Ilmarë

Ilmarë, or Varda I, full designation 174567 Varda I Ilmarë, is the single known natural satellite of the Kuiper belt object 174567 Varda. It was discovered by Keith Noll et al. in 2009, at a separation of about 0.12 arcsec, using discovery images taken by the Hubble Space Telescope on 26 April 2009, and reported in 2011. At approximately 326 km in diameter (about 45% that of its primary), it is the fourth or fifth-largest known moon of a trans-Neptunian object, after Pluto I Charon, Eris I Dysnomia, Orcus I Vanth and very possibly Haumea I Hiʻiaka. Assuming that Ilmarë has the same albedo and density as Varda, Ilmarë would constitute approximately 8.4% of the system's mass, approximately $4,809 km$.

Name
Names for Varda and its moon were announced on 16 January 2014. Ilmarë is a chief of the Maiar and handmaiden to Varda, the queen of the Valar, creator of the stars, and principal goddess of the elves in J. R. R. Tolkien's fictional mythology.

Characteristics
Ilmarë and Varda are tightly bound, with a separation of about 13 Varda radii, and a consequently low angular momentum. Along with the high inclination of Varda's orbit, they are similar in this way to the Orcus–Vanth and Salacia–Actaea systems. As of 2015 two mirror orbital solutions are possible with slightly different orbital parameters. The calculated eccentricity is inconsistent with the likely age of the system, suggesting that it might be spurious, but the expected age is also contradicted by suggestions that Varda may not be tidally locked.

If Ilmarë and Varda have the same albedo, Ilmarë would be $0.018$ in radius, or approximately 8.4% the volume of Varda. If the two bodies also have the same density, Ilmarë would then have approximately 8.4% the system mass of $0.025$. If, however, the albedo of Varda is 50% greater than that of Ilmarë, Ilmarë would have a radius of $0.022$ and the bulk density of the system would be $5.751 days$. If Ilmarë has a 50%-greater albedo, then its radius would be $101$ and the bulk density would be $85.1$. Because the absolute magnitudes of the two bodies at different wavelengths are similar, it's not likely that their albedos differ by much, so Ilmarë is likely to be in this size range.