Astner
The Ghost Who Walks
Originally posted by One Big Mob
A map of our galaxy would help put it in perspective though. It would either ease my concern, or keep it the same. Mind you this is assuming it's all on the same plane as well, hmm.
The issue is that you wouldn't find a map of it that is to scale.
Just take out solar system, it's 80 astronomical units in diameter. The sun is less than a hundreth of an astronomical unit in diameter, and the Earth is less than less than a thousandth the diameter of the Sun.
Just looking at this in terms of a plane (like you suggested) we have to look at this in terms of area.
The area of the solar system is π/4×80² AU.
Sun: π/4×0.01²
Mercury: π/4×(3×10⁻⁵ )²
Venus: π/4×(8×10⁻⁵ )²
Earth: π/4×(9×10⁻⁵ )²
Mars: π/4×(5×10⁻⁵ )²
Jupiter: π/4×(10⁻³ )²
Saturn: π/4×(8×10⁻⁴ )²
Uranus: π/4×(3×10⁻⁴ )²
Neptune: π/4×(3×10⁻⁴ )²
So if we sum up all area of all the celestial bodies in the solar system and divide it by the space of the solar system we end up with:
π/4×(10⁻⁴ + 9×10⁻¹⁰ + 6.4×10⁻⁹ + 8.1×10⁻⁹ + 2.5×10⁻⁹ + 10⁻⁶ + 6.4×10⁻⁷ + 9×10⁻⁸ + 9×10⁻⁸ ) / π/4×6,400
The above expression isn't even two percent larger than the area of the sun, and since we're only working with one significant digit, the expression may as well be simplified as 10⁻⁴/6,400 = 2×10⁻⁸.
In other words your probability of hitting matter traveling through the solar system would be 0.00002%, but that's assuming that the area occupied by matter is evenly distributed across the solar system in discrete parts the same area as the area of the projectile going through the solar system (which it isn't), so the probability is significantly lower than that.
And once you get outside of the solar system you have to contend with the empty space between solar systems, which is significantly larger than the solar systems themselves.
So it's extremely unlikely that you'll hit something if you're traveling in a straight line.