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Table 1

Observational, physical, and orbital parameters of Varda.

Quantity Value Ref. Comments
Radius (km) V14 Varda radius
V14 Effective radius(a) from radiometric modelling (Herschel data)
G15 Assuming that Varda and Ilmarë have spherical shapes and the same albedo,
with brightness difference of Δmag = 1.734 ± 0.042,
using photometric data of HST, Keck II, and Gemini North Telescopes,
resulting in km and km.
Mass (1020 kg) 2.664 ± 0.064 G15 System mass
Geometric albedo 0.102 V14 Radiometric modelling, Herschel data (“TNOs are Cool" programme)
Absolute magnitude (HV) 3.61 ± 0.05 V14
3.988 ± 0.048 A16 with a phase coefficient(b) β = −0.455 ± 0.071
Rotational period (h) 5.9/7.87 T10 Single-peaked light-curve with an amplitude of 0.06 ± 0.01 mag
5.91 T14 Other possible solutions (aliases) are mentioned: 4.76 h and 7.87 h
Spectral slope (%/100 nm) 19.2 ± 0.6 F09
Density ρ (g cm−3) 1.12/0.63 T10 Associated with the periods (5.9 and 7.87 h) and sizes, respectively
Bulk density of the system V14 Assuming that Varda and Ilmarë have equal albedo and density values
Varda-Ilmarë (g cm−3) G15 Using the mass and radius described above

Ecliptic orbital elements of Varda

a (AU) 46.046 LS NIMA ephemeris, see text
e 0.140 LS
i (deg) 21.498 LS

Orbital elements of Ilmarë (ref:G15)
solution 1 solution 2

a (km) 4812 ± 35 4805 ± 35
e 0.0181 ± 0.0045 0.0247 ± 0.0048
Orbital pole (J2000)
αp (deg) 273.0 ± 1.5 229.5 ± 1.5
δp (deg) − 11.0 ± 1.9 4.9 ± 1.8

Notes. (a) Vilenius et al. (2014) defined the radiometric (area-equivalent) effective diameter of a binary system as , where D1 and D2 are the primary and secondary diameters, respectively. (b)This assumes a linear trend of the phase curves and considers a magnitude variability that is due to the rotational light-curve.

References. T10: Thirouin et al. (2010), T14: Thirouin et al. (2014), F09: Fornasier et al. (2009), V14: Vilenius et al. (2014), G15: Grundy et al. (2015), A16: Alvarez-Candal et al. (2016), LS : NIMA ephemerides (

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