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Four-way Doppler measurements and Four-way Doppler measurements and

inverse VLBI observations inverse VLBI observations

for the Mars rotation observationsfor 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 Japan3Shanghai Astronomical Observatory, China

* 岩田 隆浩： iwata.takahiro@jaxa.jp

1M-S3 Oct. 11-15, 2010

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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.

Introduction

MarsMapcContribution to Mars System Science via Rotation

Atmosphere-Cryosphere System Short-Term Variation

(Comparative Meteorology)

Long-Term Variation

(Atmospheric Escape Studies)

Rotation Measurements

Precession & Nutation

Orbiters

Polar Motion & LOD Variation

MEPAG (March 2009)

Simultaneous observation is needed.

Core-Mantle System

Landers

What’s the Physical Origins of Nutation?

(the SOLID core)

流体核有り

流体核無し

Wikipedia (Nutation)

angular momentum interaction between its core and mantle

time-varying tidal torque (& fluid core resonance???)

(the LIQUID core)

Mechanisms of Polar Motion & LOD Variation

The atmosphere-cryosphere system are the most important source.

Angular Momentum

Interaction

Shear Stress by Wind

Moment of Inertia

Perturbation

Loading by Atmosphere & Ice

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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.

Observations of Mars Rotation

MarsMapcPrecision 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)

Viking 1 & 2 + Pathfinder

--- ≈ 100

Barriot et al. (2001)*

NetLander* (NEIGE)

1 ~ 14 ‡ 2 ~ 4 ‡

Yseboodt et al. (2003)*

NetLander* (NEIGE)

1 ~ 7 ‡ 1 ~ 3 ‡

Dehant et al. (2009)*

ExoMars (LaRa*)

2 ~ 5 ‡ 1 ~ 7 ‡

*) not approved as missions, †) mas: mil-arc second, ‡) simulated values.

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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.

MELOS

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Lander1

Lander2

Orbiter

tracking stationKa(30GHz), X, or S-band

Four-Way Doppler FWD Measurements fo MELOS

<- <- 4-way<- <- 2-way<- 2-way

FWD

The connected lines express the coherent signals.

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.

MarsMapcComparison with LaRa

Dehant et al. (2008)

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).

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・ 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.

Inverse VLBI for MELOS

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differentialVLBI

Orbiter

Lander

single station

inverseVLBI

Orbiter

Lander

phase differencesare measured

sensitivity for positioning; σ(x) σ(x) = σ( L) *⊿ d / B = 6 munder　 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 mmunder

　 σ( τ) = 1ps = 10⊿ -12

L1

L2

d:

dis

tan

ce

B: baseline length

Fig. 5: Inverse VLBI (left) and differential VLBI (right)

The connected lines express the coherent signals.

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Barriot, J. P., et al., Adv. Space Res.., 28, 1237 (2001).

Dehant, V., et al., Planet. Space Sci., 57, 1050 (2009).

Folkner, W. M., et al., Science, 278, 1749 (1997).

Iwata, T., Transact. JSASS Spa. Tech. Japan, in press (2010).

Kawano, N., et al., J. Geod. Soc. Japan., 45, 181 (1999).

Konopliv, A. S., et al., Icarus, 182, 23 (2006).

Matsuo, K. and Heki, K., Icarus, 202, 90 (2009).

Namiki, N., et al., Science, 323, 900 (2009).

Smith, D. E. et al., Science, 294, 2141 (2001).

Yoder, C. F., and Standish E. M., J. Geophys. Res., 102, 4065 (1997).

Yoder, C. F., et al., Science, 300, 299 (2003).

Yseboodt, M., et al., J. Geophys. Res., 108, 12 (2003).

References