**2. Evolution of the Moon's orbital motion**

### **2.1 Coordinate system and orbital parameters**

When solving the problem of the evolution of the rotational motion of the Earth over millions of years [1], it is necessary to have data on the coordinates of bodies acting on the Earth at any time from this time interval. The Moon exerts two-thirds of the total influence exerted on the Earth's rotational motion. The evolution of the Moon's orbital motion is therefore an important component of the posed problem.

The evolution of the orbits of Solar-system bodies can be determined by solving the problem of interaction for those bodies. For solving this problem, a Galactica system was developed [2–4]. The accuracy ensured by this software is several orders of magnitude higher than the accuracy ensured by other similar systems [5, 6]; this made it possible to solve the problem of the evolution of the Solar-system over 100 million years [7]. This problem is solved in the barycentric coordinate system *xyz* (**Figure 1**) attached to the fixed equatorial plane *A0A0'*. The origin *O* is located at the center of mass of the Solar-system. The results of solving this problem were saved in files following each 10 thousand years. Then, for those epochs, the interaction problem was solved, with the help of the Galactica program, per one orbital revolution of the body, and 11 parameters of its orbit were determined from its coordinates. For the Moon, the parameters of its orbit relative to the Earth are to be determined.

The Moon's orbital period is very short compared to that of planets. Therefore, the oscillation periods of the parameters of the Moon's orbit repeated many times over an interval of 10 thousand years. Therefore, with this interval, the evolution of the Moon's orbit was studied during its 736 continuous revolutions around the Earth, which took place during 56.7 years.

The position of the Moon's orbital plane, *γMoA1B*, is specified by its angle of inclination *iMo* to the plane of the stationary equator *A0A0'* and by the angle of the ascending angle *φΩMo*, both defined in the caption to **Figure 1**. The position of the perigee of the Moon's orbit is specified by the angle *φp*. When analyzing the Moon's orbit, the origin *O* is located at the center of the Earth.

#### **Figure 1.**

*The coordinate system and the main characteristics of the Moon's orbit:* C *is the celestial sphere;* A0A0' *and* E0E0' *are the fixed planes of the equator and the Earth's orbit (ecliptic) for the epoch of 2000.0,* JDS *= 2451545;* AA' *and* EE' *are the moving planes of the Earth's equator and orbit as of the current date;* γMoA1B *is the Moon's*

*orbital plane; S*! *<sup>E</sup> and S*! *Mo are the axes of the Earth's and Moon's moving orbits, respectively* EE' *and* γMoA1B, *which are perpendiculars to the orbital planes. The angles of the Earth's orbital plane relative to its equatorial plane* A0A0'*:* φΩ<sup>E</sup> *=* γ0γ2*,* iE *=* A1γ2γMo*; and same angles of the Moon's orbital plane relative to the Earth's equatorial plane:* φΩMo *=* γ0γMo*,* iMo *=* A1γMoA0'*.* B *is the projection of the perigee of the Moon's orbit on the celestial sphere, and* φ<sup>p</sup> *=* γMoB *is its angular position;* ψMo *и* θMo *are the precession and inclination angles of the Moon's orbit relative to the moving plane of the Earth's orbit* EE'*.*

*The Evolution of the Moon's Orbit Over 100 Million Years and Prospects for the Research… DOI: http://dx.doi.org/10.5772/intechopen.102392*
