Spin Orientation of the Galilean Satellites

The four Galilean satellites (Io, Europa, Ganymede, and Callisto) are locked in a 1:1 spin-orbit resonance. Their rotation axis is assumed to be in a Cassini state, meaning that the rotation axis follows the long-term precession of the orbit normal. The obliquity of the satellites, which is the angular separation between the rotation axis and the orbit normal, is expected to be small. The satellites move on eccentric orbits and may have forced longitudinal librations.

The orientation/rotation angles can be described using at least two different sets of angle:

• the Euler angles with respect to the Laplace plane: the obliquity θ and the node longitude ψ. Additionally, the rotation angle Φ gives the direction of the prime meridian. These angles are regularly used for the physical modeling of the torques, see for example Baland et al. (2012).
• the equatorial coordinates with respect to the ICRF equatorial plane: the right ascension α_S and the declination δ_S angles express the orientation of the rotation pole while W also gives the direction of the prime meridian. These angles are used in the IAU reports (e.g. Archinal et al. 2018).

We computed analytical expressions to transform the orientation angles of the Galilean satellites between the Laplace plane and the ICRF equatorial plane, up to the first order in small parameters like the obliquity. This method is an improvement with respect to zero obliquity models. It does not require any fit of the amplitudes and frequencies on numerical series and the physical meaning of the frequencies is kept from the input series. It will be useful for the interpretation of future Earth based observations or JUICE data. The link between the geophysical interesting parameters and the IAU angles is more direct.

Our method is similar to Yseboodt et al. (2023) that convert the Martian Euler angles into IAU angles. The coordinates are the position of the spin axis of the synchronous satellites projected onto the Laplace Plane s_x = sin θ sin ψ, s_y = -sin θ cos ψ. They can be described as trigonometric series given the orbital theory of Lainey et al. (2006) transformed to spin into a multi-frequency Cassini state as in Baland et al. (2012).

References:
- B.A. Archinal, C.H. Acton, M.F. A'Hearn et al. Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015. Celest. Mech. Dyn. Astron. 130(3):22, 2018.
- R.M. Baland, M. Yseboodt, and T. Van Hoolst. Obliquity of the Galilean satellites: The influence of a global internal liquid layer. Icarus, 220:435-448, 2012.
- V. Lainey, L. Duriez and A. Vienne. Synthetic representation of the Galilean satellites'orbital motions from L1 ephemerides. Astronomy & Astrophysics, 456(2):783-788, 2006.
- M. Yseboodt, R.M. Baland and S. Le Maistre, Mars orientation and rotation angles. Celest. Mech. Dyn. Astron. 135(50), 2023.