NEAR/Shoemaker Science Update

As NEAR Shoemaker descends ever closer to Eros, the spacecraft’s orbit
becomes ever more sensitive to the details of the gravity field produced by
the asteroid. Just as NEAR Shoemaker must orbit close enough to Eros to
detect any magnetic field from the asteroid (April 7 update), it must also
get close to Eros to feel disturbances from the irregular shape of the
asteroid and to search for any mass concentrations or voids within it. Both
the gravity investigation and the magnetic field investigation are studying
the interior of Eros, whereas the other investigations – imaging, laser
ranging, infrared, x-ray and gamma ray spectroscopy – study the surface. The
surface for gamma rays is much deeper than that for visible light (more on
that another time), but even gamma rays see only some ten centimeters deep.

Although both gravity and magnetism have the property of decreasing in field
strength away from the source of the field, they are fundamentally different
from each other. As was mentioned on April 7, the simplest possible
configuration of magnetic poles is the dipole consisting of one
north-seeking pole paired with one south-seeking pole. Isolated magnetic
poles (e.g., north-seeking only) do not exist. However, the exact opposite
is true for gravity. The simplest configuration of gravity is that of an
isolated “pole”, which we actually call a “point mass”, and gravitational
dipoles do not exist. This is a fancy way of saying something that everyone
knows, namely, that all masses attract one another by gravity. This is
different from the situation with magnetic poles – there are two types
(north-seeking and south-seeking), of which opposite types of pole attract
each other, but like poles repel.

The simplest possible gravity field is that of a point mass which has no
structure whatsoever. It turns out that any spherical mass distribution
produces the same gravity field above its surface as it would if all its
mass were concentrated at the center (making a point mass there). This
simplest possible gravity field obeys the familiar inverse square law, where
the field strength decreases as the inverse square of the distance from the
center. Since planets like Earth have almost spherical mass distributions,
planetary gravity fields are very close to those of point masses.

We now know that Eros is not at all close to spherical, so neither is its
gravity field. Since there is no such thing as a gravitational dipole, the
next simplest gravity field configuration is what we call a “quadrupole”.
The degree of distortion of the shape from spherical is measured by the
“quadrupole moment” which is analogous to the dipole moment mentioned on
April 7, but quadrupoles are more complicated than dipoles, and indeed they
are too complicated to be described as ordinary vectors. There is more to a
quadrupole than one magnitude and one direction, because there are many ways
to distort a sphere by squashing it flatter or stretching it into a cigar
shape (both of which are examples of quadrupoles).

We have now encountered the three most basic configurations of fields – the
familiar point mass field (also called a “monopole field”), the less
familiar but still friendly dipole field, and now the quadrupole field. The
monopole field decreases as the inverse square of the distance from the
center; the dipole field decreases as the inverse cube as we saw on April 7;
and the quadrupole field decreases as the inverse fourth power of the
distance. Again, quadrupole fields have a characteristic angular dependence
that is distinct from those of the dipole and the monopole fields (the
latter is spherical).

So the nonspherical shape of Eros distorts its gravity field, creating in
the simplest case a quadrupole field because there is no gravitational
dipole. This distorted field has a strength that decreases as the inverse
fourth power of the distance, so it is most important close to the body. In
the 100 km orbit around Eros, the quadrupole field is 16 times stronger than
it is in a 200 km orbit. Indeed, it is only in the 100 km orbit, where NEAR
Shoemaker has spent the past week, that the quadrupole gravitational field
of Eros is expected to become a major factor in disturbing the orbit.
Previously, the effects of solar perturbations were more important (again, a
story for another time).

Our gravity investigators must separate out the effects of the nonspherical
gravity field of Eros. To search for the possible presence of mass
concentrations or voids, they need to examine not only the mass quadrupole
but even more complicated configurations (or moments of “higher order” than
the quadrupole). Likewise, the magnetic field investigation must search
first for a dipole but then consider more complicated fields, such as a
magnetic quadrupole field. However, we don’t know if Eros has any magnetic
field at all, and that is the primary issue for the magnetometer team. On
the other hand, the real issue for our gravity investigators is not whether
a nonspherical gravity field exists, but it is whether that field requires
the presence of mass concentrations or voids. This will be investigated by
comparing the mass quadrupole and higher order moments with the observed
shape of Eros. Which team has the harder job? I don’t know.

Andrew Cheng

NEAR Project Scientist