# Perigean Spring Tides

In this section we will investigate another special type of tide called the perigean spring tide. Sometimes they are also referred to as king tide. These are naturally occuring tides that are higher than usual. To understand their origin we first have to look at the orbit of the Moon.

## Shape of the Moon Orbit

The tidal models discussed so far were based on simplified circular orbits. Although this has been a justifiable simplification it is a tad too simple to explain the finer details of tides. Lets now have a closer look at the Moon orbit and how it is affecting tides. We already learned about Spring tides and Neap tides. Now lets look into a special type of spring tide called the perigean Spring Tide. To understand perigean spring tides let us first look at the orbit of the Moon.

Schematic view of the orbit of the Moon as seen from above. The eccentricity is overemphasised, sizes and distances are scaled differently.

Moon orbits Earth in prograde direction. Prograde direction is the direction in which Earth is spinning. It completes one revolution with respect to the stars in 27.32 days. This is also called the siderial period. Both Earth and Moon are orbiting a common center of mass, the barycenter. The Orbit of the Moon is elliptical. Its average eccentricity is 0.0549 which brings the ellipse pretty close to a cirlce. The greatest distance between Moon and Earth is 405400 km (Apogee) the shortest distance is 362600 km (Perigee).

Perigean Spring Tides occur when Sun, Earth and Moon are arranged in a line and the Moon is at its Perigee at the same time. In other words: The Moon is either full or new and it is closest to Earth [6]. Such an arrangement happens three to four times per year. The difference in water level between ordinary Spring Tides and Perigean Spring Tides is usually a couple of centimeters with a maximum difference of 15 cm being on record for parts of the Alaska coast. When seen with respect to the tidal range of 9 m in the same area the effect is rather small (<2 %).

## Tides and Lunar and Solar Eclipses

Another property having an influence on the height of local tides is the tilt of the axis of the Earth and the tilt of the Moon orbit against the Ecliptic. The Ecliptic is the plane in which the Earth orbits the Sun. The Earth axis is tilted 23.44° against the ecliptic. The Moons orbit is tilted 5.14° against the ecliptic.

Schematic view of the orbit of the Moon as seen from the side.

It is rather trivial to imagine, that spring tides are a bit stronger if the Moon happens to be located at a point in its orbit where it intersects with the ecliptic. Only then Sun, Moon and Earth are located exactly at a straight line. This is also the only arrangement under which lunar or solar eclipses will occur. From that we can draw the conclusion that at the times of lunar or solar eclipse tides are a bit stronger stronger than usual.