Rotation, libration, and gravitational field of Mercury Véronique Dehant,
Tim Van Hoolst,
Pascal Rosenblatt,
Mikael Beuthe,
Nicolas Rambaux,
Severine Rosat,
Marie Yseboodt,
Gregor Pfyffer
Royal Observatory of Belgium,
BrusselsAnne Lemaître,
Jacques Henrard,
Sandrine d’Hoedt,
Nicolas Rambaux,
Julien Dufey
Facultés Universitaire Notre Dame de la Paix, Namur We acknowledge PRODEX support/Belspo/ESA
Rotation, libration, and gravitational field of Mercury Véronique Dehant,
Tim Van Hoolst,
Pascal Rosenblatt,
Mikael Beuthe,
Nicolas Rambaux,
Severine Rosat,
Marie Yseboodt,
Gregor Pfyffer
Royal Observatory of Belgium,
Brussels
Anne Lemaître,
Jacques Henrard,
Sandrine d’Hoedt,
Nicolas Rambaux,
Julien Dufey
Facultés Universitaire Notre Dame de la Paix, Namur We acknowledge PRODEX support/Belspo/ESA
Rotation and libration of Mercury
Rotation of the terrestrial planets
Mercury Venus Earth Mars
MERCURY: Spin/orbit coupling; 3:2 resonance
What are librations?
Revolution (orbit)
87,98 jours Rotation (spin)
58,64 days Solar torque 3:2
spin-orbit
resonance
La libration est donc u mouvement periodique de rotation
Oscillation autour de la rotation moyenne causée par une couple de force solaire sur la deformation equatoriale de mercure
Cm = C du manteau dans l’hypothèse d’un le noyau liquide ne participant pas à la libration
Capture en résonance 3:2 est aidée/influencée par les marées solaires
Les courtes periodes de libration ne diminuent pas en amplitude vers 0/ disparaissent pas en présence d’une dissipation interne
Notation
C B A Mariner10 values: C22= 10.5 10-5 and C/Mr2=0.325-0.380 Moment of inertia from gravitational harmonics
Torque (2)
C B A Sun x The z-component of the Liouville equations for a solid Mercury:
where r = distance Mercury-Sun
x = angle between Sun and A
Effect of the core on the libration of Mercury
Solid core Liquid core Peale (1976): amplitude of the longitude 88-day libration is at least twice as large if the core is decoupled from the mantle (liquid).
Impact of the core on the angle of libration in longitude of 88 days from SONYR model Cm/C ~1 ; solid core Cm/C ~0.5 ; liquid core 40 as 20 as
Earth Tracking Photographic measurements Orientation wrt the stars
« Revisiting » a same place
30
km 10 km Only very high latitudes have a very frequent « flyover » rate
But lower latitude measurments contain more information
-> « Ideal » strategy?
Track of the BC NAC (narrow angle camera) on Mercury
30km 10 km BepiColombo narrow angle camera groundtrack, in the case of the nominal orbit.
At low altitudes two subsequent tracks do not cover the whole area between them.
Opposite side of the planet
This represents the tracks on the opposite side of the planet of the preceding slide.
At high altitudes two subsequent tracks do cover the whole area between them.
Possible observations of the surface
Excentric polar orbit (alt. 400 – 1500 km)
Periherm moving towards north pole (~16 ° in 200 days)
Illumination conditions heavily constrain the possible observations
Albedo features are best candidates for observation
To correctly observe their patterns very low (less than 10°) or very high (more than 70°) phase angles are not permitted
Peale’s procedure
~ Aγ-1 Gravitational field and obliquity (+ Cassini state equation) We can determine the state of the core of Mercury through the measurement of the gravitational field, the obliquity and the libration. (Peale, 1976)
Si assez d’informations même sur la taille du noyau
Alors si:
A
Libration observation from Earth-based radar measurements
Wavefront corrugations
tied to Mercury’s rotation . 1sec telescope
on Earth The time delay for the pattern to reproduce at both stations is a direct measure of the rotation rate. Radar echoes from solid planets are speckled.
Earth-based libration observing strategy Illuminate Mercury with monochromatic radio signal from Goldstone radar (l=3.5 cm) during ~10 minutes round-trip light time.
Record echoes at Goldstone and at the Green Bank Telescopes for ~10 minutes.
Perform cross-correlations between amplitude fluctuations recorded at both telescopes.
Principle of Earth-based measurements of libration.
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