids.  But only ~13 20-km asteroids.

In terms of what is known, there are about 20,000 asteroids between 2-3 km, which is about the smallest that we likely have a complete sampling of.  What that statement means is that, while we have identified asteroids that are smaller, our detection technology is not good enough to have found all of the asteroids that are smaller.

If we extrapolate, assuming a -3 power low, down to, say, 100-meter asteroids, there are probably ~82 million asteroids that are ~100-200-meters across.  If we extrapolate further, down to 1-meter asteroids, then we really have a gargantuan number of objects – about 1014 (100 quadrillion) objects of that size.  That’s quite a lot.

What Does this Mean for Navigation?

If we add up all of those objects, we have about 1.2×1014 asteroids larger than 1 meter.  Now, let’s look at the asteroid belt.  It stretches from 1.8 to 3.3 A.U., which is a distance of 1.5 A.U., or about 225,000,000 km.  That’s a fairly large distance (that’s actually about the distance between the Sun and Mars).

The area of a disk that size, however, is gargantuan:  A = π · r2 = π · ((3.3 A.U.)2 – (1.8 A.U.)2) = π · (1.7·1017 km2) = 5.4·1017 km2.  That is a huge area.  Simple division shows that each asteroid, regardless of its own size, could have 4,500 km2 all to itself – a little bit more than the entire U.S. state of Rhode Island.

And that’s if they were all just in one plane.  In reality, they occupy a volume of space, some orbiting “above” or “below” others (where those terms are relative to the plane that the Earth’s orbit makes).

Even if we cut the size of asteroids in half again, and were interested in all asteroids larger than half a meter (1.5 ft) in size, then we have 8 times as many asteroids, but each one still has over 500 km2 all to itself, and even more space if we consider the vertical component.

What does this mean for navigation?  It’s easy!  In fact, you really have to try to hit an asteroid, at least in our own belt.  And so, the next time you see a tiny ship careening through an asteroid field in a TV show or movie, remember that in real life, asteroid belts really aren’t that dangerous for navigation.

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