An estimation of Envisat’s rotational state accounting for the precession of its rotational axis caused by gravity-gradient torque☆

Abstract The rotational state of Envisat is re-estimated using the specular glint times in optical observation data obtained from 2013 to 2015. The model is simplified to a uniaxial symmetric model with the first order variation of its angular momentum subject to a gravity-gradient torque causing precession around the normal of the orbital plane. The sense of Envisat’s rotation can be derived from observational data, and is found to be opposite to the sense of its orbital motion. The rotational period is estimated to be ( 120.674 ± 0.068 ) · exp ( 4.5095 ± 0.0096 ) × 10 - 4 · t s , where t is measured in days from the beginning of 2013. The standard deviation is 0.760 s, making this the best fit obtained for Envisat in the literature to date. The results demonstrate that the angle between the angular momentum vector and the negative normal of the orbital plane librates around a mean value of 8.53 ° ± 0.42 ° with an amplitude from about 0.7 ° (in 2013) to 0.5 ° (in 2015), with the libration period equal to the precession period of the angular momentum, from about 4.8 days (in 2013) to 3.4 days (in 2015). The ratio of the minimum to maximum principal moments of inertia is estimated to be 0.0818 ± 0.0011 , and the initial longitude of the angular momentum in the orbital coordinate system is 40.5 ° ± 9.3 ° . The direction of the rotation axis derived from our results at September 23, 2013, UTC 20:57 is similar to the results obtained from satellite laser ranging data but about 20 ° closer to the negative normal of the orbital plane.