Never Tell Me The Odds

One of the best getaway scenes in movie history is in The Empire Strikes Back, when Han Solo navigates the Millennium Falcon through an asteroid field, with TIE Fighters in hot pursuit.

The famous chase scene. Start at 1:44

The scene starts with the Falcon getting hit by two asteroids. The asteroid field appears to have thousands of asteroids all flying around as far as the eye can see. The asteroids range in diameter from small rocks to the size of a small city. Han successfully navigates the asteroids while the Imperial fighters get pulverized by the rocks.

Star Wars’ portrayal of the asteroid field propagates a common misconception about the likelihood of colliding with, or even encountering, an asteroid.

As a bonus, I figure out how much kinetic energy the space rocks would carry in our solar system and the equivalent force in TNT.

What are the odds?

NASA’s Dawn Mission FAQ estimates the the volume of the Asteroid Belt is 16 cubic AU. An AU is the distance from Earth to the Sun. NASA estimates that there are 2 million asteroids greater than a mile in diameter within the asteroid belt. If the asteroids were distributed evenly, the distance between the asteroids would be about 1.9 million miles. This is 760 times the distance from NYC to Los Angeles.

A spacecraft has almost no chance of getting hit by an asteroid. In fact, it would be hard for someone sitting in a spaceship to see an asteroid with their naked eye. If the spacecraft was NYC, the nearest asteroid could be hundreds of Los Angeles(es) away.

What is the damage?

An asteroid does not have to be a mile long to inflict catastrophic damage to a spaceship. Imagine a space probe in our own solar system (miraculously) collides with an asteroid similar in size to the asteroids that hit the Falcon. Let’s calculate the kinetic energy of one of these tiny asteroids, and the equivalent force in kilotonnes of TNT.

What do we need to know for this calculation (we will use mks units):

  • Asteroid Shape: The asteroid definitely looks like a potato, but for math’s sake, I am going to pretend the asteroid is a perfect sphere.
  • Asteroid Diameter: The Millennium Falcon is about 35 meters in length. Since the asteroids were a bit smaller, we will use a diameter of 30 meters, and a radius of 15 meters.
  • Orbital Distance: Many asteroids orbit at 2.4 AU. This is 3.9E11 meters.
  • Asteroid Density: Average of 2g/cm^3 is 2000 kg/m^3

Now we do the math (on a separate sheet of paper):

Circumference of Orbit =  \pi 2r = 2.26 \, E12 \, \, m
Orbital Period =  \sqrt{a^{3}} = 3.72 \, \, y = 1.28 \, E8 \, \, s
Avg Orbital Speed =  \frac{dist}{time} = 3000 \, \, \frac{m}{s}
Asteroid Volume =  \frac{4}{3} \pi r^{3} = 14000 \, \, m^{3}
Asteroid Mass =  \rho V = 2.8 \, E7 \, \, kg
Kinetic Energy =  \frac{1}{2} m V^{2} = 2.8 \, E15 \, \, \frac{kg \, \, m^{2}}{s^{2}}

We got an answer! A spherical asteroid travelling at 3000 m/s should carry a kinetic energy of 2.8 quadrillion joules. This is equivalent to 2800 terajoules (a standard for nuclear weapon yields). For comparison, the Ivy King was the largest pure-fission bomb tested by the US, and yielded about 2100 terajoules.

Conclusion

Asteroids are incredibly deadly, even the extremely tiny ones. But, the odds of getting hit by one is astronomically low. You could fall asleep in an asteroid field expect to never get hit. Try not to dream about nuclear space rocks.

Sources:

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