Tides, bridges, sailboats

Earlier this week, June 25, a sailor got his sailboat stuck under the Roosevelt Island bridge!  His mast was stuck in the girders.  The coast guard had to be called out, and the firemen. Bridge traffic had to be stopped so the bridge could be opened up, and the mast freed, then the coast guard tugged him away.  I also heard that the coast guard had considered just leaving him there for a few hours until low tide ( and laughed about it)! Really, what kind of sailor does not check the tides when out on water.

It got me thinking about tides, so here’s an essay on it.


Tides are what we call the rise and fall in the levels of water in the ocean and coastal rivers twice a day.

Tides also occur in large lakes and the atmosphere, but in such a tiny amount that it’s almost unmeasurable.

Why are there tides?

Mainly because of the gravitational attraction of the moon and earth and the sun.

The bigger gravitational pull is between the earth and the moon, because we are close to each other.  Luckily, we do not fall into each other because the equal and opposite centrifugal force produced by their individual revolutions around the center-of-mass of the earth-moon system, keeps us apart.

 The water on the hemisphere of the earth turned toward the moon, is pulled toward the moon because of gravity.  At the same time, the water on the opposite side (furthest from the moon) is pulled away from the moon, in the direction of the greater centrifugal force. So we get two simultaneous high tides.

Low tides are created by water sinking in regions around the earth midway between these two high tides. The alternation of high and low tides is caused by the daily rotation of the earth.

The Monthly Revolution of the Earth and Moon around the Barycenter of the Earth-Moon System

The Monthly Revolution of the Earth and Moon around the Barycenter of the Earth-Moon System

This revolution is responsible for a centrifugal force component (Fc) necessary to the production of the tides. 
(Note that the earth revolves around G, but does not rotate around G. There is no monthly rotation of the earth as it revolves around the barycenter such that the same point on the earth’s surface always faces the moon.) 

Not to forget the sun …

The earth and the moon are both rotating round the sun.  The same forces of gravitational attraction and centrifugal force exist here.

The force of gravitation exerted by the moon (and sun) upon the earth and the centrifugal forces produced by the revolutions of the earth and moon (and earth and sun) around their common center-of-gravity (mass) are usually in balance.  However, when they are not in equilibrium at some local points, we get tides.

The Effect of the Centrifugal Force.  As the earth and moon whirl around the earth-moon center-of-mass, the centrifugal force produced is always directed away from the center of revolution. Since the center-of-mass of the earth is always on the opposite side of this common center of revolution from the position of the moon, the centrifugal force produced at any point in or on the earth will always be directed away from the moon.

 The Effect of Gravitational Force. While the effect of this centrifugal force is the same all over the earth, the gravitational force produced by another astronomical body may be different at different positions on the earth because the magnitude of the gravitational force exerted varies with the distance of the attracting body.

Spring tides and Neap tides.

Spring and Neap tides happen due to the combined effect of gravity of the sun and moon on the earth.  

When the sun is lined up with the moon, their combined pull is harder on the earth’s oceans.  This is called a Spring tide, and happens at New Moon and Full Moon.

When the sun is at right angles to the moon, the combined gravitational effect is less, as they cancel each other out. This is called a Neap tide, and happens at the two quarters.

The Phase Inequality: Spring and Neap Tides

The Phase Inequality: Spring and Neap Tides

The gravitational attractions (and resultant tidal force envelopes) produced by the Moon and Sun reinforce each other at times of new and full moon to increase the range of the tides, and counteract each other at the first and third quarters to reduce the tidal range.

Diagrams courtesy of NOAA.gov

Variations in the tide times

The earth rotates on its axis in 24 hours. The moon revolves in its orbit around the earth with an angular velocity of approximately 12.2 degrees per day, in the same direction in which the earth is rotating on its axis with an angular velocity of 360 degrees per day.  So, the rotating earth must complete a rotation of 360 deg. plus 12.2 deg. or 372.2deg., in order to “catch up” with the moon. Since 15deg. is equal to one hour of time, require a period of time equal to 12.2/15 x 60 min/hr., or 48.8 minutes – if the moon revolved in a circular orbit, and its speed of revolution did not vary. On the average it requires about 50 minutes longer each day.  As a result, the recurrence of a tide of the same phase and similar rise would take place at an interval of 24 hours 50 minutes after the preceding occurrence.

Then there’s the friction between the sea waters and the sea floors which also change the tide flows.

Tides changes gradually.  The waters do not suddenly pop up and down.  Various Atmospheric and Climate offices maintain tide tables to ease navigation. Tides are levels are announced in the weather sections of most newspapers or weather sites.

Distances and masses:

Earth to Sun: 1 AU. ( 92,955,807 miles)

Earth to Moon: 238,900 mi

Mass of Earth: 5.972 × 10^24 kg

Mass of Moon: 7.34767309 × 1022  kg

Mass of Sun: 1.989 × 10^30 kg

Historical notes

Ptolemy of Egypt:

Wrote about tides in the Tetrabiblos.

Claudius Ptolemy

Johannes Kepler:

In 1609 Johannes Kepler correctly suggested that the gravitation of the Moon causes the tides, basing his argument upon ancient observations and correlations. The influence of the Moon on tides was mentioned in Ptolemy’s Tetrabiblos as having derived from ancient observation.

Galileo Galilei:  

In 1616Galileo Galilei wrote Discourse on the Tides. He tried to explain the tides as the result of the Earth’s rotation and revolution around the Sun, believing that the oceans moved like water in a large basin: as the basin moves, so does the water. Galileo rejected Kepler’s explanation of the tides.

Justus Sustermans - Portrait of Galileo Galilei, 1636.jpg

Isaac Newton:

F = G m1m2/r*2

where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the two.

Portrait of man in black with shoulder-length, wavy brown hair, a large sharp nose, and a distracted gaze

Pierre Simon Laplace:

In 1776, Laplace formulated a single set of PDEs for tidal flow. Laplace obtained these equations by simplifying the equations of fluid motion.

Laplace, Pierre-Simon, marquis de.jpg

Thomas Young:

(1773 – 1829). He ran the Nautical Almanack, and developed a theory of tides using harmonic analysis.  (Yes, he also did the diffraction slit experiment for the wave theory of light, and deciphered the Rosetta stone! among other things)