mechanisms

There is a contribution from the gravitational attraction of the celestial body that pulls water towards the equatorial region:

image

The hypotenuse of the triangle is related to the vertical leg by:

$R\sin\theta$

and the horizontal leg by:

$d - R\cos\theta$

Using the Pythagorean theorem, we have:

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

There is a contribution from the gravitational attraction of the celestial body that pulls water towards the radius, which tends to displace the water towards the equatorial zone:

image

The hypotenuse of the triangle is formed by the vertical leg:

$R\sin\theta$

and the horizontal leg:

$d - R\cos\theta$

According to the Pythagorean theorem, we have:

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

model

To determine the variation of the acceleration perpendicular to the radius, we can use triangle similarity to equate the relation

$\displaystyle\frac{\Delta a_{cy}}{a_c}$

with the length

$d-R\cos\theta$

and the hypotenuse

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

.

By triangle similarity, we have with the list that

kyon.

Con la ley de la gravitaci n de Newton, con list=9238, es:

Se puede, con la definici n de la fuerza, con list=10975:

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

Calcular la aceleraci n reemplazando el radio en la fuerza y despejando la aceleraci n. Esto da con list la aceleraci n:

With list=11643, the relationship between the variation of acceleration and acceleration is:

And since the expression for acceleration is with list=11644:

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

Therefore, in the approximation d\gg R, we can approximate with the list by:

kyon

To determine the variation of the acceleration parallel to the radius, we can use triangle similarity to equate the relation

$\displaystyle\frac{\Delta a_{cx}}{a_c}$

with the length

$d+R\cos\theta$

and the hypotenuse

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

By triangle similarity, we have with the list that

kyon

With list=11647, the relationship is:

And as for list=11644,

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

Therefore, in the approximation d\gg R, we can approximate with the list by:

kyon