mechanisms

The attraction on the opposite side of the celestial body acting on Earth is weaker due to the greater distance. This facilitates water displacement towards the equator. On the side facing the celestial body, its gravitational attraction weakens Earth's gravitational acceleration, leading to a reduction in gravity that further aids water displacement towards the equator:

image

In this case, we work with similarity in the triangle, where we take the proportion

$\Delta a_{ox}/a_o$

and the leg

$d + R\cos\theta$

and the hypotenuse

$(d+R\cos\theta)^2+R^2\sin^2\theta=d^2+R^2+2dR\cos\theta$

There are multiple explanations for the tides on the opposite side of the celestial body. One of them is the effect of centrifugal acceleration due to the fact that the system rotates around the center of mass of the Earth-celestial body system, which is not at the center of the Earth. However, the values obtained for the case of the moon are very different on the side facing the moon compared to the opposite side of the Earth. Additionally, it would be difficult to explain the phenomenon in this way if the sun is taken as the celestial body since in that case the center of mass is near the center of the sun.

The simplest explanation that yields values like those observed is to assume that it is a problem of gravity differences and displacement of objects. Therefore:

• The tide toward the side of the celestial body originates from its attraction, which reduces the gravitational acceleration of the Earth.
• The tide on the opposite side of the celestial body occurs both due to the reduction of the celestial body's attraction and also because the Earth is displaced "within the water."

image

model

To determine the variation of acceleration along the radius, we can equate the relationship

$\displaystyle\frac{\Delta a_{ox}}{a_o}$

with the length

$d+R\cos\theta$

and the hypotenuse

$\sqrt{d^2+R^2+2dR\cos\theta}$

By similarity of triangles, we obtain with the list that:

kyon

With Newton's law of gravitation, represented by list=9238,

,

we can define the force with list=10975,

$r^2=d^2+R^2+2dR\cos\theta$

,

to calculate the acceleration with the list:

kyon

With list=11646, the relationship is

,

and with list=11651, the expression is

$\Delta a_{ox} =GM\displaystyle\frac{d + R\cos\theta}{(d^2 + R^2 + 2dR\cos\theta)^{3/2}}\sim \displaystyle\frac{GM}{d^2}\left(1-\displaystyle\frac{2R\cos\theta}{d}\right)$

,

so in the approximation d\gg R and considering only the variation with respect to the opposite side, it can be approximated with list as: