Число Лава

Следствия:

Munk, 1964 - Геоид - Пизанская башня и ускорение свободного падения

values h and k which characterize the overall elastic response of the Earth to the tides... third Love number, l, which was needed to obtain a complete overall description of the solid Earth's response to the tides.

h

[math]h[/math] читается как h

ratio of the body tide to the height of the static equilibrium tide also defined as the vertical (radial) displacement or variation of the planet's elastic properties

For a liquid Earth, one would expect h=1.

k

ratio of the additional potential (self-reactive force) produced by the deformation of the deforming potential. It can be represented as [math]k V(\theta, \phi)/g[/math]

l

ratio of the horizontal (transverse) displacement of an element of mass of the planet's crust to that of the corresponding static ocean tide

consequences

h, k, l = 0 for a rigid body

According to Cartwright, "An elastic solid spheroid will yield to an external tide potential [math]U_2[/math] of spherical harmonic degree 2 by a surface tide [math]h_2U_2/g[/math] and the self-attraction of this tide will increase the external potential by [math]k_2U_2[/math].

Love numbers [math]h_n[/math], [math]k_n[/math], and [math]l_n[/math] can also be calculated for higher orders of spherical harmonics.

For elastic Earth the Love numbers lie in the range: [math]0.616 \leq h_2 \leq 0.624[/math], [math]0.304 \leq k_2 \leq 0.312 [/math] and [math]0.084 \leq l_2 \leq 0.088[/math].