Tides and Tide Raising Forces

This presentation addresses three points about tides: What causes tides? Why do tide times change? Why do tide heights vary?

There two high tides approximately 12 hours apart each day. They are separated by two low tides. How does this happen? One tide raising force is widely known - the moon. The moon’s mass causes gravitational pull all over the surface of the earth. This creates a bulge of water (a high tide) under the moon (the sublunar point) at all times. As the earth rotates on its axis once every 24 hours, it therefore follows that a place on the earth (eg., an island) would pass “through” the bulge once a day. But causes the other high tide?

Earth Moon High Tide Low Tide

To understand this, we first must understand the nature of the relationship of the earth and the moon. It is commonly held that the moon revolves (goes around) the earth once every 28 days, which is the period from new moon to new moon. Reality is a little more complex …..

Balance or center of gravity for two objects with the same mass. (Mass = M) M = 10 Assume there are two objects in space …..

M = 10 M = 5 Balance or center of gravity for two objects where one object has a mass twice the other’s. Now, a bit of a change …..

Earth Moon Because of the much larger mass of the earth compared to the moon, the center of gravity of the earth-moon system is actually inside the earth’s crust by about 1100 km. This means that the earth and moon actually revolve around a common point of gravity once every 28 days. Finally, the earth and moon...

Common center of gravity of earth-moon system. Direction of revolution Earth Moon

How does this explain the two high tides daily? This revolution of the earth about the common center of gravity causes centrifugal force all over the surface of the earth. This causes there to be a bulge of water (another high tide) on the opposite side of the earth as the moon. Therefore, a place on the earth (eg., an island) would in the course of the earth’s rotation pass through two high water bulges in a 24 hour period.

On the earth’s hemisphere facing the moon, the main tide raising force is in the direction of the moon’s gravitational attraction, or toward the moon. On the opposite side, the main tide raising force is in the direction of the centrifugal force, or away from the moon. In between, where there is a low tide, the two forces balance each other out.

Why? Gravitational pull gets weaker as distance is increased and so the farther from the moon the less tide-raising force it has. However, centrifugal force gets stronger as the radius of rotation increases (think of “crack the whip”).

Moon G1G1 C1C1 C2C2 G2G2 G3G3 C3C3 Therefore, G 1 > G 2 > G 3 and C 1 >C 2 >C 3, where G= gravitational force and C= centrifugal force.

Moon G1G1 C1C1 C2C2 G2G2 G3G3 C3C3 With G 2 = C 2, it follows that on the moon side G 1 >C 3 and therefore there is a high tide at the sublunar point caused by the gravitational pull of the moon. Conversely, on the opposite side C 1 >G 3 and so there is a high tide at the antipodal position caused by centrifugal force.

Common center of gravity of the earth-moon system. Gravitational forces Centrifugal forces

But the high tides don’t occur at the same time each day. Why? As the earth rotates on its axis, the earth and the moon revolve around their common center of gravity. So as a place on the surface of the earth makes one complete rotation (in 24 hours), it is not in the same position with respect to the moon. If the moon was directly overhead at hour “zero”, 24 hours later the moon will not be directly overhead as the moon has “moved” or revolved in its orbit. Actually it takes another 52 minutes (approximately) for the earth and moon to aligned again. This accounts for the (on average) 12 hour and 26 minute between each high (and low) tide.

Rotation Revolution Passamaquoddy Island - directly under moon - high tide Day One - 08:00 hours North Pole

Day Two - 08:00 hours Rotation Moon on Day One Moon 24 hours later: Day Two 24 hours later Passamaquoddy Island is not under the moon because the moon has “moved” or revolved in its orbit.

Rotation Moon on Day One Moon on Day Two Day Two - 08:52 hours In order for Passamaquoddy Island to be at high tide takes another 52 minutes.

The two high tides each day are not the same size. Why? This is due to the fact that the earth’s axis is on a tilt. It is not at right angles to the plane of its orbit about the earth-moon system.

Passamaquoddy Island at 12:25 (next high tide). Tide is only 3m. Passamaquoddy Island at 12:00 a.m. Tide is 4.5m. Latitude line High Tide North Pole South Pole

End