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