3.2.3 The Gaia orbit

Author(s): Sergei Klioner

An important part of Gaia data processing is the Gaia ephemeris allowing one to compute Gaia position and velocity in the BCRS for any moment of time covered by observations. Clearly, the accuracy of Gaia ephemeris is crucial for the project. The required accuracy of Gaia velocity is driven by the aberration of light: 1 $\mu$as in direction corresponds to about 1 mm s${}^{-1}$ in velocity. The requirements for the accuracy of Gaia position comes from the paralactic effect for the near-Earth objects (NEOs) and was assumed to be 150 m. The latter requirement is only important for data releases that include solar-system data.

The Gaia ephemeris is provided by the European Space Operation Centre (ESOC). The original ESOC ephemeris is based on the same INPOP10e ephemeris that is used in the Gaia DPAC data processing. The ephemeris is based on radiometric observations of the spacecraft (radio ranging and Doppler pseudo-ranging data) and is constructed using standard orbit reconstruction procedures that include fitting a dynamical model to the observational data.

The standard ESOC orbit ORB1 is delivered once per week in the form of an OEM orbit file (OEM – Orbit Exchange Message). The orbit file contain three time segments of different nature: (1) final reconstructed orbit – the orbit is fitted to all available data and may change in the future only when new sort of data (e.g. DDOR – Delta-Differential One-Way Range, an observational technique giving high-accuracy directional positions of the spacecraft – or optical tracking, Section 3.2.2); this part starts with the launch and ends about 1 week before the date of delivery; (2) preliminary reconstructed orbit – the orbit is preliminary fitted to observations; this part of the orbit that starts about 1 week before the delivery and ends at the date of delivery will change in the next delivery; (3) predicted orbit – the orbit is not fitted to the data, but obtained from dynamical modelling with best known parameters of the satellite, its orbit and planned manoeuvres; this part covers from approximately date of delivery to the planned end of mission. The ORB1 ephemerides are used in the daily processing.

Approximately once per year ESOC delivers a more sophisticated version of Gaia orbit that is called ORB2 and based on both radiometric and DDOR data. The ORB2 orbits are valid till certain time in the past and in general have better accuracy than the ORB1 orbits. The astrometric solution (AGIS) of Gaia DR2 is based on the ORB2 ephemeris valid till the end of 2016.

The delivered ESOC ephemerides are geocentric and parametrized by TDB. They are converted to barycentric using INPOP10e and re-parametrized (and rescaled) to TCB when importing into DPAC software environment. The import process results into a set of Chebyshev polynomials for the barycentric Gaia orbit in TCB. The parameters of those Chebyshev polynomials are chosen so that the difference between the delivered OEM orbit file and the Chebyshev representation is negligible compared to the required accuracy of the orbit mentioned above.

In the delivered OEM files the $6\times 6$ variance–covariance matrix of 3 components of the position and 3 components of the velocity is delivered with a step of 30 seconds. This gives realistic estimates of the actual uncertainties of the Gaia orbit.

The Gaia orbit determination satisfies the accuracy requirements imposed by Gaia DR2: the uncertainty of the BCRS velocity of Gaia is believed to be below a few mm s${}^{-1}$ giving uncertainties in individual astrometric observations at the level below a few  $\mu$as.

The effect of an error in Gaia velocity in the astrometric solution (AGIS) is, to first order, equivalent to that of a specific small variation of the basic angle and an additional small variation of the Gaia attitude. The variation of attitude has no further consequences on the scientific parameters of the solution. In Gaia DR2 possible effects of basic angle variations are calibrated in AGIS using a simple model of periodic variations parametrized by the heliotropic phase of the satellite (see Section 3.3.7). This basic angle calibration not only improves our knowledge of the physical basic angle variations, but also diminish possible effects of Gaia ephemeris errors. For future releases, this sort of calibration will be more sophisticated.