2. CHAMP’s TRIPLE PASSAGE THROUGH 31 st /62 nd -ORDER ORBIT RESONANCE R.H. Gooding, C.A. Wagner, J. Klokočník, J. Kostelecký

3. Lagrange planetary equations the case of orbital inclination 1. Allan/Kaula expression 2.after choice of resonant indices 3.final resonant form with lumped coefficients 1.

5. Lagrange Planetary Equations with resonant choice for (l,m,p,q)

7. Lagrange Planetary Equation for Orbital Inclination in terms of Lumped Geopotential Coefficients (LC)

8. DEFINITIONS Resonant angle Lumped coefficients

10. Location of resonances what is semi-major axis / mean motion at exact resonance Two types of semi-major axis: Brouwer Kozai what is semi-major axis / mean motion at exact resonance Two types of semi-major axis: Brouwer Kozai

13. CHAMP and RESONANCES CHAMP mission Location of resonances in CHAMP orbit simulation of forthcoming resonances in inclination preparation for analysis of individual resonances analysis of inclination variations at 46/3 and 31/2 resonances

16. Comparison of approaches to analyse CHAMP resonances: long-arc vs short-arc general geopotential recovery from tracking data is to analyse full spectrum of effects in many short-arcs [e.g. 1.5 day for CHAMP] traditional “resonant analyses” work with long-arc approach and concentrate on few “resonant frequencies” (31/2, 46/3….etc)

26. Resonance 31/2

50. Conclusions Introduction to theory of resonant phenomenon in orbits of Earth artificial satellites Historical analyses (Gooding etc) lumped coefficients rotation of upper atmosphere calibration of comprehensive solutions for geopotential

51. CHAMP: Location, estimation of expected orbit effects and analysis of particular high-order resonances in CHAMP orbit Comparison of computed lumped geopotential coefficients from resonances with those from comprehensive Earth models Interpretation of existing discrepancies (due mainly to insufficient modelling of tides and non- gravitational effects in our resonant software), and a possibility to calibrate the Earth models by results from resonances

52. To get a copy Anonymous ftp: sunkl.asu.cas.cz pub/jklokocn files: PPT_RES_CHAMP_GFZ.ppt PPT_RESON.ppt Web: www.asu.cas.cz/~jklokocn e-mail: jklokocn@asu.cas.cz

53. The End