On February 29, 2000 NEAR recorded another first: the NEAR Laser
Rangefinder (NLR) detected the first laser returns from Eros at a range of
290 km. This is the first time that ranging returns have been detected from
an asteroid (see the image-of-the-day for 2000
March 2 http://near.jhuapl.edu/iod/20000302/).

NLR was designed to operate at 50 km range, and its successful detection of
Eros at 290 km augurs well for the future. The laser rangefinder
data will give us a
three-dimensional view of the asteroid surface, nicely
complementing the information from images. This is
because imagers record the distribution of brightness as
a function of angles perpendicular to the
line-of-sight, whereas the laser rangefinder measures distance
to the surface along the line-of-sight. The
combination of the two data sets will be powerful, as we hope it
will
enable us to probe into shadowed regions (because the
laser does not depend on solar illumination), and to
distinguish between effects of albedo variations and
effects of height variations. In an image, a spot may
look brighter or darker because of reflectivity
differences or because of lighting differences caused by
topography (such as shadowing). Laser rangefinder
data can be used to separate these effects and to measure
topography – e.g., the heights of ridges, the depths of
grooves and craters.

The image-of-the-day for 2000 February 25 shows the
“eastern and western hemispheres” of Eros. The image
shows an amazing diversity of geologic features,
which will be the subjects of updates in the coming weeks. For
now, I will focus on how we define eastern and
western hemispheres and how we locate positions on a celestial
body. I feel I should apologize for using the
word
“hemisphere” to refer to an irregularly shaped body like
Eros, but I don’t have another word that means
“the surface within a 180-degree longitude range”. To locate
any point on the surface, we use what we call
“spherical polar coordinates”: the longitude and latitude
angles, and the distance from the center of Eros.

These three
numbers specify the position of any point in three
dimensions, but we need to specify which way is “north”
and which way is “east”. To accomplish this, we
first locate the rotation axis of Eros using (for example)
image data, and we choose the North pole direction as
the reference for latitude, the same as is done for
Earth. When viewed from above the north pole, the
asteroid rotates counterclockwise; when viewed from the
south, it rotates clockwise. The latitude angle is
measured from the equator of Eros, which is the plane
perpendicular to the rotation axis. Having defined the
polar axis, the next step is to define the prime
meridian, from which longitudes are measured. On Earth,
the prime meridian runs through the poles and
through
Greenwich, UK. On Eros, a particular crater has been
selected to mark the prime meridian. If one walks from
the prime meridian in the direction of the rotation,
one is going east. In the opposite direction, one is going
west. Longitudes can be measured going east from
the
prime meridian, in which case we speak of east
longitude, or they can be measured going west from the
prime meridian, giving west longitude. Just to keep
us on our toes, geophysicists commonly use east longitudes
whereas geologists and cartographers
commonly use west longitudes. Unfortunately, there is still another
complication, which is that the International
Astronomical Union defines “north” in reference to the
so-called “invariable plane” which is close to the
ecliptic plane defined by Earth’s mean motion around the Sun,
whereas we have just defined it in reference to the
rotation of Eros – but fortunately, the two definitions
of “north” coincide for Eros, so we can forget about the
invariable plane. I guess scientists have a talent for
making even the simplest things seem complicated.

Andy Cheng

NEAR Project Scientist