Venus rotational motion and its resolution through the upcoming EnVision mission

Introduction
Venus is an intriguing planet because it is similar to Earth in terms of mass and size, but has followed a different evolutionary path, with a thick atmosphere and inhospitable surface. Future space missions EnVision (ESA) and VERITAS (NASA) will explore Venus to better understand this planet. In particular, Envision will carry out Radio Science Experiment, RSE [1] and radar measurements VENSAR experiment [1]. Here, we focus on the potential determination of Venus's rotational motion through these observations. Rotational and gravity data are crucial for revealing the planet's internal structure and the atmospheric coupling.

Rotational model
Venus' spin axis motion is described in space in terms of precession and nutation [2], which are the secular motion of the rotational axis and its periodic motion, variation in length-of-day [3], and through polar motion that is the rotation axis motion relative to the surface [4]. Today, the precession motion has been determined by the radar interferometry measurements [5], while length-of-day variations have been detected through VEX and radar interferometry measurements, but these determinations are still debated [6,5,7,2]. The polar motion has been recently investigated and its amplitude may be detectable through Envision mission [3]. Here, we will present updated precession-nutation and length-of-day models of Venus rotation.

Doppler tracking and radar tie-point
The RSE experiment will determine the gravity field, which is, by definition, attached to the body, thereby enabling the determination of the body's orientation and spin rate [8]. The VENSAR experiment will acquire radar images of selected regions of interest, covering approximatively 20% of Venus's surface with spatial resolution of 30 meters and 10 meters [1]. The planned temporal coverage spans six Venusian cycles, equivalent to 1400 Earth-days. We present first simulations of spin recovery through the control point network, suggesting that it will be possible to constrain Venus' precession to within few percent. Additionally, combined simulations of Doppler tracking and tie-points monitoring in VENSAR images show a two to three improvement in the determination of rotational parameters.

References:
[1] ESA. 2023, EnVision - Understanding why Earth’s closest neighbour is so different, Definition Study Report (Red Book), ESA document reference
[2] Cottereau, L., Souchay, J., 2009. Rotation of rigid Venus: a complete precession-nutation model. Astron. Astrophys. 507, 1635–1648.
[3] Cottereau, L., Rambaux, N., Lebonnois, S., and Souchay, J. (2011). The various contributions in Venus rotation rate and LOD. Astronomy and Astrophysics, 531:A45.
[4] Phan P.L, and Rambaux, N., Polar motion of Venus, Astronomy and Astrophysics, submitted
[5] Margot, J.-L., Campbell, D. B., Giorgini, J. D., et al. 2021, Nature Astronomy,5, 676
[6] Mueller, N.T., Helbert, J., Erard, S., Piccioni, G., Drossart, P., 2012. Rotation period of Venus estimated from Venus Express VIRTIS images. Icarus 217, 474–483.
[7] Campbell, B.A., Campbell, D.B., Carter, L.M, Chandler, J.F., et al., 2019, Icarus 332, 19-32
[8] Rosenblatt, P., Rambaux, N., Dumoulin, C., Marty, J.-C., Phan, P.-L., and Laurent-Varin, J.: EnVision gravity experiment: Joint inversion of Doppler tracking data and tie-points monitoring from SAR images., Europlanet Science Congress 2024, Berlin, Germany, 8–13 Sep 2024, EPSC2024-410, https://doi.org/10.5194/epsc2024-410, 2024.