Asteroid Ephemeris, 1900 to 2050: Including Chiron and the Black Moon Lilith

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We refine the algorithm in Martikainen et al. (2021) for the derivation of absolute magnitudes and phase functions from Gaia photometry. As in their study, first, we start from the phase function slope parameter β S retrieved from MCMC inversion, recalling that β S describes the intrinsic surface-element properties of an asteroid. Second, using the full asteroid model available from the inversion, we move to the reference geometry of equatorial illumination and observation at the epochs and phase angles of the individual photometric points. Third, by computing the asteroid model brightnesses over one full rotation for each epoch, we determine the magnitudes of lightcurve brightness maxima. Martikainen et al. (2021) then carried out linear least-squares fitting to determine their phase curve slope parameter β max, from which they derived the full H, G 12 phase function. As a small improvement, we fit, directly, the H, G 12 phase function to the magnitudes of the brightness maxima. The resulting H and G 12 parameters then allow us to predict the lightcurve brightness maxima at arbitrary phase angles within 0°–120°. Fourth, a reference phase curve is computed for selected phase angles by averaging the magnitudes over one full rotation. Fifth, magnitudes of lightcurve brightness maxima are computed for the selected phase angles, together with the values for the integrated disk function (∝ μ 0/( μ+ μ 0) in Eqs 3, 4) and single-scattering phase function, all in the magnitude scale for the geometries corresponding to the brightness maxima. Sixth, a phase function is computed for an equal-projected-area spherical asteroid with the help of the single-scattering phase function, made possible by the fact that the mean projected area of a convex object in random orientation is one fourth of its total surface area ( van de Hulst, 1957). An absolute magnitude then follows from the prediction to zero phase angle. Seventh, we fit the equal-sphere phase function using the full H, G 1, G 2 phase function. Finally, we compute the slopes of the mean-magnitude reference phase curve ( β ref) and the phase function ( β S) at the 20° phase angle. Repeating the computations above for all the MCMC solutions allows us to obtain uncertainty estimates for the absolute magnitudes and phase functions throughout the entire phase curve analysis. 4 Results and Discussion In the case of convex inversion, after in-depth studies using least squares and MCMC, the error model for relative photometry was chosen to be the conventional one presented in Muinonen et al. (2020), whereas the error model for absolute photometry was taken to be the one with a unit weight for each dense ground-based lightcurve. The latter, conservative error model was required to account for, primarily, the systematic errors arising from the forward modeling of the inverse problem. Likewise, in ellipsoid inversion concerning both relative and absolute photometry, a unit weight was assigned for each dense ground-based lightcurve.

Asteroid Ephemeris for the Next Years, 2026 and 2027, in PDF format only for now: AsteroidsEphemeris2026 The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Photometric phase curves provide information about the intrinsic light-scattering properties of the surface that are intimately related to the regolith composition and structure. Since the composition and structure determine also the reflectance properties observed at different wavelengths, phase curves are strictly related to the taxonomic classification of asteroids. Phase curves are often represented with the help of a few parameters. The classical two-parameter H, G magnitude system has been used for a long time ( Bowell et al., 1989). H is the asteroid’s absolute magnitude, namely the magnitude (corresponding to unit distance from the Sun and the observer) measured at zero phase angle, and G is a parameter describing the overall variation of magnitude at different phase angles, including a nonlinear brightness surge at phase angles smaller than 10° (opposition effect). In recent years, it has been replaced by the so-called H, G 1, G 2 magnitude system, a three-parameter model developed by Muinonen et al. (2010) to remove the caveats of the H, G system in the case of low-albedo and high-albedo asteroids. Further refinements and applications of the H, G 1, G 2 system have been published, among others, by Penttilä et al. (2016) and Shevchenko et al. (2016). Note: Time is Noon GMT. If you’re in a different time zone other than UT or GMT, you will need to adjust for the time zone offset. For example, UT is 5 hours ahead of Eastern Time and 8 hours ahead of Pacific Time. The reflection coefficient in Eq. 5 belongs to a class of photometric models consisting of a Lommel-Seeliger-type volume-element part and a part describing scattering among volume elements in a particulate medium (e.g., Lumme and Bowell, 1981; Muinonen and Lumme, 1991).

Retrograde planets are marked with a red Rx symbol in the top ephemeris. In the asteroid ephemeris, however, they’re shown in pink/red. Display the orbits of all the planets, planetary satellites, and optionally one or more small bodies.

About this Ephemeris:

Where Sappho is, there is greater vulnerability, yearning, desire for poetry and transcendence, and love. The “Stations” section shows planets when they change direction, either retrograde (marked with an Rx) or direct (marked with a D). b) you compute the position for one moment with the speed flag set. Then you look at the speed in longitude value, whether it is positive or negative. This value is found in xx[3]. In earlier work ( Muinonen et al., 2020), models of observational uncertainties were developed for dense relative photometry and sparse relative photometry. The former entailed ground-based lightcurves that were treated, in lightcurve inversion, on a relative magnitude scale. The latter comprised lightcurves of sparse Gaia photometry that were incorporated on a relative magnitude scale, too. Martikainen et al. (2021) then treated the Gaia photometry in the absolute sense, deriving absolute magnitudes for a large number of asteroids. In the present work, we provide a complete set of four models for observational uncertainties, including models for dense relative, sparse relative, dense absolute, and sparse absolute lightcurves.

The ephemerides above show the daily positions, month to month in the year 2021, of the four major asteroids, Chiron, and the minor asteroids Eros, Psyche, and Sappho. specify an observing point with respect to a user-input artifical satellite. User-Defined TLE Objects as Observatories Selected by the user. It can be a major-body or small-body. Center (or coordinate origin, or observering location)

References

Yearly/monthly ephemerides offer daily zodiacal longitudes/positions of planets, asteroids, and points.