Ever heard of of planet Eris?

This is planet Eris, in the outskirts of the Solar System, as seen through the eyes of the Hubble Space Telescope:

Hubble Telescope's Advanced Camera for Surveys has taken this image of Eris in December 2005. The analysis of several such photos yields a diameter of Eris of 2400±100 km, or 1500±60 miles. (Credits: HubbleSite News Release STScI-2006-16, M. Brown)

It's such a faint and blurred blob even in the Hubble Space Telescope because it is quite small, and far away from Earth: At the moment, Eris is close to its aphelion, at a distance of 97 astronomical units - that's 97 times the mean distance of the Earth from the Sun! You can explore its eccentric and highly inclined orbit with this applet from the JPL.

In fact, according to the new definition of the International Astronomical Union from last August, Eris is not a planet, but only a dwarf planet. However, it is larger than Pluto, and it has more mass than Pluto, as was reported in a beautiful short note in Science two weeks ago [Ref 5]! So, for all those who prefer to stick to the old definition of a planet, it may be the true ninth planet - unless some other, even larger guy shows up from out there in the Kuiper belt.

Eris was discovered in October 2003 by astronomers Michael Brown, Chad Trujillo, and David Rabinowitz [Ref 1]. It was given the provisional name 2003 UB₃₁₃, or Xena for short. Soon after the discovery, its size could be measured by observations with a radio telescope of the Max-Planck Society [Ref 2] and the Hubble Space Telescope [Ref 3], and it came out that the new planet is larger than Pluto!

Moreover, there is a small moon in orbit around Eris, which was given the nickname Gabrielle. On September 14, 2006 the International Astronomical Union made official the names Eris for the planet and Dysnomia for its satellite.

A comparison of the sizes of (left to right) Eris, Pluto and Charon, the Moon, and the Earth. Eris' moon Dysnomia is not shown, but it is much smaller than Eris (diameter: 2400±100 km from HST, 3000±400 km from radio observation), Pluto (2300 km), Charon (1200 km), the Moon (3500 km), and the Earth (12800 km). (Credits: Max-Planck Gesellschaft Press Release News/SP/2006(10), Frank Bertoldi)

The discovery of Eris, and of several other large objects in orbits beyond Neptune, had spurred the hot debate about what is a planet, which then lead to the degradation of Pluto from planet to "dwarf planet" in August 2006. So it is fitting that Eris is the Greek goddess of strife and discord - Dysnomia, her daughter, is the goddess of lawlessness.

But in a time when ancient Greek gods and goddesses are reduced to large balls of rock and gas in space, even the goddess of lawlessness is subject to Newton's universal law of gravitational attraction. And this allows, in an elementary and elegant, classical way, to determine the mass of Eris.

The photo on the left is an image of Eris and its moon Dysnomia, the small spot left of Eris, taken with the Hubble Space Telescope on 30 August 2006. Dysnomia's projected orbit around Eris is superimposed on this photo in the image on the right (Credits: HubbleSite News Release STScI-2007-24, M. Brown)

In a first step, the orbit of Dysnomia around Eris has been determined from several observations with the Hubble Space Telescope and the Keck telescope in Hawaii.

The orbit of Dysnomia, the moon of Eris, as reconstructed from observations using the Keck telescope on 20, 21, 30, and 31 August 2006 and the Hubble Space Telescope on 3 December 2005 and 30 August 2006. Observations are show as crosses, the predicted positions at the time of observations are shown by circles. The solid circle in the center is 10 times the actual angular size of Eris. (Fig. 1 from Brown and Schaller, Science 316 1585 (2007 June 15), doi:10.1126/science.1139415. Reprinted with permission from AAAS.)

The observation of Dysnomia as shown in this figure reveals an apparent diameter of the orbit of roughly 1.1 arcsec, which, at the distance of 97 Astronomical units, or 97 × 150 million km ≈ 1.46·10¹⁰ km, corresponds to a diameter of 1.46·10¹⁰ × 1.1 × 2π / (360 × 3600) km ≈ 78000 km. A more detailed analysis yields an indeed circular orbit with a semimajor axis of r = 37500±200 km.

Now, this can be used to deduce the mass M_E of Eris!

Using elementary Newtonian mechanics, we equal the gravitational attraction between Eris and Dysnomia at distance r with the centrifugal force,

GM_Em_D/r² = m_Drω².

The frequency ω = 2π/T has to be calculated from the orbital period T of Dysnomia. With the equivalence principle at work, the mass of the satellite cancels out, and we can solve for the mass of Eris:

M_E = r³ω²/G.

Now, the orbital period of Dysnomia has been determined quite precisely to 15.772±0.002 days. This yields ω = 2π/(15.77 d × 24 h/d × 3600 s/h) ≈ 4.63·10^-6 s^-1. Newtons constant is 6.673·10^-11 m³ kg^-1 s^-2, and plugging everything together, the mass of Eris comes out as

M_E = 1.7·10²² kg.

For comparison, Pluto has a mass of 1.3·10²² kg, the Moon of 7.35·10²² kg, and the Earth of 5.97·10²⁴ kg. This means, the masses of Eris, Pluto, the Moon, and the Earth compare as 1.3 : 1 : 5.6 : 459.

And so, indeed, Eris and Pluto are on equal footing, revealed by the goddess of lawlessness and Newton's law!

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Here are some "historical" references about Eris:

1. Discovery of a Planetary-sized Object in the Scattered Kuiper Belt, by M.E. Brown, C.A. Trujillo, and D.L. Rabinowitz, The Astrophysical Journal 635 L97-L100 (2005 December 10) [PDF, ADS entry], arXiv:astro-ph/0508633 [see also: Eris webpage by Michael Brown]


2. The trans-neptunian object UB₃₁₃ is larger than Pluto, by F. Bertoldi, W. Altenhoff, A. Weiss, K.M. Menten and C. Thum, Nature 439 563-564 (2006 February 2) [PDF, ADS entry], doi:10.1038/nature04494 [see also: Press release by the Max-Planck Gesellschaft, comment by Frank Bertoldi]


3. Direct Measurement of the Size of 2003 UB313 from the Hubble Space Telescope, by M.E. Brown, E.L. Schaller, H.G. Roe, D.L. Rabinowitz, and C.A. Trujillo, The Astrophysical Journal 643 L61-L63 (2006 May 20) [PDF, ADS entry] [see also: Press Release by the HubbleSite]


4. Satellites of the Largest Kuiper Belt Objects by M.E. Brown et al., The Astrophysical Journal 639 L43-L46 (2006 March 1) [PDF, ADS entry], arXiv:astro-ph/0510029 [see also: Press Release by the Keck Observatory, News Item by Marcos van Dam, Dysnomia, the moon of Eris - webpage by Michael Brown]


5. The Mass of Dwarf Planet Eris by Michael E. Brown and Emily L. Schaller, Science 316 1585 (2007 June 15), doi:10.1126/science.1139415 [see also: Press Release by the HubbleSite News item by the Planetary Society, Press Release by the Keck Observatory]

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TAGS: physics, planets, Eris