# Equation: How the FAA Estimates Space-Junk Risks

Space is full of junk. Beginning with the launch of Sputnik in 1957, humankind has boldly flung one heavy metallic gadget after another into orbit, often without much regard for the return trip. As a result, more than 16,000 uncontrollable objects, collectively weighing more than 6,000 tons, now circle the planet.

The problem: Whisper-thin traces of air gradually put the brakes on objects in low Earth orbit and create earthbound showers of hot metal bits. Between 10 and 40 percent of a crashing satellite can reach the ground as charred chunks ranging in size from a pebble to a cow. Some satellites come equipped with a rocket engine and propellant tank so controllers can aim their descent into an ocean instead of a neighborhood, but not all. To determine whether a satellite requires this kind of costly deorbiting system, the Federal Aviation Administration uses this equation to estimate the odds that a piece of it will someday hit someone on the ground. Care to calculate your chances?

Pf : Probability that a piece of space junk will survive reentry. For things like falling satellites, the equation is run separately for each chunk expected to result from its eventual breakup.

Ni : Average population density in area i. To simplify the analysis, Earth’s surface is divided into a grid of squares i, and the distribution is assumed to be uniform in each.

Pi : Probability that the object will hit area i—a function of latitude (lat) and the inclination (inc) of the object’s orbital path relative to the equator.

A : Casualty area. The bigger the object, the larger the area. Multiplying Ni by this tells how many people would get whacked if it falls in area i.

Ec : Expected casualties. It’s evaluated for every area i and every chunk from a given spacecraft. If the sum total exceeds .0001—i.e., a 1 in 10,000 chance of a single casualty—that craft requires a controlled deorbit.

Illustration: Josh Cochran
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}