Abstract
THE annual variation in latitude1 causes a disturbance in the gravitational potential with an amplitude: U = a 2 Ω2 m sin θ cos θ = 880 sin θ cos θ cm.2 sec.−2 where a is the radius and Ω the angular velocity of the Earth, and where m is the angular displacement of the pole along the meridian of a station located at co-latitude θ . For the annual term, Jeffreys1 obtained m ≈ 0.084″ = 4.07 × 10−7 radians, and the numerical value 880 follows from this. In comparison, the equilibrium tide S a associated with the annual variation of the heliocentric distance has a potential2: 472( − cos2θ)cm.2 sec.−2 The mean square values, are equal to (321 cm.2 sec.−2)2 for the ‘pole tide’, and (141 cm.2 sec.−2)2 for the S a, so that the pole tide is larger. Yet it appears to have been overlooked. This simply means that there is a larger effect from a movement, north or south, by 10 ft. than from a variation by 2 per cent of the Sun's distance.
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References
Jeffreys, H., “The Earth” (Cambridge, 1952).
Doodson, A. T., and Warburg, H. D., “Admiralty Manual of Tides” (Hydrographic Dept., Admiralty, 1941).
Pattullo, J., Munk, W., Revelle, R., and Strong, E., J. Mar. Res., 14, 88 (1955).
Stoyko, N., Bull. Astron., 15, Fasc. 3, 14 (1951).
Jeffreys, H., Mon. Not. Roy. Astron. Soc., Geophys. Supp., 2, 58 (1928).
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MUNK, W., HAUBRICH, R. The Annual Pole Tide. Nature 182, 42 (1958). https://doi.org/10.1038/182042a0
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DOI: https://doi.org/10.1038/182042a0
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