Relativity of Wavelength According to the Relative Velocity between the Observer and the Wave Source

Abstract

An observer on Earth can observe the path of the Moon and Earth around the Earth and the Sun, respectively. Both are elliptical orbits in which the Earth and the Sun are concentrated, respectively. But how do we accept both paths together, where one cannot imagine the Earth as stationary while the Moon revolves around it in one of them and at the same time the Earth itself is the one that revolves around the Sun in the other path! Two paths of the Moon and the Earth can be visualised together in the same frame, as the Moon revolves around the Earth, which in turn revolves around the Sun. So the Moon also revolves around the Sun in a wave path around the Earth. Accordingly, the path of the Moon that we observe in the form of an ellipse from the Earth is in the form of a wave motion whose axis is the Earth's path around the Sun when observed from the Sun. The two observed paths of the Moon’s movement coincide in their estimated periodic time of 27.3216 days, while differing in wavelengths for each. The speed of the Moon along the elliptical path is 1023 m /s, while in the wavy path is 2.97 x 10⁴ m / s, which is the same as the Earth’s speed around the Sun as both of them revolve together around it. The ratio of their wavelengths has been shown to be equal to [1023/(2.97×10⁴)]. Thus, the wavelength of the detected image is proportional to the relative velocity between the observer and the wave source (the Moon).