Desaturation manoeuvres and precise orbit determination for the BepiColombo mission

Mon. Not. R. Astron. Soc. 423, 2270–2278 (2012) doi:10.1111/j.1365-2966.2012.21035.x Desaturation manoeuvres and precise orbit determination for the BepiColombo mission E. M. Alessi, S. Cicalò, A. Milani and G. Tommei Dipartimento di Matematica, Università degli Studi di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy Accepted 2012 April 2. Received 2012 March 30; in original form 2012 February 22 ABSTRACT Key words: celestial mechanics – planets and satellites: individual: Mercury. 1 I N T RO D U C T I O N BepiColombo is a joint ESA/JAXA mission aimed at the exploration of Mercury. It represents a challenging project which demands a really advanced technology, not just for the ambitious goals, but also for the severe thermal environment it will face. Two spacecraft, the ESA Mercury Planetary Orbiter (MPO) and the JAXA Mercury Magnetospheric Orbiter (MMO), are expected to be launched together in 2014 on an Ariane V. On their arrival in 2020 the two probes will be inserted on separate orbits as a consequence of the different quantities they are supposed to measure. The objectives of the MMO regard mainly the magnetosphere, the magnetic field and the atmosphere of the planet, while the MPO will study the surface, the inner structure, the gravity field, the orbit and the exosphere of Mercury and will perform fundamental physics experiments. The nominal duration of the whole mission is one year, with a possible extension to two years (Garcia et al. 2009). The Celestial Mechanics Group of the University of Pisa is responsible for the orbit determination of the MPO and the parameter estimation corresponding to the Radio Science Experiment. With this, we mean the gravimetry, rotation (Milani et al. 2001a; Sánchez Ortiz, Belló Mora & Jehn 2006; Pfyffer, Van Hoolst & Dehant  E-mail: (EMA); (SC); (AM); (GT) 2011) and relativity (Milani et al. 2001b) experiments carried out by means of very accurate range and range-rate observations, and optical camera images of the Mercury surface. Following Iess & Boscagli (2001), with a full 5-way1 link between the orbiter and the ground station, we will be able to obtain measurements with an accuracy of 10 cm in range and 3 × 10−4 cm s−1 in range rate (at 1000 s integration time). In this work we will analyse the role of the desaturation manoeuvres, needed to maintain the desired attitude of the s/c, in the precise orbit determination required by the Radio Science Experiment. In the neighbourhood of Mercury, the probe is subjected to a strong radiation pressure which would change its attitude, which instead should be kept aligned for the nadir pointing instruments for the specific objectives of the mission. To avoid this effect, a set of reaction wheels are mounted on the s/c: by varying their rotation state, they accumulate the torque produced by the solar radiation pressure and hence ensure the pointing needed for the probe. When these wheels cannot be accelerated any more, they are slowed down while realigning the s/c attitude by thruster pulses. A desaturation (or off-loading) manoeuvre results from this process. Because of the s/c design, the resulting velocity changes are 1 The configuration of the 5-way link is: an X-band downlink with an X-band uplink, a Ka-band downlink with the same X-band uplink and a Ka-band downlink with a Ka-band uplink.  C 2012 The Authors C 2012 RAS Monthly Notices of the Royal Astronomical Society  This work analyses the consequences that the desaturation manoeuvres can have on the precise orbit determination corresponding to the Mercury Orbiter Radioscience Experiment (MORE) of the BepiColombo mission to Mercury. This is an ESA/JAXAjoint project with challenging objectives regarding geodesy, geophysics and fundamental physics. We will show how these manoeuvres affect the orbit of the s/c and the radio science measurements and how to include them in the orbit determination and parameter estimation procedure. The non-linear least-squares fit is applied on a set of observational arcs separated by intervals of time where the probe is not visible. With the current baseline of two ground stations, two manoeuvres are performed per day, one during the observing session and the other in the dark. To reach the scientific goals of the mission, they have to be treated as ‘solve for quantities’. We developed a specific methodology based on the deterministic propagation of the orbit, which is able to deal with these variables, by connecting subsequent observational arcs in a smooth way. The numerical simulations demonstrate that this constrained multi-arc strategy is able to determine all the manoeuvres together with the other parameters of interest at a high level of accuracy. BepiColombo desaturation manoeuvres in MORE 2271 where m is the number of observations and ξ = O − C is the vector of residuals, difference between the observed quantities O and the predicted ones C(u), computed following given suitable models and assumptions. In our case, O are range and range-rate data, while C(u) are the results of the light-time computation (Tommei, Milani & Vokrouhlický 2010) as a function of all the quantities u listed above. Finally, wi is the weight associated with the i-observation. Among the parameters u, (1), (2), (3), (4) and (5) are present in the equations of motion for the mercurycentric orbit of the probe, while (6) and (7) in those for the heliocentric orbits of Mercury and the Earth–Moon barycentre. Other information required for such orbit propagations is supposed to be known: position and velocity for the other planets of the Solar system are obtained from the JPL ephemerides DE421 (DE421; Folkner, Williams & Boggs 2008); the rotation of Earth is provided by the interpolation table made public by the International Earth Rotation Service (IERS) and the coordinates associated with the ground stations are expected to be available. The procedure to compute u∗ is based on a modified Newton’s method known in the literature as the differential corrections method; see e.g. Milani & Gronchi (2010, Chap. 5). Let us define 2 BAC K G RO U N D is applied iteratively until either Q does not change meaningfully from one iteration to the other or u becomes smaller than a given tolerance. The BepiColombo Radio Science Experiment consists in determining the following quantities, which appear as coordinates in the parameter vector u: (1) initial conditions of the s/c at given times (orbit determination); (2) spherical harmonics of the gravity field of Mercury (Milani et al. 2001a; Sánchez Ortiz et al. 2006) and tidal Love number k2 (Kozai 1965); (3) parameters defining the model of the Mercury’s rotation (Milani et al. 2001a; Sánchez Ortiz et al. 2006; Pfyffer et al. 2011; Cicalò 2012); (4) digital calibrations for the Italian Spring Accelerometer (ISA) (Iafolla et al. 2011); (5) desaturation manoeuvres; (6) initial conditions for Mercury and Earth–Moon barycentre at some initial time; (7) G (...truncated)