1. 40 years of observation of the mutual events
J.E. Arlot
IMCCE/obs. de Paris

2. Phenomena Solar and lunar eclipses
Eclipses of the satellites de Jupiter
Transits of Venus in front of the Sun
Occultations of stars by the Moon
Occultations of stars by asteroids
Mutual occultations and eclipses

3. A need of accurate observations for the natural satellites
Satellite systems look like small solar systems gathering all gravitational and non gravitational forces.
Measuring the acceleration, signature of the dissipation of energy needs accurate observations.
Dynamical models are available for this challenge and observations are wanted.
The observation of mutual events aim to provide data for these purposes.

4. The prediction of the events
The mutual events are very sensitive to small dynamical effects and the predictions were possible only starting in the 1970s thanks to the arrival of computers
We must avoid predicting events which will not occur!

5. Ephemerides elaboration
Step 1: Dynamical model
Planet's gravity field
(Cnp, Snp coefficients)
Rotation
Precession
Satellites gravity field
J2, C22 coefficients
(if known)
« Equations of motion »
Sun and other planets
as mass point
t2 term in the longitude
Tides raised by the satellites on the planet
Tomsk, July 2008

6. Ephemerides elaboration
Step 2: Observations
Corrections of:
-time scale
-frame
-aberration
-light time
Astrometric observations
Few different kind,
but many different format!
flux
The mutual events (occuring each 6 years)
Photometric observations
time (hours)
Tomsk, July 2008

7. ! Ephemerides elaboration Step 3: Fit Theory
Integration of partial derivatives
Observations
Linear system
approximation
=>Least squares
method
unknown
If the observational errors are gaussian and assuming a perfect modelling…
If not, use a random hold out or bootstrap method for the fit !
Tomsk, July 2008

8. « EPHEMERIDES » Ephemerides elaboration
Interpolation
Step 4: Making a representation
Polynomials of time
Chebychev polynomials
« EPHEMERIDES »
Fourier analysis
Mixed functions
Tomsk, July 2008

9. Ephemerides elaboration
Step 5: Predicting events
Ephemerides
 Predictions
Geometrical configuration
Tomsk, July 2008

10. Choosing the observational techniques (1 mas = 3 to 10 km)
Accuracy
Objects
Remarks
Transit circle
50  100 mas
mag 6-15
Obs. of a passage
Scanning telescope
 mag 20
RA & DEC measure
Tangential focal plane images
20  2000 mas
all
CCD imaging
AO, IR
a few mas (relative)
inner objects
objects close to their primary
Photometric events
1  10 km (relative)
i.e. 0.3 3 mas
main planetary satellites, asteroids
Occultations and eclipses
Gaia
0.1  1 mas
mag 7  20
50 obs./5 years
VLBI, Doppler space probes
2  10 mas
objects visited by space probes
Precise but few observations
Radar
10  100 m
Near Earth Objects
Galilean sat.?
LLR
1  3 cm
The Moon

11. Why the mutual events?
Satellites are orbiting in the equatorial planetary plane
During the planetary equinox, the Sun and the Earth go through this plane and events occur
Mutual events needs at least two large satellites to occur
Mutual events are possible for Jupiter, Saturn and Uranus systems

12. Since when the mutual events are observed?
The first ones were observed by chance when watching eclipses by the planet Jupiter
Predictions are possible only since the 1970 using accurate complete dynamical models and computers
A event occurs or not for a few tens kilometers since the accuracy of the ephemerides was 3000 km before the 1970s!
First systematical observations in 1973
At that time, the measure of the diameters of the satellites was a challenge
Nowadays we may reach an accuracy of a few kilometers in position

13. Accuracy in kilometers and in arcsec or mas
One mas in kilometers
Jupiter
3 km
Saturn
6 km
Uranus
10 km

14. Equinoxes on the giant planets
Jupiter: 1973, …, 2003, 2009, 2015, 2021,… (every 6 yr)
Saturne: 1980, 1995, 2009, 2024, … (every 15 yr)
Uranus: 2007 (every 42 years)

15. Favorable occurrences: either for the Northern hemisphere either for the Southern hemisphere

16. The dates of the 2014-2015 campaign of observation
The dates of the campaign of observation
Jupiter
opposition
6 February 2015
conjunction
16 July 2014
and 18 August 2015
passage of the Sun in the equatorial plane (equinox)
5 February 2015
passage of the Earth in the equatorial plane (disappearance of the rings)
8 November 2014,
10 April and 5 May 2015
observing period
September 2014-June 2015
declinations of the planets
+22 to +20 degrees

17. Number of events each monthD J F M 2 3 13 38 63 69 67 79 59 42 43 25 32
All events  A S O N D J F M 4 8 27 21 41 30 26 7 2
Visible in Paris 

18. The saturnicentric declination of the Earth and the Sun

19. Equinox on Uranus in 2007
Uranus to bright and too close to the satellites  difficult observation, (methane or K band):
Ariel: magnitude 14.4
Umbriel: magnitude 14.8
Titania: magnitude 13.8
Oberon: magnitude 14.2
Miranda: magnitude 16.5

20. The classical phenomena with the planet are more numerous

21. Eclipses by Jupiter Events known since Galileo
The first models were built thanks to the observation of the eclipses
An observation of an eclipse = the measure of the timing of the disappearance and the reappearance of the satellite in the shadow of Jupiter
At that time, the configuration corresponds to a specific position of the satellite

26. Observation of an eclipse = photometric observation
 here, the effect of the atmosphere of Jupiter
The astrometric accuracy is of several hundreds kilometers

27. The effect of the atmosphere ,of Jupiter

28. The eclipses may be used to probe the atmosphere of Jupiter

29. An observation made by Delambre in 1800 still useful
The timing is good but the time scale is uncertain
(the precision is good but the accuracy is doubtful)
True solar time mean time universal timeterrestrial time

30. Jupiter and Ganymede as seen by the HST

31. The mutual events A good photometric light curve
An occultation as seen in adaptive optics

33. The measure during a mutual event
Light coming from the satellites is recorded during the event (in UTC to the nearest 0.1 second of time)

34. The four galilean satellites
The observation
The four galilean satellites
A photometric timing:
0,1 sec = 1 km
An astromeytric measure:
0.1 arcsec = 300 km
Tomsk, July 2008

35. A 2D photometric observation
satellite 3 eclipses satellite 2

36. A 2D photometric observation
Lsatellite 2 occults satellite 4

37. Observation of a mutual event
Ex: occultation of a satellite by another: a movie will become a photometric lightcurve
-the images are slightly out of focus to avoid saturation

38. Exemples of lightcurves inV or R
Courbe symétrique
Courbe asymétrique
Phénomène rasant
Phénomène total

40. An event observed through clouds!
An event observed through clouds!
The minimum is quite well defined but the inversion of the light curve is difficult…

41. IoEurope1

42. IoEurope2

43. IoEurope3

44. IoEurope4

45. IoEurope5

46. IoEuropeS

47. Extracting the astrometric parameters X and Y
The photometric model
Extracting the astrometric parameters X and Y
The function S(X, Y) is the integration of the light flux received and emitted by each point of the satellite. It depends on the relative position of the satellites and on the laws of diffusion and reflection of light (photometric function).

48. The more simple model: only geometric disks with a constant albedo

49. The photometric model
Extracting the astrometric parameters through the inversion of the light curve
For each point of the surface of the satellite we must consider:
- albedo and reflectivity of the ground,
- laws of diffusion of light,
- variation of albedo depending on the location on the satellite,
- the limb darkening on th Sun for the eclipses.
- the sensitivity of the detector depending on the wavelength
The photometric function is the resulting of all the light emitted by the illuminated surface of the satellite
The photometric function may include an albedo map of the satellite or an albedo only depending on the central meridian

50. Law of reflection-diffusion
Flux
incident
Flux réfléchi
diffusion dans le milieu

51. Increasing the accuracy
For large bodies such as the Galileans, the distance « center of light » - « center of mass » may be improved through albedo maps (60 mas maximum for Ganymede)
© J. Goguen
Jupiter and Ganymede
from Pic du Midi 

52. The photometric function
P() - the integrated albedo of the satellite

53. The observed light-curve
Each point S(X,Y) provides a conditional equation with the photometric function  Relative positions of the two satellites

54. The accuracy of the observation of mutual events
Magnitude drop: precision from 0.01 to mag
 precision in position : 20 to 2 km
(in inclination)
Timing: precision from 1 to 0.1 second of time
 precision in position : 10 to 1 km
(along the orbit)
It does not depend on the distance of the Earth!

55. Which satellites are involved?
The Galilean satellites ofJupiter in 2009 and 2015
The icy satellites
The main satellites of Uranus in 2007
The largest satellites of Saturn in 2009

56. The accuracy depending on the type of observation
Case of the Galilean satellites of Jupiter
Type of observation
Precision in mas
Precision in km
Eclipses par Jupiter
150
450
Plaques photographiques
100
300
Transit circle 60
180
Plaques numérisées 40
120
Observations CCD
Mutual events 5 15
The precision does not depend on the distance to Earth

57. The accuracy depending on the type of observation
Case of the satellites of Saturn
Type of observation
Precision in mas
Precision in km
Transit circle 30
200
Observations CCD
Mutual events 5
Case of the satellites of Uranus
Type of observation
Precision in mas
Precision in km
Observations CCD 40
400
Mutual events 5 50

58. Explaining the volcanoes on Io by measuring an acceleration in the motion of Io

59. Observing the volcanoes of Io through mutual events?
The emitting spectrum of Io

60. Infrared observations
Occultation of Io by Europa
The first detection of a volcano from the ground in 1991
recent observation in L

61. Case of the satellites of Saturn
Image made at the Observatoire de Haute Provence using the 1m20-telescope

62. The main satellites of Saturn
Tides on Enceladus
The large eccentricity of Titan

63. Observations in 2009 (Meudon and Australia)
Residuals O-C = 300km
2%
 10%

64. Observation of a transit of Ariel by the HST on 26 July 2006
Case of the satellites of Uranus
Observation of a transit of Ariel by the HST on 26 July 2006

65. Observations of the events of the satellites of Uranus in 2007-2008
Observatories
Tel. n
Observed events
NTT (La Silla, Chile)
3.5m 5
10/7 5E2; 06/8 1O5; 13/8 1O2; 19/8 2O1; 29/9 5O1
Faulkes North (Hawaii) 2m
05/8 4O2; 20/8 5O2; 22/8 2E5; 24/8 5E3; 24/8 1O2
VLT (Paranal, Chile) 8m 1
08/12 2E3
APO, New Mexico (USA) 4
15/8 2O3; 19/8 2O1; 4/12 2E1; 7/12 1E2
Itajuba (Brazil)
1.6m 7
13/8 1O2; 14/8 2O4; 19/8 2O1; 8/10 1O5; 12/10 3E5; 28/11 1E3
Tubitak (Turkey) 2
14/8 2O4; 4/01 1E5
Marseille (France)
0.4m
30/11 3E4
TNG (Canarian Isl., Spain)
06/8 4O2
Makes obs. (Reunion, France)
0.5m
14/8 2O5 2O4; 29/11 2E4; 30/11 3E4
Hanle (Himalaya, India)
26/7 1E5
IRTF (Hawaii, USA)
30/7 5O4
Sabadell (Spain)
Pic du Midi (France) 1m ?
SALT (Sutherland, S. Africa)
10m
Athens (Greece)
14/8 2O4
Faulkes South (Australia)
04/5 4O2

66. Hanle (Himalaya) T 2m – band V
In V band, the planet is very bright.
Only the event occurring far from the planet are observable
© R. Vasundhara et al.

67. LNA (Itajuba, Brazil) T 1.6m – band R
© LNA R. Vieira-Martins

68. The events of the satellites of Uranus: La Silla – NTT 3.5m – band K
In band K (infra red 2.2 micrometres, the
planet Uranus is very dark and the phenomena are observable even close to the planet.
© ESO/NTT, F. Colas, F. Vachier

69. Paranal - VLT 8m – band K’ – NACO (adaptative optics)
Umbriel U-2 eclipses Titania U-3 on 8 Decembrer2007.
Uranus is very dark but the very narrow filter makes necessary the use of a large telescope.
The adaptive optics allows to see details on the surface of Uranus

70. Fitting the light curve through conditional equations

71. - astrometric accuracy: 10-30km i.e. 1 to 3 mas
Results from the observation of the event U-2 eclipses U-3 on 8 Decembre 2007 (VLT)
Time of minimum UTC
Flux drop
(from 0 to 1)
Impact parameter (km)
Laskar-Jacobson 1986
1h 55m 37s
0.417
425
Lainey-Arlot 2006
1h 57m 43s
0.218
790
Reduction 1
(Arlot)
1h 58m 3s +/- 6s
0.304
635 +/- 30 km
Reduction 2
(Emelianov)
1h 58m 6.6s
0.308
627 +/- 12 km
- astrometric accuracy: 10-30km i.e. 1 to 3 mas
10 km = 1 mas

72. A scientific goal: the internal structure of the satellites
Measuring an acceleration in the motion of a satellite allows to quantify the dissipation of energy in the system ( Io, Europa, Enceladus)
This measure needs a long-period observation since the effect is cumulative with time

73. A question to be solved with accurate astrometry
Tidal effects in the jovian system
Tides from satellite to planet
a, e
Satellite escapes
satellite
planet
Tides from planet to satellite
planet
satellite
Satellite falls
a, e

74. First estimations of the acceleration of the Galilean satellites
Galilean Satellites of Jupiter:
Purpose of the increasing astrometric accuracy:
- measure of the tidal effects
n’1/n1
n’2/n2
n’3/n3
De Sitter, 1928
+33 (+/- 5)
+27 (+/- 7)
-15 (+/- 6)
Greenberg, 1986
+32 (+/- 8)
-16 (+/- 4.5)
Goldstein, 1996
+70 (+/- 75)
+56 (+/- 57)
+28 (+/- 20)
Vasundhara, Arlot, 1996
+22.7 (+/- 7.9)
-6.1 (+/- 9.3)
+10.6 (+/- 10.6)
Aksnes, Franklin, 2001
+54.7 (+/- 16.9)
+27.4 (+/- 8.4)
-27.4 (+/- 8.4)

75. Long periodic term or secular term?

76. Analysis of astrometric observations
O-C residuals

77. Introduction of tides in the dynamical model
of Io on Jupiter
Tide  non discernables dans l’accélération observée directement
of Jupiter on Io
Effet des marées sur la résonance laplacienne
 décorrélation entre les deux marées dans le modèle dynamique
Dissipation dans les satellites? (détermination du k2/Q)
Équilibre thermique de Io? (flux de surface observé = énergie interne dissipée)
Premiers résultats sur Io grâce aux observations astrométriques dans :
Lainey V., Arlot J.E., Karatekin O. et Van Hoolst T.: 2009, Nature, sous presse

78. Flux from surface vs internal heat
 Flux calculated from astrometric observations fitted to the dynamical modeling
The heat flux emitted by the surface is in agreement with the flux calculated from our determination of an acceleration in the motion of Io.
 Io is in thermal equilibrium

79. Summary of observational campaigns
Number of observations
Number of sites of observation
Number of observed events
Number of observable events
Jupiter
1973 91 26 65
176
1979 18 7 9 60
1985
166 28 64
248
1991
374 56
111
221
1997
275 42
148
390
2003
361
116
360
2009
523 68
206
237
2015
Saturn
1980 14 6 13
213
1995 66 16 43
182 15 17
131
Uranus
2007 52 19 36
193

80. (amateurs) (professionals)
The progress until today
change in the observers (more amateurs)
change in the instruments (smaller aperture and 2D photometry)
change in the network (more countries)
Occurrences
Jupiter
Size of the telescopes
< 60cm > or = 60cm
(amateurs) (professionals)
Photometry
1 D D
1973 4 20 24
1979 3 7 10
1985 12 21
1991 37 19 39 17
1997 35 15 30
2003 34 8 41
2009 52 62
Saturn 1995 5 11
Uranus 2007

81. The network of observers

82. Publication of catalogues of the observed events (above in 2003 and in 2009) accessible on databases via Internet

83. Conclusion The mutual events are observed since 1973
The accuracy is quite good but may be improved thanks to a photometric survey of the satellites
Acceleration may be detected thanks to mutual events and all astrometric observations gathered in databases
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