In this study, I calculate the past and future dynamical states of the Earth-Moon system by using modified Lambeck’s formulae. I find that the ocean tidal effect must have been smaller in the past compared to its present amount. Even though the Moon is already in the spin-orbit synchronous rotational state, my calculation suggest that it will not be in geostationary rotational state in the next billion years or so. This is due to the associated Earth’s obliquity increase and slow retardation of Earth’s spin and lunar orbital angular velocities. I also attempt to calculate the precessional period of the Earth in the future. To avoid uncertainties in the time scale, the future state is described by using the Earth-Moon distance ratio as independent parameter. Effects due to solar tidal dissipation are included in all calculations.

ABSTRACT
1. INTRODUCTION
2. FORMULATION
    2.1 Satellite Orbit Dynamics
    2.2 Lambeck’s Approach and Its Modification
    2.3 Other Consideration and Approximation
3. CALCULATION AND RESULT
    3.1 Past State Calculation with Constant Tidal Parameters
    3.2 Future State Calculation with Constant Tidal Parameter
    3.3 Considering of Variable Paleo-Ocean Tide- Simple Power Law Approximation
    3.4 Precession of the Earth in Future
4. DISCUSSION
5. SUMMARY
REFERENCES

• SUNG-HO NA(Korea Astronomy and Space Science Institute)