Near-Earth Objects 293
been measured for some of the brighter near-Earth objects.
Large phase coefficients indicate a very rough surface with
significant effects due to shadowing, such that the magni-
tude changes significantly with changing phase angle. Low
values ofGindicate either a very dark surface, where the
impact of shadows is not significant against a dark surface,
or that few scattering centers exist and hence there is min-
imal shadowing. When observations are made over a range
of phase angles, fits to theoretical models with multiple
variables can be made. Combined with other observational
techniques (e.g., radar, polarimetry, lidar), constraints on
the physical characteristics of the surface regolith can be
made.
5.2 Configuration
Lightcurves are measurements of brightness as a function
of time (Fig. 11). If the object is perfectly spherical such
that its cross section does not change with time, there will
be no variation, and the lightcurve would be flat. There are
no such objects known, although there are lightcurves with
very small amplitudes (not commonly found among near-
Earth asteroids). Lightcurves of NEOs often show two or
more maxima and minima, often with inflections embedded
within. Thetriaxial ellipsoidshape of each NEO can be
modeled using observations. Inflections in the lightcurves
represent changes in the object’s cross section that reflect
either the large-scale shape or albedo variations across the
surface or both.
Radar measurements are also analyzed to produce im-
ages that reveal the shape of asteroids. Coded wave packets
transmitted from Earth to an asteroid reflect back and are
FIGURE 11 Lightcurve for Amor asteroid 3908 Nyx indicating
its irregular shape. (Courtesy of Petr Pravec, Astronomical
Institute, Academy of Sciences of the Czech Republic.)
received as a radar echo. The bandwidth of the echo power
spectrum is proportional to the cross section of the aster-
oid presented to Earth and normal to the line of sight at
the time of interaction with the surface, convolved with
Doppler shifts in the returned signals caused by the ob-
ject’s rotation. The signal can be built up as the asteroid
rotates, producing an image that represents its shape. For
those objects that have approached Earth at close enough
range to employ this technique, such as 4769 Castalia, 4179
Toutatis, 1627 Ivar, 1620 Geographos, and 433 Eros, the re-
sults show shapes varying from slightly noncircular to very
irregular. [SeePlanetaryRadar.]
Knowledge of the objects’ shapes provides clues to the
collisional history of this population. If all objects were
spherical, astronomers would believe them to have formed
from a viscous and rotating material that was not disturbed
since formation. The fact that many near-Earth objects are
irregularly shaped implies that they are products of colli-
sions that have knocked off significant chunks of material
from a larger body. Images of 433 Eros (Fig. 12) show it
described as an ellipse measuring 33×10.2×10.2 km. Its
shape is irregular and controlled by large impact craters.FIGURE 12 Asteroid 433 Eros’s eastern and western
hemispheres. Two mosaics created from 6 images when the
NEARspacecraft was orbiting 355 km (220 mi) above the
surface. Smallest detail is 35 m (120 ft) across. The large
depression on the top image is Himeros (10 km across). In the
bottom image, the 5.3 km crater Psyche is prominent. Bright
exposures can be seen on interior walls of craters. (Credit:
NASA/JHU/APL.)