# Tides and celestial mechanics

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Tides and celestial mechanics

Role of celestial mechanics in relation to tides

The customary rise and fall in sea levels globally is a phenomenon known as tides. Studies in the field of celestial mechanics have shown that tides come about as a result of the collective gravitational forces exerted by the movement of these three celestial bodies; the sun, moon and the earth. Fitzpatrick points out that celestial mechanics apply principles from physics and classical mechanics to come up with quantifiable, workable data on the mechanics of tides (p.5). Isaac Newton came up with the theory of universal gravitation, citing the gravitational forces of celestial bodies as the cause of tides. Pierre-Simon Laplace later came up with the partial differential Laplace tidal equations which are still currently in use (Fitzpatrick, p. 7). The tide-generating force resulting from differential field of lunar gravity is the major mechanism resulting in the equipotent two daily tides. The tidal oscillations result in dissipation, majorly through oceanic tide movements.

The role of tides as a tide generating force

Denny and Paine describe tide generating forces as the force produced as a result of a combination of gravitational forces of attraction between the sun, moon and earth; and the forces resulting from the rotation of the moon around the earth and the earth’s rotation around the system. As discussed earlier, this is the main force that generates tides on the ocean surfaces. The combination of these two forces results in a deformation of ocean surfaces, which in turn give the earth an elliptical appearance (p. 2). The bulges at opposite ends of the earth result from one force pulling towards the moon and the other pulling away from the moon. Celestial mechanics explain the different roles each of the bodies involved play in relation to tide generating forces. The earth and moon rotate on the barycenter, along their respective center of mass (Denny and Paine, p. 6). This provides centripetal force which maintains this motion. However, since the moon is much closer to the earth, its’ gravitational force field has a much stronger variation compared to that of the sun.

The role of celestial mechanics in relation to the four principle harmonic constants

Further developments in celestial mechanics provided scientists and other experts in that field with the ability to predict tidal behavior in a particular place. This study and prediction is made possible through the analysis of harmonic constants. Casotto and Biscani explain that the principle of harmonic constant analysis was improved upon by A. T. Doodson. He developed the system allowing production of tide generating potential (TGP) in harmonic form. This in turn allowed scientists to point out the different harmonic constants involved in the production of TGP (p. 23). Celestial mechanics facilitates a platform for the analysis of the principal harmonic constants. Thus allowing them the ability to predict tidal behavior based on the various tidal constituents.

Tidal data collection requirements to determine tidal levels

In determining tidal levels, the oceanographer requires some critical information which makes it possible for him to compute and come up with the information providing answers as to the tidal levels. These different pieces of information are referred to as the tidal constituents. They include the: principal lunar semidiurnal constituent; principal solar semidiurnal constituent; larger lunar elliptic semidiurnal constituent; luni-solar declinational diurnal constituent; lunar declinational diurnal constituent. These are the major tidal constituents that are computed together with other relevant data to determine tidal levels and other tidal features such as tidal ranges and amplitude differences between different waves according to Brumberg (p.68).

Works cited

Brumberg, V. Essential relativistic Celestial Mechanics. Adam Hilger, Bristol, 2008

Casotto, S. and Biscani, F. A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession, nutation, and perturbations due to figure and planetary terms. AAS Division on Dynamical Astronomy. 2004

Denny, Mark W., and Robert T. Paine. “Celestial mechanics, sea-level changes, and intertidal ecology.” The Biological Bulletin 194.2 (1998): 108-115.

Fitzpatrick, Richard. An introduction to celestial mechanics. Cambridge: Cambridge University Press, 2012.