Measuring Asteroids

Although cartoonists often depict asteroids as being spherical, in fact they are mostly of irregular shape, so it is incorrect to think of them having a "radius." The major planets are spherical because of their huge masses: energetically a sphere is the form that any large body would assume, if self-gravity were the only significant factor. Without the Earth's geologically active interior, producing continental drift and volcanoes, the Earth would have no mountains and would be a solid sphere covered by continuous ocean.

For a large object to obtain a basically spherical form, the tensile strength of its component material must be overcome.

Therefore the shape attained depends on the comparative values of that strength—the ability to withstand distortion—and the gravitational force trying to pull it into a sphere. A fluid has essentially zero strength, so it attains a spherical form no matter what the size. For a solid body it is different.

In the case of an arbitrary asteroid ("minor planet" is an equivalent term), the rocks and metals of which it is composed would be strong enough to maintain an irregular shape, unless it were more than a hundred miles or so in size. There are only a few dozen asteroids of such dimensions. There are also about a million closer to one mile in size, most of them in the main belt between Mars and Jupiter. The total mass of all the asteroids in the main belt is less than that of the Moon.

The largest asteroid is called 1 Ceres, and it was the first discovered minor planet (which is why it has that preceding number one in the master list), on the opening day of the nineteenth century; it has a diameter of 580 miles. Along with a handful of other minor planets, Ceres is large enough to be resolved to some extent using the Hubble Space Telescope. These really large rocks are found to be spherical, due to their self-gravity, whereas the more-numerous smaller asteroids have all sorts of convoluted shapes (see Figure 12-1).

Small asteroids are not spherical, then, and one would like to measure both their shapes and sizes. Given that most asteroids appear merely as pinpricks of light in our telescopes, how can we fathom their dimensions? It happens that occultations enable astronomers to obtain such measurements.

If an asteroid were to pass across the face of the Sun, then we might see it in transit (as is discussed at the end of Chapter 13) but it would be so tiny that all that could be seen would be a little dark

FIGURE 12-1. Minor planet 433 Eros photographed by NASA's NEAR-Shoemaker satellite during 2000. Eros is about 20 miles long, but less than ten miles wide: it is obviously irregular in shape and has been struck by many smaller objects.

spot. No shadow would be cast on the Earth's surface because the Sun appears much larger than the asteroid. No measurement of the asteroid size would be possible unless it were very close to us. It happens that Mars has two moons, named Phobos and Deimos, which are captured asteroids orbiting very close to that planet. As a result they do cast distinct shadows on the Martian surface (see Figure 12-2). For an asteroid observed from the surface of the Earth, to get an effective "shadow" whose size might be measured we would need a smaller light source than the Sun, such as a star

FIGURE 12-2. Phobos, one of the two moons of Mars, is only about eight miles across but it is still big enough to cast a shadow on the surface of the planet below, as in this image obtained with the Mars Global Surveyor satellite.

far away within our galaxy. This could produce an occultation, if the alignment were right.

Imagine that a 100-mile wide asteroid cuts across our line of sight to some distant star. We will probably not have its trajectory determined with enough precision to be sure where its shadow will pass, and as of yet we do not know its size or shape. If the movement of the shadow is west—east one might organize a team of a dozen or so observers stretched along a line north—south for

300 or 400 miles, to be sure of intercepting that shadow. Each astronomer would be armed with a small telescope and stopwatch, plus some absolute time reference such as a GPS receiver or their wristwatch accurately calibrated against standard time, and they would watch as the asteroid closed in on the star. Some would see the star blink off for a short while, as the asteroid eclipses or occults it, whereas those at the northern and southern extremes of the line would not see the star disappear at all, but just slip close past the asteroid. (Such an event is termed an appulse.)

The limits along the line of humans from where the star was occulted will render the asteroid dimension along that axis, perpendicular to its apparent motion. But its size in the other direction (that is, along the shadow path) and even shape may also be deduced from the observations. The duration of the occultation timed by each observer indicates the length of the star's path behind the asteroid as seen from the particular viewing location. The idea is sketched in Figure 12-3.

Because it is difficult to predict the eclipse path for an asteroid far ahead of time, due to uncertainty in its orbit, occultation chasing may be a haphazard and frantic affair. One afternoon in October 1981, while I was a graduate student at the University of Colorado, with a colleague I got a call from astronomers at the Lowell Observatory in Flagstaff, Arizona. They said that an asteroid occultation had just been predicted for that evening and we asked if we could please observe it from the on-campus observatory. This we did without any great trouble and sent off our timings. (That colleague, by the way, was Chris McKay, now one of America's most prominent planetary scientists; he works at NASA-Ames Research Center in California.) The Lowell observers had some problems though. They had found that the track was going

FIGURE 12-3. How the size of an asteroid can be determined from occultation data. Observers spread out over the shadow ground track and measure how long the starlight blinks off, each viewing a different path for the star behind the asteroid as shown here by the arrows. Knowing the speed of the asteroid, its dimensions along the direction of motion may then be ascertained. Any astronomer in the team who was located too far north or south would not see any occultation, and so the size of the asteroid crosswise can also be determined in this way.

FIGURE 12-3. How the size of an asteroid can be determined from occultation data. Observers spread out over the shadow ground track and measure how long the starlight blinks off, each viewing a different path for the star behind the asteroid as shown here by the arrows. Knowing the speed of the asteroid, its dimensions along the direction of motion may then be ascertained. Any astronomer in the team who was located too far north or south would not see any occultation, and so the size of the asteroid crosswise can also be determined in this way.

to pass north of them, over Utah, and so they scrambled in their cars carrying two portable telescopes. Ideally one would organize for the observation points to be well separated so as to give the best distribution of chords across the asteroid. On campus in Boulder, Colorado, our telescope was fixed; but the mobile teams could in principle drive to locations giving an equable spacing over the occultation track. In the rush the teams lost contact with each other, and by chance the two sets of mobile observers managed to choose sites giving precisely the same chord. With the whole of the Utah wilderness to choose from, they had picked separated but equivalent points. As the final publication reported, "As a result, they were deployed in accordance with Murphy's Law."

The specific minor planet observed in that case was 88 Thisbe. The result of the analysis was that it measures about 144 miles across, around 10 percent more than the value estimated from earlier data (it is possible to estimate asteroid sizes by seeing how bright they are, and couple that with a guess at the fraction of sunlight they reflect). Ten percent in size means 20 percent in area, or 30 percent in volume and density. It was also obvious from the results that Thisbe is not precisely spherical. Clearly occultation measurements are scientifically useful.

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