Asteroid lightcurve inversion with Lommel-Seeliger ellipsoids

We derive initial rotation, shape, and scattering properties for asteroids from sparse and dense photometry based on the so-called Lommel-Seeliger ellipsoid (LS ellipsoid). Due to the analytical disk-integrated brightness, the LS ellipsoid allows for fast rotation-period, pole-orientation, and shape analyses, as well as efficient Markov-chain Monte Carlo solutions (MCMC). We apply the methods to simulated sparse Gaia photometry, as well as to ground-based photometry composed of dense lightcurves. For a specific Gaia simulation, we make use of a numerical reflection coefficient developed for particulate surfaces, and utilize the LS ellipsoid in the inversion of the simulated data. We conclude that, in a majority of cases, initial LS ellipsoid retrieval of the parameters is satisfactory. Finally, we formulate a single-scattering phase function that, for a spherical asteroid, results in the H,G1,G2 photometric phase function.