Basics about asteroids

Asteroids are small bodies of the solar system. Most of them orbit between Mars and Jupiter in the so-called main belt. Some of them, however, have orbits that come close to the Earth's orbit or even cross it. These are called near-Earth asteroids. Asteroids can be described as irregular solid bodies without any atmosphere or coma. Their size ranges from hundreds of kilometers for the largest ones to meters for the smalles ever detected.

So far, there are almost half a million known asteroids - we know their orbit in the solar system (by measuring their position at different times) and their approximate size (by measuring their brightness and knowing their distance). To learn more about their physical properties, other observing techniques have to be used. One of them is photometry - we measure brightness variations caused by rotation. By this technique, rotation periods were derived for several thousands of asteroids

Asteroid lightcurves

Similarly to planets, asteroids shine by the reflected sunglight. Because the distance of an asteroid to the Sun and the Earth changes as the asteroid and the Earth orbit the Sun, the brightness of the asteroid also changes with time. Apart from this easily predictable change of brightness, asteroids also exhibit brightness variations that are caused by their irregular shape and their rotation.

Asteroids rotate, the cross-section of the visible and illuminated part of their surface varies with time and so varies their brightness. This brightness variation is called a lightcurve. By measuring lightcurves, we can measure asteroid rotation periods. The shape of a lightcurve depends on the mutual geometry of the Sun, the Earth, and the asteroid (which is known because we know the orbit of the asteroid in the solar system), and on asteroid spin axis orientation and shape (which we do not know).

Lightcurve inversion

If there are enough lightcurves from different geometries available, the shape model, the spin axis direction, and the rotation period of an asteroid can be derived. For example, an almost spherical asteroid would be constantly bright, whereas an elongated asteroid would exhibit large brightness variations when viewed edge-on and small variations when viewed pole-on. The process of the shape and spin reconstruction from lightcurves is called lightcurve inversion. From a mathematical point of view, lightcurve inversion is a nice and interesting example of an inverse problem. It can be shown that a uniqe convex shape model of an asteroid can be derived from its lightcurves. From an astronomical point of view, the lightcurve inversion method enables us to reveal basics physical characteristics of individual asteroids by inverting their lightcurves. So far, models for more than 200 asteroids have been derived this way. They are stored in the Database of Asteroid Models from Inversion Techniques (DAMIT).