The orbit of asteroid (317) Roxane’s satellite Olympias from Gemini, Keck, VLT and the SOR, and (22) Kalliope’s Linus from the SOR

Abstract

A definitive orbit is derived for asteroid (317) Roxane’s satellite Olympias [S/2009 (317)1] by combining the 2009 discovery images from Gemini North (Merline et al. 2009) with images from Keck and the VLT obtained in 2012, as well as images from its 2016-2017 apparition from the Starfire Optical Range. The orbit is retrograde with respect to the ecliptic but in the same sense as Roxane’s spin. Olympias has a period of P=11.9440±0.0005 days, a semi-major axis of a=245±3 km, and an orbital pole at RA=97∘, Dec=−71∘, or ecliptic coordinates λ=245∘, β=−85∘, close to the south ecliptic pole. This satellite orbital pole is only 3∘ from Roxane’s orbital pole (but in a retrograde sense) and restricts all observations of Olympias from Earth to within 4∘ of the satellite’s orbital plane. By fitting the brightness ratios between Roxane (rotational period of 8.16961±0.00005 h) and Olympias as a Fourier series, we find a rotational period for Olympias of 8.2587±0.0001 h, making this an asynchronous wide binary. From the brightness ratios, and with the average infrared modeling diameter found in the literature of 19.16±0.39 km (error of the mean), we estimate triaxial ellipsoid radii of 14.5×8.5×7.2 km for Roxane and 3.6×2.5×2.0 km for Olympias. We can then apportion the mass between the two objects and find a density for both (assumed to be the same) of 2.16±0.18 g/cm3. There are only a few E-type binaries known and this is the first direct determination of E-type density from a binary. We suggest that the system was formed by the Escaping Ejecta Binary (EEB) mechanism of Durda et al. (2004a), probably forming closer together, and then undergoing the complex evolution steps described by Jacobson et al. (2014) involving synchronization, BYORP orbit expansion, loss of tidal lock, and then YORP spinup. Roxane and Olympias may be the only known EEB system to date.From the same 2016-2017 apparition the orbit of Linus around asteroid (22) Kalliope is derived from the SOR. This well-observed bright satellite is found to have a circular orbit with a period of P=3.5956±0.0004 days, in good agreement with the latest elements of Vachier et al. (2012) of P=3.5957±0.0001 days, and a semi-major axis of a=1099±6 km, somewhat greater than their a=1082±11 km for a slightly eccentric orbit (e=0.007±0.010). With a diameter for Kalliope of 161±6 km (Hanuš et al. 2017), we derive a density for Kalliope of 3.72±0.25 g/cm3 from our one apparition study, the same as Hanuš et al. (2017) but greater than the 3.24±0.16 of Vachier et al. (2012).