1. Four-way Doppler measurements and inverse VLBI observations
1M-S Oct , 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： 1 1

2. 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.

3. 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

4. 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

5. 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

6. 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.

7. 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.

8. 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.

9. 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
< way
Ka(30GHz),
X, or S-band
tracking station
The connected lines express the coherent signals.

10. 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)

11. 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.

12. 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

13. References 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).