Signatures of the Martian rotation parameters in the Doppler and range observables

Abstract

The position of a Martian lander is affected by different aspects of Mars' rotational motions: the nutations, the precession, the length-of-day variations and the polar motion. These various motions have a different signature in a Doppler observable between the Earth and a lander on Mars' surface. Knowing the correlations between these signatures and the moments when these signatures are not null during one day or on a longer timescale is important to identify strategies that maximize the geophysical return of observations with a geodesy experiment, in particular for the ones on-board the future NASA InSight or ESA-Roscosmos ExoMars2020 missions. We provide first-order formulations of the signature of the rotation parameters in the Doppler and range observables. These expressions are functions of the diurnal rotation of Mars, the lander position, the planet radius and the rotation parameter. Additionally, the nutation signature in the Doppler observable is proportional to the Earth declination with respect to Mars. For a lander on Mars close to the equator, the motions with the largest signature in the Doppler observable are due to the length-of-day variations, the precession rate and the rigid nutations. The polar motion and the liquid core signatures have a much smaller amplitude. For a lander closer to the pole, the polar motion signature is enhanced while the other signatures decrease. We also numerically evaluate the amplitudes of the rotation parameters signature in the Doppler observable for landers on other planets or moons.

MoMo: a new empirical model of the Mars ionospheric total electron content based on Mars Express MARSIS data

“…11). This is about one order of magnitude below the estimated noise of those instruments, but is of same order of magnitude as the contribution of the liquid core in the Doppler (~10 À3 -10 À2 mm s À1 , Yseboodt et al, 2017). Consequently, the predictions made with MoMo suggests that the radio-science teams will have to either correct their data using our model for instance or adapt the mission programmatic to avoid operating during sunrise and sunset when the TEC rapidly varies.…”

“…Doppler measurements from RISE and LaRa instruments are at a precision as high as 0.02 mm s À1 at 60 s integration time corresponding to the instrument precision requirement. However, the impact of a liquid core on Martian Orientation Parameters is lower than 0.004 mm s À1 in X-band (Yseboodt et al, 2017) and could be detected from data time-series. To reach this accuracy, the ionospheres of Mars and Earth as well as the interplanetary plasma contributions need to be corrected for along the line of sight.…”

LaRa after RISE: Expected improvement in the Mars rotation and interior models

“…2. When δ Earth is close to zero, the sensitivity of the DTE (direct-to-Earth) Doppler measurements to the nutation is null because the rotation axis of Mars is then perpendicular to the LOS [Yseboodt et al, 2017]. Unfortunately, the Earth declination maxima, when DTE Doppler sensitivity to nutation is maximum, are close to the solar conjunctions when data are discarded because of large plasma noise (i.e.…”

“…4. These quantities crucially because they affect the sensitivity of the Doppler measurements to the MOP[Yseboodt et al, 2017. is between 35 and 45 degrees above the horizon.…”

Mars orientation parameters determination based ondirect-to-Earth measurement

“…因此极移参数可表示为 ( ) 值按照当前实际精度的两倍来设置. 目前还没有确切 的研究给出火星极移的振幅, 但已有研究表明, 火星 极移的量级在0-15 mas之间, 钱德勒摆动量级约在10-100 mas之间 [25,26] , 依据文献 [23] 图 4 (网络版彩图)岁差与自转速率收敛曲线, 实线为标准差, 红色圆圈表示真实误差, 黄色虚线表示当前参数的精度, 数值来 源于已有的着陆器跟踪数据计算的结果 [13] . 使用双程多普勒数据计算岁差参数I 0 (a), 0 (b)和自转速率 0 (c)的收敛曲线; 使用 双程测距数据计算岁差参数I 0 (d), 0 (e)和自转速率 0 (f)的收敛曲线 Figure 4 (Color online) Precession and spin rate parameters versus tracking duration.…”