The Mass of Dwarf Planet Eris
Michael E. Brown* and Emily L. Schaller
category called “dwarf planets”: objects in orbit
around the Sun that are large enough to be in
hydrostatic equilibrium but have insufficient
mass to gravitationally dominate their region of
the solar system. Eris is larger than Pluto (2, 3)
and thus the largest currently known member of
The subsequent discovery of Dysnomia (4),
a satellite of Eris, presented the opportunity to
directly measure the mass of Eris by determining
the Keplerian orbit of the satellite. Observations
of Eris and Dysnomia were obtained on 20, 21,
30, and 31 August 2006 (UT) with the Keck
Observatory laser guide star adaptive optics
(LGS AO) system (5, 6). Observations from the
Hubble Space Telescope (HST) were taken on 3
surements of the relative positions of Dysnomia
on these six nights (Fig. 1 and table S1) plus the
position from the discovery on 10 September
2005, we determined the orbit of Dysnomia by
using a Powell c2minimization scheme to find
to fit a purely circular orbit in which the five free
parameters are semimajor axis, orbital period,
inclination, longitude of the ascending node, and
6.5 or a reduced c for nine degrees of freedom
(14 x, y coordinates minus 5 orbital parameters)
of 0.7, indicating an excellent fit to the model.
Expanding the model to allow an eccentric orbit
gives a best-fit eccentricity of ~0.007 and only a
marginally lower reduced c2of 0.6, suggesting
evidence for a noncircular orbit. Derived orbital
elements along with uncertainties from Monte
Carlo analysis appear in table S2.
From the 30 August 2006 HST image at a
wavelength of 0.6 mm, we measured a relative
brightness ratio between the two objects of only
of Dysnomia is inconsistent with the dynamical-
majority of KBO satellites (7), but detailed
simulations show that such small satellites can be
formed from the debris after a giant impact (8). A
collisionally produced satellite of the size of
Dysnomia that tidally evolved outward from an
initial location near the Roche limit would be
predicted to have a roughly 15-day circular orbit
[Supporting Online Material (SOM) text], con-
to the low mass of Dysnomia,this outward orbital
he discovery of Kuiper belt object (KBO)
2003 UB313 (1), now officially named
Eris, prompted the recent reevaluation of
expansion would have slowed the spin period of
Eris by only a part in ~10−5.
Whereas the other two KBO systems that
appear to be products of giant impacts, Pluto and
2003 EL61, contain multiple satellites, satellites
almost an order of magnitude fainter than
Dysnomia can be ruled out beyond the orbit of
Dysnomia from deep HST observations (SOM
text). For a purely tidally evolved system, any
satellite beyond the orbit of Dysnomia must be
larger than Dysnomia, and thus such a system
can be ruled out. Interior to ~0.4 arc sec, how-
ever, the expected fractional brightness of a
tidally evolved satellite is ~0.0007, which is
beyond our detection ability (SOM text). Any
additional purely tidally evolved satellites of Eris
would be expected to be closer and fainter than
these limits. Although such additional small faint
satellites cannot be ruled out, the current limits
and the apparently circular orbit of Dysnomia
suggest that Eris might indeed be a single-
From the period and semimajor axis of the
orbit of Dysnomia, we can use Kepler’s laws to
calculate a mass for the Eris-Dysnomia system
of 1.66 ×1022± 0.02 × 1022kg or 1.27 ±0.02 of
the mass of Pluto. With any plausible assump-
tions of albedo and density, Dysnomia’s mass in
the system is negligible. In addition to being the
largest, Eris is also the most massive known
From this mass measurement and the previ-
ous size measurements, we can calculate the
density of Eris. The initial indirect IRAM radio-
metric measurement suggested a diameter of
3000 ± 400 km (2), whereas the later HST
direct measurement found a smaller diameter of
2400 ± 100 km (3). By using the more direct
measurement with the smaller uncertainty, we
is consistent with the moderately high 2.03 ±
0.06, 2.06 ± 0.01, and ~ 2.6 g cm−3densities
EL61, respectively (9–11). Using the earlier in-
direct IRAM diameter measurement would give
a density of only 1.2 ± 0.6 g cm−3, which is
significantly lower than other objects of compa-
rable size in the outer solar system, giving con-
fidence, although not confirmation, in the more
direct HST diameter measurement with the
Recent direct and indirect measurements of
lower-than-expected densities for objects in the
outer solar system and thus a deficit of rocky
high densities of Eris, Pluto, Triton, and 2003
EL61, in contrast, all require rock fractions of
~70% or higher (14), as anticipated from ex-
pected cosmochemical abundances in the proto-
References and Notes
1. M. E. Brown, C. A. Trujillo, D. L. Rabinowitz, Astrophys. J.
635, L97 (2005).
2. F. Bertoldi, W. Altenhoff, A. Weiss, K. M. Menten,
C. Thum, Nature 439, 563 (2006).
3. M. E. Brown, E. L. Schaller, H. G. Roe, D. L. Rabinowitz,
C. A. Trujillo, Astrophys. J. 643, L61 (2006).
4. M. E. Brown et al., Astrophys. J. 639, L43 (2006).
5. P. L. Wizinowich et al., Pub. Astron. Soc. Pacific 118, 297
6. Materials and methods are available on Science Online.
7. P. Goldreich, Y. Lithwick, R. Sari, Nature 420, 643 (2002).
8. R. M. Canup, Science 307, 546 (2005).
9. M. W. Buie, W. M. Grundy, E. F. Young, L. A. Young, S. A.
Stern, Astron. J. 132, 290 (2006).
10. B. A. Smith et al., Science 246, 1422 (1989).
11. D. L. Rabinowitz et al., Astrophys. J. 639, 1238 (2006).
12. D. C. Jewitt, S. S. Sheppard, Astron. J. 123, 2110 (2002).
13. J. A. Stansberry et al., Astrophys. J. 643, 556 (2006).
14. W. B. McKinnon, J. I. Lunine, D. Banfield, in Neptune and
Triton, D. P. Cruikshank, Ed. (Univ. Arizona Press, Tucson,
1995), pp. 807–878.
15. This research is supported by a Presidential Early Career
Award to M.E.B. In addition, E.L.S. is supported by a
NASA graduate student research fellowship. We thank
J. Aycock, R. Campbell, A. Conrad, K. Grace, J. Lyke,
C. Melcher, C. Sorenson, M. van Dam, and C. Wilburn at
Keck Observatory, without whom these complicated LGS
AO observations would not have been possible.
Supporting Online Material
Materials and Methods
Tables S1 and S1
29 December 2006; accepted 14 March 2007
Division of Geological and Planetary Sciences, California
Institute of Technology, Pasadena, CA 91125, USA.
*To whom correspondence should be addressed. E-mail:
Fig. 1. The projected orbit of Dysnomia around
Eris. Observations are show as crosses of the size
of the 1-s uncertainty. The predicted positions
at the time of observations are shown by open
circles. The solid circle in the center is 10 times
the actual angular size of Eris.
VOL 31615 JUNE 2007