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tokens: to the nucleus, e n directed along the orbital angular momentum perpendicular to the orbital plane, and e t being orthogonal to both e r and e n . By comparing 14 cometary orbits, Marsden et al. (1973) derived the following model for the non-gravitational acceleration: with the constant parameters A 1 , A 2 , and A 3 and the empirical activity function The solar distance r ′ = r ( t − Δ t ) includes a time-shift Δ t introduced by Yeomans Chodas (1989) to account for activity asymmetries with respect to perihelion, as studied by Sekanina (1988) . As we discuss later, g ( r ) is not directly proportional to the sublimation flux, as originally stated by Marsden et al. (1973) , Eq. ( 4 ). The Marsden parameters provide an excellent albeit empirical description of the non-gravitational acceleration. The integration of a Marsden-type orbit proceeds by solving Eq. ( 1 ) with the non-gravitational acceleration Eq. ( 2 ). 2.2 Orbit determination based on spacecraft data Moving beyond the Marsden model requires more detailed data from spacecraft missions or radar observations about the magnitude and direction of the observed non-gravitational acceleration in space. For 67P, the Rosetta mission provides a two-year data set for the rotation-axis orientation (see Kramer et al. 2019 ) and the orbital evolution, but an iterative process was required to obtain the three-dimensional non-gravitational acceleration with high precision. We started with the multi-arc orbital solution from the flight dynamics team at ESOC, which is available as SPICE kernel (CORB_DV_257_03___T19_00345.BSP) and is returned from the Horizons system as the position for 67P during the Rosetta mission. In the following we refer to it as r ESOC ( t ). Before and after the Rosetta mission, Horizons returns the solution 67P/K154/2 based on Marsden parameters with a discontinuous jump by 2000 km into the Rosetta period. In addition to this discontinuity in Horizons, further discontinuities in the ESOC position vector r ESOC ( t ) during the Rosetta mission exist, which do not allow us to obtain the acceleration by a second derivative of the position vector (see the discussion by Attree et al. 2019 ). Table 1 Representative initial conditions for the orbit integration at JDB 2 456 897.71970 (≈ −350 days from perihelion), mean equator, and equinox of the terrestrial J2000 frame. Notes. An additional 30 nearby initial conditions have been identified that differ on average by less than 22 km over the (−400, 400) day interval from the partly nonphysical ESOC orbit. Table 2 Non-gravitational acceleration parameters used by Horizons in conjunction with the standard parameters α = 0.1112620426, k = 4.6142, m = 2.15, n = 5.093, and r 0 = 2.808 for g ( r ) in Eq. ( 3 ). An accurate estimate of the non-gravitational acceleration is tied to finding the best possible initial condition during a time with negligible cometary activity. We iteratively refined the orbit to identify the initial conditions