A Model of the Rotation of Venus Based on 5 Parameters. J.Souchay, L.Cottereau (SYRTE, observatoire de Paris)

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1 A Model of the Rotation of Venus Based on 5 Parameters J.Souchay, L.Cottereau (SYRTE, observatoire de Paris)

2 Plan General Remarks on Venus and its rotation How to model the Venus rotation The «polar motion» (polhody) The precession-nutation motion The l.o.d. (Length of Day) Conclusion

3 General Remarks on Venus and its rotation

4 Vénus

5 Les passages de Vénus Next Venus transit : June 6, 2012

6 Les passages de Vénus Next Venus transit : June 6, 2012

7 Magellan probe (1991)

8 Vénus : résultats de Magellan

9 Vénus : résultats de Magellan

10 Vénus : le planisphère Venus planisphere

11 Comparisons Venus % Earth

12 Precession rate

13 is taller The Earth Venus

14 Solar time and sideral time Eccentricity Reduction at equator

15 Equation du temps

16 Solar day on Venus T ~ 116 d

17 Rotation of Venus / Previous studies Peculiar spin rate (Smith,1963; Goldstein, 1964, Carpenter,1964) Balance gravitational vs. thermical tides (Gold and Soter,1969) Friction at core-mantle boundary (Goldreich and Peale,1970) Various scenarios starting from tidal dissipation (Lago and Cazenave,1979;Dobrovolskis,1980, Shen and Zhang,1989, ) Wide set of possible spin rates explaining chaotic variations of obliquity (Laskar and Robutel,1993) Tilt of the spin axis from any initial value to 180 (Néron de Surgy,1996; Yoder,1997; Correia and Laskar,2001) Variations in the rotation rate due to orbital eccentricity modulation of solar tidal torques (Bills, 2005) Etc.

18 Solid tides exerted by the Sun on Venus

19 Tidal thermal atmospheric friction of the Sun on Venus

20 4 Scenarii (Correia and Laskar, 2001)

21 How to model Venus rotation

22 A model of rotation based on 5 parameters Polhody ( X,Y) (Orlov, 1895) Precession & Nutation (Δψ, Δε) (Bradley,1749) l.o.d /UT1/φ (De Sitter, 1923, Stoyko, 1937)

23 M = M 1 (X,Y) * M 2 (φ) * M 3 (ψ,ε, Δψ, Δε) [TRF] = M [CRF] Polhody ( X,Y) (Orlov, 1895) Precession & Nutation (Δψ, Δε) (Bradley,1749) l.o.d /UT1/φ (De Sitter, 1923, Stoyko, 1937)

24 Euler angles Woolard s theory (1953)

25 Parametrization with Andoyer variables Andoyer canonical variables l, g, h => angle variables L,G,H => action variables Kinoshita s theory (1972,1977)

26 Venus precession & nutation

27 Precession-nutation of Venus precession nutation J I=2 63 Inertial axis of Venus If Angular momentum axis Figure axis : coincides with the axis of the largest moment of inertia Inertial plane : the orbit of Venus at J The reference point is the intersection between the orbital plane and the mean equator of Venus at J2000.0

28 Yoder (1995)

29 Motion of Venus due to an external disturbing body 1 F 0 : free rotation E, E : moving reference orbit plane U 1 : disturbing potential

30 Canonical equations (Kinoshita,1977)

31 λ longitude along the orbit β inclination (here β = 0 )

32 Developments for the potential

33 Precession. ψ venus = 4474".35 ± 66.5 / cy. ψ terre = 1583".99 / cy (Sun only). ψ terre = 5000".3/ cy (Sun + Moon) L.Cottereau and J.Souchay Rotation of rigid Venus : a complete precession-nutation model A&A-2009

34 Nutation depending on the triaxiality

35 Calculation of Oppolzer terms Difference of nutation [ Figure axis Angular Momentum axis ]

36 Indirect planetary effect on nutation nutation in longitude arcsecond temps days

37 Indirect planetary effect on nutation

38 Comparison between the nutations of the figure axis and of the angular momentum axis Longitude Obliquity nutation in longitude arcsecond nutation in obliquity arcsecond times days times days ---- angular momentum axis ---- figure axis L.Cottereau et Al. A&A (2010)

39 Long time scale evolution of the motion of rotation of Venus Longitude Obliquity variation h degre 0 10 Variation of I degre times thousand of years times thousand of years

40 Motion of venus axis of figure in space 2,6328 Coordinate Y of pole of Venus (degree) 2,6326 2,6324 2,6322-0,06-0,05-0,04-0,03-0,02-0,01 0 Coordinate X of pole of Venus (degree)

41 Conclusion The precession in longitude due to the Sun is more than two times larger than the corresponding term for the Earth and slightly smaller than the combined effect of the Moon and of the Sun for the Earth. The nutation of the figure axis (calculated for the first time) is significantly different than the nutation of the angular momentum axis (smaller and dominated by three sinusoids) The evolution of Venus obliquity on a long time scale (~ y) is small as it is the case for the Earth The periodic variations of the speed of rotation of Venus due to the solid tides, atmospheric pressure, and core have been modeled => effects above the detection threshold (Venus Express) Possibility to represent Venus rotation with 5 parameters X,Y (polar motion), (ε + Δε, ψ + Δψ), VT (l.o.d.)

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