Talk:Love number
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Ref.[2]
editthe link does not work any more Ra-raisch (talk) 20:34, 4 February 2019 (UTC)
kL
editI found the definition of kL = 3J2vo²/vt² in [1] with J2=(Jz-Jx)/r²m, vt²=ω²r² and vo²=Gm/r. Ra-raisch (talk) 18:31, 10 February 2019 (UTC)
First Reference
editThe 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)
editMeasures 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