## Abstract

The motion of the Moon is principally determined by two bodies, the Earth and the Sun. If we consider the gravitational forces that affect the Moon, we find that it is not its nearest neighbour, the Earth, that has the greatest effect, but the more distant Sun. Although gravitational force decreases as the square of the distance, the Sun’s gravity exceeds that of the Earth, because of its far greater mass. Putting figures to this (Earth-Moon distance
Regardless of the relative positions of the Sun, Earth, and Moon, the sum of the two forces therefore always has a component directed towards the Sun, and never away from it. The Moon may thus be described as following an elliptical orbit around the Sun at a distance of some 150 million km, superimposed upon which there are small monthly oscillations. Because the gravitational force is never directed away from the Sun, the orbit, despite these oscillations, is always concave towards the Sun.

*r*≈ 380000 km, Sun-Moon distance*R*≈ 150 million km, Sun/Earth mass ratio*M/m*≈ 330 000), we find that the Sun’s gravitational attraction is about twice as great as that of the Earth:$$ \frac{{{F_ \odot }}}{{{F_ \otimes }}} = \frac{M}{{{R^2}}}/\frac{m}{{{r^2}}} \approx 2 $$

## Keywords

Chebyshev Polynomial Perturbation Term Lunar Orbit Earth Radius Chebyshev Approximation
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## References

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*Himmelsmechanik II by*Bucerius and Schneider [2]. The method of approximating functions by Chebyshev polynomials is explained in textbooks on numerical mathematics (see [11] and [13]).Google Scholar

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© Springer-Verlag Berlin Heidelberg 1998