Talk:Love number

Ref.[2]

the link does not work any more Ra-raisch (talk) 20:34, 4 February 2019 (UTC)

k_L

I found the definition of k_L = 3J₂v_o²/v_t² in [1] with J₂=(J_z-J_x)/r²m, v_t²=ω²r² and v_o²=Gm/r. Ra-raisch (talk) 18:31, 10 February 2019 (UTC)

First Reference

The following paper was submitted in 1908, then read early 1909. It is available as a free .pdf from Roy Soc. LOVE, A. E. H., 1909. "The yielding of the earth to disturbing forces". Proc. Roy. Soc. London, A 82, pp. 73 – 88. King of Tea Tree (talk) 11:53, 24 February 2020 (UTC) The Love numbers h and k are first introduced at the end of section 3 of Love's 1909 paper “The Yielding of the Earth to Disturbing Forces”. That paper was submitted on 18 Nov 1908. King of Tea Tree (talk) 07:28, 1 March 2020 (UTC)

Tidal Love Numbers (k₂) of Solar System Objects (plus notes, analysis and empirical formulas)

Measures the rigidity of a planetary body and its susceptibility to change shape in response to a tidal potential.

The first numbers are the ones that I decided are probably the most correct, and the ones in parentheses are others I found online.

• Earth: 0.308
• Moon: 0.024±0.002 (0.02405, 0.0222, 0.02664)
• Mercury: 0.485±0.04 (0.0965, 0.52, 0.45)
• Venus: 0.275±0.02 (0.295, 0.254)
• Mars: 0.168 (0.168, 0.0712)
• Jupiter: 0.58±0.07 (0.525, 0.565, 0.66)
• Io: 0.09 (or as much as 0.5 with a very high melt fraction, i.e. magma ocean)
• Saturn: 0.36±0.03 (0.341, 0.39)
• Titan: 0.47±0.1 (0.36, 0.57)

The tidal Love number k₂ can be approximated from planet mass (m) by the formula "k₂ = 2e24m^0.82" for smaller terrestrial worlds, "k₂ = 5e25m^2.03" for earth-like worlds, and "k₂ = 2e28m^3.5" for giant planets. These formulas are extrapolated from the above data.

• Higher core mass = higher love number
• Higher mantle mass = lower love number

• More homogenous interior = higher love number
• More stratified interior = lower love number

SnailsAttack (talk) 15:09, 30 June 2021 (UTC)