FOR RELEASE: 9:20 AM EST JANUARY 9, 1998 

NEW MASSES AND DENSITIES ARE COMPUTED FOR THE THREE LARGEST ASTEROIDS 

Dr. James L. Hilton, an astronomer at the U.S. Naval Observatory, announced today at the
American Astronomical Society meeting that he has computed more accurate masses and
densities for the three largest asteroids. More accurate masses of the asteroids are important
for improving our knowledge of the motions of the planets, the compositions of the
asteroids, and the histories of the asteroids, including those that have the potential of colliding
with the Earth. 

The asteroids are small rocky bodies ranging from a few hundred feet to a few hundred miles
in diameter. Most asteroids are located in the main asteroid belt between the orbits of Mars
and Jupiter. Ceres, Pallas, and Vesta are the three largest asteroids. Even though they are
much smaller than the planets (Ceres, the largest asteroid, has only 1% the mass of the
Moon), they are still capable of causing changes in the orbits of Mars and the Earth. These
changes are seen in data returned by interplanetary satellites such as Viking, Mars Pathfinder,
and Mars Global Surveyor. The best available planetary positions are calculated using
perturbations from 300 asteroids; however, the masses of only a hand full of asteroids are
known with any precision. The masses of the other asteroids are estimated by comparing
them with asteroids which do have known masses. 

Computing the masses of the three largest asteroids, Ceres, Pallas, and Vesta, was part of a
larger project computing the motions of fifteen of the largest asteroids. These computations
will be used in producing future editions of The Astronomical Almanac, a yearly publication
of the U.S. Naval Observatory and Her Majesty's Nautical Almanac Office, used by
astronomers worldwide. 

The masses of Ceres, Pallas, and Vesta were determined by calculating their positions to high
accuracy and then comparing those positions with tens of thousands of positions actually
observed by astronomical observatories worldwide. The gravitational forces of the asteroids
on each other affects the observed positions of the asteroids in their orbits. The observed
positions of the asteroids are compared with positions calculated using a mathematical model
of the solar system. The masses are determined by finding the values that make the
differences between the observed positions and calculated positions as small as possible.
Observations covered the period from 1801, shortly after Ceres was discovered, through
1996. Using observations over such a long period of time allows the most accurate
calculation of both the positions of the asteroids and their masses. The masses of all three
asteroids were calculated simultaneously using a special computer program known as the
Planetary Ephemeris Program, or PEP for short. 

The mass for Ceres was found to be (8.7 +/- 0.1) x 1020 kilograms ( 9.5 x 1017 tons), the
mass of Pallas is (3.18 +/- 0.08) x 1020 kilograms (3.50 x 1017 tons), and the mass of Vesta is
(3.0 +/- 0.2) x 1020 kilograms (3.3 x 1017 tons). For comparison, this means that Ceres has
1.18% of the mass of the Moon while Pallas has 0.43% the Moon's mass and Vesta is
0.41% of the mass of the Moon. 

The mass of Pallas is greater than previously thought, while the mass of Ceres is somewhat
smaller. The change in the mass calculated for Ceres is a direct result of the change in the
mass calculated for Pallas. Confusion is caused by the fact that the two asteroids take nearly
the same time to go around the Sun and have been in the same part of the sky ever since they
were discovered. Since these two asteroids always appear close to one another, separating the
amount of gravitational pull caused by each asteroid is difficult unless a simultaneous solution
for their masses is used as was done at the Naval Observatory. Dr. Hilton said, "These
results reduce the uncertainty in the mass of Pallas by a factor of five, and show that to get a
good mass for Ceres you need to know the mass of Pallas. However, calculating the mass of
Pallas is tricky and it would be nice to have some one else check this value." The mass
calculated for Vesta is in very good agreement with previous calculations. 

In addition to the masses, densities can be calculated for these three asteroids because several
groups of astronomers have determined their radii within a few kilometers. The density of
Ceres is 1.98 +/- 0.03 grams per cubic centimeter, the density of Pallas is 4.2 +/- 0.2 grams per
cubic centimeter, and the density of Vesta is 3.9 +/- 0.3 grams per cubic centimeter. For
comparison, water has a density of 1 gram per cubic centimeter and the average rock has a
density of 3 grams per cubic centimeter. Although Pallas has long been considered to be
similar to Ceres, the new densities indicate that Pallas may, in fact, be more like Vesta. 

For more information contact Dr. James L. Hilton, U.S. Naval Observatory, 3450
Massachusetts Ave. NW, Washington, DC 20392. Phone: 202-762-1432. FAX
202-762-1612. E-mail: jhilton@usno.navy.mil. 

An html version of this press release can be found at
http://aa.usno.navy.mil/ephemerides/asteroid/masses/PressRelease.html. There is also a
scientific paper describing in detail the calculation of orbits, masses, and densities of the
asteroids at
http://aa.usno.navy.mil/ephemerides/asteroid/astr_alm/asteroid_ephemerides.html.