Astronomical Theory Section - Planetary Phenomena


The Tides  (4)

  • Prologue
  • Introduction
  • The gravitational force between bodies
    • The inverse-cube relationship
  • The dynamics of orbital motion
  • Centrifugal force - does it really exist?
  • The gravitational force between bodies
  • Non-rotational orbit around the barycentre
  • Orbital motion plus axial rotation
  • Synchronous orbit
  • The same or different? Frames of reference and
    Free-fall vs. Orbit
  • The tide-generating force on a spherical body
  • The formation of the tidal bulges
  • Lunar and Solar tides
  • Interim Summary
  • Diurnal vs. Semi-Diurnal
  • Dynamic Theory
    • Viscocity vs. Friction
    • Tidal lag
  • The height of the tides
  • The influence of the Earth's landmasses
  • The actual tidal picture
  • Tidal dissipation and the distance of the Moon
  • Are there tidal bulges after all?
This article gives a complete, from first principles, explanation of how the influence of the Moon and Sun generates the tides we experience on the Earth. It firstly establishes the two different types of influence - static (or gravitational) and dynamic (or orbital) - before showing how they combine to produce not one but two tidal bulges. This explanation dispels the commonly-held notion that the bulge nearer to the Moon is caused by gravitation and the one further away by "centrifugal force" by a detailed analysis of the situation in frames of reference both moving with the Earth and separate from it. This results in some unexpected conclusions concerning the forces exerted on the Earth and its oceans by the Moon and the Sun.

Having explained the theory, the article then moves on to the practice. Models of steadily increasing complexity are developed, taking into account the frictional forces between the body of the Earth and the tides and the way the Earth's landmasses dramatically alter the tidal patterns. This involves an examination of forced harmonic motion and leads to a calculation of expected tide heights. The mechanism causing the Moon to recede from the Earth is then discussed - this issue is examined in much greater detail in the article "The Recession of the Moon" - before questions are asked as to whether the "tidal bulge" model actually has any reality at all.

Click on the title to read the article from the beginning.
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