Four-way Doppler measurements and inverse VLBI observations 1M-S3 Oct. 11-15, 2010 Four-way Doppler measurements and inverse VLBI observations for the Mars rotation observations T. Iwata1*, Y. Ishihara2, Y. Harada3, K. Matsumoto2, F. Kikuchi2, and S. Sasaki1 1Institute of Space and Astronautical Science/JAXA, Japan 2National Astronomical Observatory of Japan 3Shanghai Astronomical Observatory, China * 岩田 隆浩： iwata.takahiro@jaxa.jp 1 1

Introduction Variation of planetary rotation provides us information concerning both of an interior structure and surface mass redistribution. Such information is valuable for elucidating not only present condition but also evolution of a planet as a system. Precession and nutation of Mars reveal the core-mantle sub-system, besides length-of-day variation and polar motion of Mars show atmosphere-cryosphere sub-system.

Contribution to Mars System Science via Rotation Simultaneous observation is needed. Atmosphere-Cryosphere System Short-Term Variation (Comparative Meteorology) Polar Motion & LOD Variation Rotation Measurements Precession & Nutation MEPAG (March 2009) Long-Term Variation (Atmospheric Escape Studies) Core-Mantle System Landers Orbiters

What’s the Physical Origins of Nutation? time-varying tidal torque (& fluid core resonance???) 流体核有り 流体核無し Wikipedia (Nutation) (the SOLID core) (the LIQUID core) angular momentum interaction between its core and mantle

Mechanisms of Polar Motion & LOD Variation The atmosphere-cryosphere system are the most important source. Loading by Atmosphere & Ice Shear Stress by Wind Moment of Inertia Perturbation Angular Momentum Interaction

Observations of Mars Rotation Precession and length-of-day variation have been measured by means of tracking data of Viking 1 and 2, and Mars Pathfinder . Results of the Love number k2 obtained by two Martian explorers, namely, Mars Global Surveyor (MGS) and Mars Odyssey, predict existence of a liquid core on Mars. Seasonal variation of the polar caps on Mars was estimated mainly based on the laser altimeter data on MGS in conjunction with gravity data.

Precision by previous lander missions Articles (*simulated) Landers (*cancelled) accuracies [mas] † Polar Motion Length-of-day Folkner et al. (1997b)* Viking 1 & 2 + Pathfinder 7 ~ 101 ‡ 7 ~ 50 ‡ Yoder & Standish (1997) Viking 1 & 2 only --- ≈ 100 Folkner et al. (1997a) Barriot et al. (2001)* NetLander* (NEIGE) 1 ~ 14 ‡ 2 ~ 4 ‡ Yseboodt et al. (2003)* 1 ~ 7 ‡ 1 ~ 3 ‡ Dehant et al. (2009)* ExoMars (LaRa*) 2 ~ 5 ‡ *) not approved as missions, †) mas: mil-arc second, ‡) simulated values.

MELOS These measurements had, however, limitations in terms of accuracies within the framework of traditional technologies concerning space geodesy and astrometry. Thus, the new configurations of orbiter-to-lander tracking have been proposed. On the other hand, the Japanese research group has started to plan the new Martian explorer; MELOS (Mars Exploration with Lander-Orbiter Synergy). As one of the missions of MELOS, we are proposing areodetic observations using space geodetic techniques like as four-way Doppler measurements and inverse VLBI.

FWD Four-Way Doppler FWD Measurements fo MELOS Four-way Doppler measurements (FWD) are ranging rate measurements of target spacecrafts via relay spacecrafts. Utilizing the heritage of FWD by SELENE, we plan to track the MELOS Lander relayed by the MELOS Orbiter. Two-way ranging and ranging rate (RARR) measurements for each spacecraft are executed simultaneously. Lander1 Orbiter Lander2 <- <- 4-way <- <- 2-way <- 2-way Ka(30GHz), X, or S-band tracking station The connected lines express the coherent signals.

Comparison with LaRa The expected accuracies for these observations are almost in the same order as that in the case of satellite-to-lander tracking (Yseboodt et al., 2003). Dehant et al. (2008)

Inverse VLBI for MELOS ・We also introduce the new technology called inverse VLBI 　　(Kawano et al., 1999). One ground radio telescope, not a VLBI network, observes both the orbiter and the lander with same-beam or switching differential VLBI. The signals from the orbiter are coherently locked with those of the lander. ・One of the remarkable performances of inverse VLBI is that the theoretical accuracy of positioning depends only on the observation frequency and does not depend on the baseline length. Therefore, X-band observation of inverse VLBI will achieve the accuracy of 0.3 mm which is much better than that of FWD, RARR, and differential VLBI. ・Including the systematic phase noise, the accuracy for the rotation is estimated as less than 3 mas.

Fig. 5: Inverse VLBI (left) and differential VLBI (right) Orbiter Orbiter phase differences are measured L1 d: distance L2 Lander Lander inverse VLBI differential VLBI B: baseline length single station The connected lines express the coherent signals. sensitivity for positioning; σ(x) σ(x) = σ(⊿L) * d / B = 6 m under 　σ(⊿L) = 0.3mm 　 d = 40,000,000km*, B = 2,000km *) minimum sensitivity for positioning; σ(x) σ(x) = σ(⊿L); ⊿L = L1-L2 = 0.3 mm under 　 σ(⊿τ) = 1ps = 10-12

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