Near-Earth Object Population and Distribution of Rotation Rates

Grant Proposal

Asteroid 2007DS84: one of 8 asteroids I'm investigating.

"The goals of this project are to determine observationally, and interpret theoretically, the spin state distributions of the NEO (Near-Earth Object) population in the sub- and trans-km regime: specifically, to (1) delineate the envelope of the fastest rotating objects as a function of size and shape and (2) map the distribution of obliquities; and then to use this information to (3) probe the material strengths of asteroids in the trans-km regime, (4) constrain the role of the YORP (Yarkovsky - O'Keefe - Radzievskii - Paddack) effect in modifying NEO spins, and (5) model the spin state evolution of the NEO population."

- Tom Statler, "The Spin Distribution of Near Earth Objects: A Window on Material Properties" (grant proposal)

What does that mean?

Imagine the moon is a flat disc, reflecting all incident sunlight, like a mirror. Now imagine this flat disc is rotating. When the flat side is presented to the earth, we see the maximum reflected brightness, and when the thin edge is presented, we see the minimum reflected brightness. If we keep track of how often we see the bright part, and how often we see the dim part, we can figure out how fast the flat disc is rotating. We can apply this same idea to an asteroid, provided it has some asymmetry (i.e., it's not perfectly spherical). By measuring the time elapsed between brightness maxima, we can calulate the rotation rate of the asteroid.

From the rotation rate, we can infer certain properties of the asteroid's tensile strength (i.e., what's it made of?). For example, imagine a pile of pebbles held together by gravity (ok, so maybe pebbles don't stick together very well due to gravity, so just imagine HUGE pebbles). For this porous regolithic body (look it up), a relatively low "centrifugal force" is sufficient for catastrophic destruction; in other words, a slow rotation rate is enough to make the pebbles fly apart, even more so if it's a large pebble pile. On the other hand, an asteroid made of solid granite (we say "monolithic") will hold together under much higher doses of stress, and is capable of higher rotation speeds. Knowing the size and composition of an asteroid is useful in devising ways to change its trajectory; we need to know how much of a nudge it takes to adjust the course of an earth-bound rock, but without splitting it into hundreds of smaller pieces.

A radiometer is a reasonable conceptual
model to help explain YORP torque.

Asteroids can speed up or slow down their rotation rates through a mechanism called YORP torque. Picture that science experiment from elementary school: the glass from a light bulb encompasses a pinwheel of fins, colored black on one side and white on the other (it's actually called a radiometer - see left). When you shine light on the fins, they spin around the axle. Here's why: the fins absorp the energy from the light unevenly; the black side absorbs more than the white side. Then, the energy absorbed by the black side is released, or reradiated in the form of a photon (a particle of light), which carries away momentum. Because every action must have an equal and opposite reaction (Newton's 3rd Law), the fins react by moving in the direction opposite the emitted photon, thus conserving the net momentum throughout the procedure, and making the pinwheel "spin up."

Now imagine instead of the pinwheel, we have a huge rock in space. As long as the rock is asymmetrical, it will absorb light energy unevenly, just like the fins, and the reradiation process will either speed up or slow down the rock's spin rate. Although this description isn't perfectly analogous to reality, it is a very crude example of the Yarkovsky - O'Keefe - Radzievskii - Paddack torque, or YORP.

Origins of Asteroids and Comets

About a hundred million years after planetary formation ended in our solar system, extra material was left over in certain regions. Picture all solar system material, including planets, asteroids, comets, gas, and interplanetary dust orbiting the sun in the same direction. Now remember that massive bodies exert gravitational influence on each other, so the large planets are tugging on the smaller objects, changing their orbits. Then as this tugging occurs, we expect certain regions within the solar system to be more stable than others; small bodies that aren't already orbiting in these regions may be drawn there through gravitational interations. Similarly, we expect to find very UNSTABLE regions as well; over time, small objects within these areas of gravitational instablitiy should be ejected into the more stable regions.

Through this process, small bodies initially located in the inner solar system were pushed into a semi-stable region between the orbits of Mars and Jupiter at ~2.7 AU (AU = "astronomical unit," the earth-sun distance, or 149,598,000 kilometers) to form the Main Asteroid Belt, with which most people are familiar. Probably unfamiliar, however, is the Kuiper Belt, the leftover objects from a nebular disk beyond Pluto, between 40 and 400 AU. Finally, comets and small bodies gravitationally ejected from the solar system by the gas giants Uranus and Neptune are found in the Oort Cloud, between 50,000 and 100,000 AU away from the sun.

Gravity, the same mechanism that formed the Main Asteroid Belt, is also responsible for freeing asteroids from it. Frequently, Mars or Jupiter passes near a smaller object and tugs, or perturbs it out of its orbit gravitationally. The same process occurs in the Oort Cloud; a passing star may rip a comet out of its previous orbit, sending it hurling back towards the sun. Comets or asteroids passing within 1.3 AU of the sun are classified as Near-Earth Obects, or NEOs.

Risk Analysis

Every day, about one hundred tons of interplanetary material (in addition to our own space junk) impacts our planet. Most of it burns up in the earth's atomosphere; anything left that makes it through isn't big enough to cause much concern. Although a catastrophic collison with a sizeable object is an EXTREMELY LOW PROBABILITY event (we're talking orders of 1 in 100,000), NASA is compiling a list of potentially hazardous asteroids. There is no "the big one" which will "definitely hit us in the year 20XX;" only a list of maybe's with very low chances of actual impact. See NASA's Impact Risk Assessment page for more information.