Non-gravitational forces acting on the Lageos satellite over more than 30 years, following Farinella studies.

Florent Deleflie (IMCCE / Observatoire de Paris, GRGS)," Gilles Metris, and François Barlier "

(Geoazur / Observatoire de la Côte dʼAzur,GRGS)"

1 International Workshop on Paolo Farinella Pisa, June 14-16 2010

•  We had the privilege to work with Paolo Farinella on non-gravitational forces acting on satellite motion as Lageos and to appreciate the human qualities of a great scientist. In that framework, the Lageos and Lageos II satellite motions have been considered and various models accounting for non-gravitational forces have been developed. These satellites focused and attracted the interest of Paolo Farinella with our own interest including many other scientists and generating a cooperation which was always a friendly and fruitful collaboration."

•  In this paper, some past results are recalled, and then extended toward recent observations to show which changes are now observed for the orbital parameters, and which can be related in particular with the temporal evolution of the satellite rotation parameters. Orbital parameters tracked by the Satellite Laser Ranging network over more than 33 years are now available. "

•  We then discuss the interest of pursuing these studies started with Paolo Farinella more than 25 years ago."

2

Built by ALENIA-SPAZIO and launched by NASA/ASI (23/10/1992)

3

Weekly Orbital Fit (cm)

Müller et al., 2004 4

Tangential empirical accelerations determined by the University of Texas and

adopted in Farinella et al.1996.

5

N- G- forces acting on a satellite in Pisa with P. Farinella in the beginning of 80 (Examples)

Radiation pressure on a sphere including thermal Thrust Direct radiation from the Sun

Radiation reflected by the Earth and albedo effects, I.R radiation reemitted by the Earth….

Anselmo, L., P. Farinella, A. Milani and A.M. Nobili, Effects of the Earth-reflected sunlight on the orbit of the LAGEOS satellite, Astr. Astrophys.

1983. Anselmo, L.,B. Bertotti, P. Farinella, A. Milani, and A.M. Nobili, Orbital

perturbations due to radiation presure for a spacecraft of complex shape, Celestial Mech., 1983b.

…..

6

A basic book in 1987 on the N-G forces and on Space Geodesy

7

Air drag - Thermosphere Models at Grasse

 Thermosphere Models ( DTM 1978, DTM 94, DTM 2000) CERGA, Institut royal d’aéronomie de Belgique, service

d’aéronomie du CNRS

Data : thermosphere temperature, densities, chemical composition

 Satellite CASTOR/CACTUS CNES (1975)

 Thermal thrust due to an anisotropic distribution of temperatures on the satellite surface and measured by the accelerometer onboard (Boudon et al.1979).

8

Charge and neutral drag

 Afonso, G., F.Barlier, C.Berger and F.Mignard, Effet du freinage atmosphèrique et de la trainée électrique sur la

trajectoire du satellite LAGEOS. C.R. Seances Acad. Ser. B,1980

 Afonso.G.,F. Barlier,C.Berger,F.Mignard and J.J Walch, Reassement of the charge and neutral drag of lageos ans its

geophysical implications, J. Geophys. Res., 1985 ….

9

Air neutral drag Charge drag

Cooperation between PISA and Grasse in N-G forces acting on a satellite with P. Farinella

(examples) Afonso,G., F.Barlier, M.,Carpino, P.Farinella, F.Mignard, A.Milani;,and A.M. Nobili, effects of LAGEOS seasons and eclipses, Ann Geophys. 1989. Farinella P., A.M. Nobili, F.Barlier, and F. Mignard, Effects of thermal thrust on the node and inclination of Lageos, Astron.Astrophys; 1990

Mignard, F.,G. Afonso, F.Barlier, M. Carpino, P.Farinella, A. Milani and A.M. Nobili, LAGEOS: Ten years of quest for the non-gravitational forces, Adv. Space Res., 1990.

The rotation of Lageos and its long-term semimajor axis decay: A self cpnsistent solution, P. Farinella, D.Vokrouhlicky and F. Barlier, J.Geophys. Res. 1996.

…..

David Lucchesi thesis at the University of Nice, 2001.

10

Role of I.R. radiation emitted from the Earth, thermal lag , Earth albedo and the orbit of Lageos, by

Rubincam ,Slabinski, Smith, Cohen,…

Rubincam et al.1980, 1982, 1987, 1988, 1990,..,

Rubincam, D.P. , On the secular decrease in the semi major axis of LAGEOS’orbit, Celestial Mech., 1982.

Rubincam, D.P., LAGEOS orbit decay due to infra-red radiation from Earth, J.Geosphys. Res., 1987.

Rubincam, D.P., Yarkovsky thermal drag on LAGEOS, J. Geophys. Res., 1988.

…. 11

Thermal forces (Yarkovsky, Yarkovsky-Schach effects)

+ +

+ - - - - - -

o o o o o

o

Heat source

+

+ - - - - - -

o o o o o

o

+

Without rotation

With a fast rotation

Over one period of rotation, the temperature and the force are averaged, and the resulting acceleration is along the spin axis + + +

o o o o

- - -

- - -

12

Thermal Lag

Heat source

+ o o

- -

+ + -

- - o o o o

Heat source

With a null thermal lag, the more hot surface is just under the heating source

Without thermal lag

With a non null thermal lag, the hot surface shifted wrt the heating source

Heat source

+ o

o

+ +

o o o o

thermal lag

+ o

o

- -

+ + - - -

o o o o

Heat source

thermal lag

With thermal lag

13

Optical reflectivity asymmetry of Lageos hemispheres

Radiation

recoil

recoil

recoil

Total resulting thrust parallel to the incoming flux

Uniform optical surface

Symmetric case

Total resulting thrust not parallel to the incoming flux

Radiation

recoil

recoil

recoil

2 hemisphere with different

optical characteristics

Asymmetric case

14

Lageos data analysis

Scharroo et al. (1991)

Farinella et al. (1996)

Lucchesi(2001)

0.015 0.014

0.023 0.015

Asymmetric Reflectivity Effect:

Afonso et al. (1989)

Scharroo et al. (1991)

Slabinski (1996)

Metris et al. (1997)

-59 -89.4 -105 -241

Yarkovsky-Schach amplitude (pm s-2)

15

SPIN AXIS MODEL: The BI Model

Bertotti, B., and L. Iess, The rotation of LAGEOS, J.Geoph. Res., 96, 2431 (1991).

•  Magnetic torque

•  Gravitational torque

16

Southward orientation

Northward orientation

Measured values of the period

Precession

•  This precession period of the spin axis is inversely proportional to the spin period and decrease as an exponential law

•  The precession period is estimated to be about 5 years in 1989 (Bertotti and Iess, 1991) and about 1 month in 2001

17

Ajustement of the BI model parameters by Farinella et al.1996 from along-track

accelerations

18

After 25 years (2001), The dashed circle is reached and imply a change in the behaviour of the spin axis motion. Its precession rate is increasing.

After 33 years (2009) , the BI model is no longer valid : 1 to 1 resonance

Farinella, P. and D. Vokrouhlicky, Thermal force effects on slowly rotating spherical artificial satellite I solar heating, Planet.Sp.Sci, 1996.

Vokrouhlicky, D. and P.Farinella, Thermal force effects on slowly rotating sperical artifical satellite II the earth IR heating, Planet. Sp, Sci, 1996.

When Tlag/Trot is no longer small (from 2000), averaging over a rotational period is not relevant and new terms appear in the orbital accelerations

Standard component of the Yarkovsky acceleration along the spin axis. Already existing in the fast rotation hypothesis

New components orthogonal to the spin axis appearing in the slow rotation case

19

Role of other non-gravitational torques (Vokrouhlicky, GRL, 1996)

Radiation pressure torques due to : •  offset h of the center of mass •  asymmetric reflectivity

20

offset h = +0.79 mm offset h = -0.79 mm

J.I. Andrès, R. Noomen G.Bianco D.G. Currie and T.Otsubo 2004 Spin axis behavior of the Lageos satellites. J. Geophys. Res., 109, B06403.

LOSSAM Model

21

3 periods to be considered

Magnetic torque dominates

Magnetic and gravitational torques equivalent

Magnetic, gravitational and non gravitational torques equivalent

D.Kuchardski, G.Kirchner, S.chillak , E. Cristea, Spin determination of Lageos from kHz laser observations, Adv in Space Res.2007

Bianco,G, Chersich, M.Devoti. R et al. Measurement of Lageos-2 rotation by SLR observations, GRL, 2001

Lageos eccentricity

•  In the mid 90’th, UT CSR group (J. Ries, R. Eanes) pointed out unexplained residual excitations on the Lageos eccentricity vector

•  Metris et al (1996) demonstrated that a modified (empirically) thermal model using Farinella et al spin axis model, allowed to reconstruct the observed residual excitation both for a, e*cosω and e*sinω

•  This was the case up to 1996…

22

23

(e*cosω)

(a)

(e*sinω)

Excitations

24

Zoom around 1997 With spin axis model (Farinella et al.)

With emmpirical spin axis

Excitations

25

Spin axis coordinates referred to the equatorial plan

Observations seem to confirm empirical values

Recent evolution of residual accelerations

•  We have recomputed empirical accelerations for Lageos over [1990-2010] using GINS software

•  Best known dynamical model but without thermal effects neither optical asymmetry

•  65 days arc with the following adjusted parameters : –  6 initial conditions –  1 set of bias (BT,BTC, BTS, BNC, BNS) every 5 days (13 sets / arc) –  typical RMS of laser range for one arc = 1.5 cm

•  The estimated biases absorb long period part of unmodeled accelerations

•  The main unmodeled accelerations are due to non-gravitational effects such as thermal effects

26

Interpretation of the estimated biases

€

along − track component : ΔT(t) = BT + BTC cos(ω + M) + BTS sin(ω + M)normal component : ΔN(t) = BNC cos(ω + M) + BNS sin(ω + M)

The estimated biases (BT,BTC, BTS, BNC, BNS) are related to the components of the acceleration in a local orbital frame :

In particular, effective BT, BTC, BTS are related to the so called along-track and eccentricity vector excitations :

€

Δ˙ a a≈

2na

BT

Δddt

ecosω( ) ≈ 1na

BTC

Δddt

esinω( ) ≈ 1na

BTS

27

Excitations Estimated biases

Comparison of residual acceleration computed by UT CSR (1980-1997) and by ourself (1990-2010) over the common period.

Semi-major axis excitation

28

(e*cosω)

(a)

(e*sinω)

29 25 years after launch 33 years after launch

THESIS D.Lucchesi (2001)

This work is dedicated to the memory of Paolo Farinella

‘’ Effects of non-gravitational Forces acting on LAGEOS Satellites:

Impact on the Determination of the

Lense–Thirring effect ‘’

Université de Nice-Sophia-Antipolis Observatoire de la côte d’azur - Grasse

December 18, 2001 - OCA/CERGA - Grasse

Ph.D. Thesis at:

30

Thank you very much to the Italian organizing comittee for giving us the

opportunity to celebrate Paolo FARINELLA who was an humanist, a great scientist and

a very good friend of us.

31