Astrophysics (index)

Love Number

(Love-Shida Number)
(measures of rigidity of a body)

The Love Numbers (or Love-Shida Numbers) are three numbers that describe the rigidity of a body, aimed at quantitatively describing the body's potential deformation due to a Tidal Force. They are scaled so 0 indicates "absolute rigidity", i.e., such a force would cause no deformation. The three Love numbers are:

  • h - ratio of deformation of the body toward or away from the body causing the tide.
  • k - ratio of that part of the deformation of the body (h) due to due to "higher order" effects, specifically due to the resulting rearrangement of the body's mass (and gravitational field).
  • l - a similar ratio capturing the horizontal deformation, e.g., toward the point closest to the body causing the tide.

h is scaled so that for a body with no rigidity, e.g., liquid, h-k would be 1. It happens that for such a body, k would be 1.5 and h would be 2.5.

In a Multipole Expansion, the numbers h2, k2, and l2 are the most interesting, the major reason being the symmetry of the nearly-spherical bodies (c.f., J2). (To me, this suggests Love numbers are actually functions on the surface of the sphere.)

The numbers are used for the calculation of tides on the Earth, which was the motivation for their development. They are also of interest in astrophysics in studying the effects of tides on solar system Moons, which offer a window into the moons' internal structure.