The perturbation of asteroids on Mars and the Earth are the largest poorly modeled problem in modern planetary ephemerides. DE200 uses perturbations of five asteroids and DE405 uses perturbations of 300 asteroids. However, the masses of only nine asteroids have been determined.

The following table gives the current best estimates of the masses that have been determined for asteroids:

Asteroid	Mass MSun	Reference
1 Ceres	(4.39 ± 0.04) × 10-10	Hilton 1999
2 Pallas	(1.59 ± 0.05) × 10-10	Hilton 1999
4 Vesta	(1.69 ± 0.11) × 10-10	Hilton 1999
10 Hygiea	(4.7 ± 2.3) × 10-11	Scholl et al. 1987
11 Parthenope	(2.58 ± 0.10) × 10-12	Viateau & Rapaport 1997
15 Eunomia	(4.2 ± 1.1) × 10-12	Hilton 1997
16 Psyche	(8.7 ± 2.6) × 10-12	Viateau 1999
20 Massalia	(2.4 ± 0.4) × 10-12	Bange 1998
45 Eugenia	(3.05 ± 0.13) × 10-12	Merline, et al. 1999
121 Hermione	(4.7 ± 0.8) × 10-12	Viateau 1999
216 Kleopatra	(1.0 ± 0.1) × 10-12*	Marchis, et al. 1999
243 Ida	(2.18 ± 0.32) × 10-14**	Petit, et al. 1997
253 Mathilde	(5.193 ± 0.022) × 10-14	Yeomans, et al. 1998
433 Eros	(3.361 ± 0.002) × 10-15	Yeomans, et al. 2000
704 Interamnia	(3.7 ± 1.7) × 10-11	Landgraff 1992
*The mass of Kleopatra is inferred from the its rotation period and evidence that its two major pieces are not in contact.
**The mass of Ida is inferred from the long term stability of its satellite, Dactyl.

The mass of Ceres is smaller than in most previous determinations of its mass. This is a direct consequence of refining the mass of Pallas. Ceres and Pallas have nearly the same semi-major axes, 2.767 and 2.771 AU respectively. They have also been very close together ever since they were discovered at the beginning of the nineteenth century; the separation in mean longitude has increased from 1° in 1802 to only 43° in Dec. 1997. As a result, if the mass of Pallas is fixed at a wrong value, misattributed perturbations are propagated into the mass of Ceres. This can be seen in the following figure. The mass of Ceres determined by other authors is given by the blue circles, the red triangles are mass of Ceres determined using the historic mass of Pallas, the red squares are the masses determined using the refined mass for Pallas, and the red circle is the best determination given in the above table.

The number of asteroid mass determinations has been increasing over the last several years. I have recently put together a reference list of all papers in which an asteroid mass determination is made.

Asteroid Densities

Knowing the masses and dimensions of an asteroid gives an opportunity to determine its mean density. The mean density gives a clue to its composition. There are only five asteroids that have both masses and shapes that are well known. The densities of these five are given in the following table.

Asteroid	Density gm cm-3	Volume Reference
1 Ceres	2.05 ± 0.05	Merline et al. 1996
2 Pallas	4.2 ± 0.3	Drummond & Cocke 1988
4 Vesta	4.3 ± 0.3	Thomas et al. 1997
16 Psyche	1.8 ± 0.6	Viateau 1999
20 Massalia	2.7 ± 1.1	Bange 1998
45 Eugenia	1.2 (+0.6,-0.3)	Merline, et al. 1999
121 Hermione	1.8 ± 0.4	Viateau 1999
243 Ida	2.7 ± 0.4*	Petit et al. 1997
253 Mathilde	1.3 ± 0.2	Veverka et al. 1997
433 Eros	2.67 ± 0.03	Yeomans, et al. 2000
*The density of Ida is inferred from the long term stability of its satellite, Dactyl.

Critical List

Aside from Ceres, Pallas, and Vesta the only current method of asteroid mass determination requires the observation of the perturbation of a small test asteroid or spacecraft by the massive asteroid. The perturbation effect most easily observed is the change in the mean motion of the test body. The masses of even the largest asteroid is relatively small, thus the typical change in the mean motion for the strongest asteroid perturbation is about 0."015 yr^-1. Observing a change this small requires that an excellent orbit be determined for the test body both before and after the encounter with the massive asteroid. And determining an excellent orbit requires numerous high precision observations of the test body.

I have chosen 36 encounters from Hilton et al. (1996) as being the encounters most likely to yield reliable asteroid masses. These encounters are listed in the following table. The most important encounters, those most likely to give accurate masses of massive asteroids, are flagged with a *. High precision observations of both the test asteroid and massive asteroid are welcomed.

Perturbed Asteroid	Perturbing Asteroid	Date of Encounter	Priority Encounter
263 Dresda	16 Psyche	June 1956	*
1313 Berna	15 Eunomia	Oct. 1965
1847 Stobbe	511 Davida	Sept. 1974
2296 Kugultinov	24 Themis	Dec. 1975	*
2589 Daniel	16 Psyche	Sept. 1981	*
1259 Ogyalla	10 Hygiea	Feb. 1984
1780 Kippes	10 Hygiea	May 1984
348 May	1 Ceres	Sept. 1984
308 Polyxo	45 Eugenia	Nov. 1985
46 Hestia	19 Fortuna	June 1986
3019 Kulin	52 Europa	Nov. 1988
720 Bohlinia	1029 La Plata	Feb. 1989
836 Jole	7 Iris	Feb. 1989
1029 La Plata	720 Bohlinia	Feb. 1989
2495 Noviomagnum	2 Pallas	Jan. 1991
2873 Binzel	4 Vesta	Sept. 1991
113 Amalthea	4 Vesta	Jul. 1994	*
3002 Delasalle	4 Vesta	Jul. 1994	*
465 Alekto	10 Hygiea	Dec. 1995
494 Virtus	24 Themis	Dec. 1995
17 Thetis	4 Vesta	June 1996
3946 Shor	10 Hygiea	Mar. 1998	*
1442 Corvina	16 Psyche	Sept. 2001
294 Felicia	45 Eugenia	Jan. 2003
1464 Armisticia	511 Davida	Jul. 2003
2455 Somville	111 Ate	Nov. 2003
1066 Lobelia	324 Bamberga	Sept. 2004
468 Lina	16 Psyche	Dec. 2004
757 Portlandia	13 Egeria	Dec. 2005
2930 Euripides	1 Ceres	Jan. 2006
3823 Yorii	511 Davida	Jan. 2006
3335 Quanzhou	704 Interamnia	Feb. 2006
3835 Korolenko	52 Europa	Feb. 2006
4499 Davidallen	324 Bamberga	June 2006
3289 Mitani	19 Fortuna	Oct. 2007
827 Wolfiana	19 Fortuna	June 2010
3071 Nesterov	65 Cybele	Apr. 2016

When Did the Asteroids Become Minor Planets?

The asteroids were not always considered to be a type of body separate from those of the other planets. For 52 years after the discovery of the first asteroid, Ceres, they were accepted as planets in their own right. To find out how and why the asteroids became recognized as their own category of solar system body, click on the title to this section.

References

Bange, J. 1998, An Estimation of the Mass of Asteroid 20-Massalia Derived from the Hipparcos Minor Planet Data, Astron. Astrophys., 1998, L1-L4

Drummond, J.D. & Cocke, W.J. 1989, Triaxial ellipsoid dimensions and rotational pole of 2 Pallas from two stellar occultations, Icarus, 78, 323-329

Hestroffer, D., Marchis, F., Berthier, J., Cellino, A., Tanga, P., & Zappalà, V. 1999, "Binary Asteroid (216) Kleopatra"

Hilton, J.L. 1997, The Mass of the Asteroid 15 Eunomia From Observations of 1313 Berna and 1284 Latvia, Astron. J., 114, 402-408

Hilton, J.L. 1999, U.S. Naval Observatory Ephemerides of the Largest Asteroids, Astron. J., 117, 1077-1086

Hilton, J.L., Seidelmann, P.K., & Middour, J. 1997, Prospects for Determining Asteroid Masses, Astron. J., 112, 2319-2329

Landgraf, W. 1992, A determination of the Mass of (704) Interamnia from Observations of (993) Moultona, in Proc. of IAU Symp. No. 152: Chaos Resonance and Collective Dynamical Phenomena in the Solar System, S. Ferraz-Mello ed., pp. 179-182

Marchis, F., Hestroffer, D., Cellino, A., Tanga, P., & Zappala, V. 1999, "(216) Kleopatra", IAUC 7308

Merline, W.J., Close, L.M., Dumas, C., Chapman, C.R., Roddier, F., Menard, F., Slater, D.C., Duvert, G., Shelton, C., & Morgan, T. 1999, Discovery of a Moon Orbiting 45 Eugenia, Nature, 401, 565-569

Merline, W.J., Stern, S.A., Binzel, R.P., Festou, M.C., Flynn, B.C., & Lebofsky, L.A. 1996, HST Imaging of 1 Ceres, Bull. American Astron. Soc., 28, 1025

Petit, J.-M., Durda, D.D., Greenberg, R., Hurford, T.A., & Geissler, P.E. 1997, The Long-Term Dynamics of Dactyl's Orbit, Icarus, 139, 177-197

Scholl, H., Schmadel, L.D., & Roeser, S. 1987, The Mass of the Asteroid (10) Hygiea Derived from Observations of (829) Academia, Astron. Astrophys., 179, 311-316

Thomas, P.C., Binzel, R.P., Gaffey, M.J., Storrs, A.D., Wells, E.N., & Zellner, B.H. 1997, Impact Excavation on Asteroid 4 Vesta: Hubble Space Telescope Results, Science, 277, 1492-1495

Veverka, J., Thomas, P., Harch, A., Clark, B., Bell, J.F., III, Carcich, B., Joseph, J., Chapman, C., Merline, W., Robinson, M., Malin, M., McFadden, L.A., Murchie, S., Hawkins, S.E., III, Farquhar, R., Izenberg, N., & Cheng, A. 1997, NEAR's Flyby of 253 Mathilde: Images of a C Asteroid, Science, 278, 2109

Viateau, B. 1999, "Mass and Density of Asteroids (16) Psyche and (121) Hermione," submitted to Aston. Astrophys.

Viateau, B. & Rapaport, M. 1997, The Bordeaux Meridian Observations of Asteroids. First Determination of the Mass of (11) Parthenope, Astron. Astrophys., 320, 652-658

Yeomans, D.K., Barriot, J.-P., Dunham, D.W., Farquhar, R.W., Giorgini, J.D., Helfrich, C.E., Konopliv, A.S., McAdams, J.V., Miller, J.K., Owen, W.M., Jr., Scheeres, D.J., Synnott, S.P., & Williams, B.G. 1998, Estimating the Mass of Asteroid 253 Mathilde from Tracking Data During the NEAR Flyby, Science, 278, 2106

Yeomans, D.K., Antreasian, P.G., Barriot, J.-P., Chesley, S.R., Dunham, D.W., Farquhar, R.W., Giorgini, J.D., Helfrich, C.E., Konopliv, A.S., McAdams, J.V., Miller, J.K., Owen, W.M., Jr., Scheeres, D.J., Thomas, P.C., Veverka, J., & Williams, B.G. 2000, Radio Science Results During the NEAR-Shoemaker Spacecraft Rendezvous with Eros, Science, 289, 2085-2088