The Moon

Tides were known to the ancients, but an understanding of their origin came only three centuries ago with the publication of Issac Newton’s Principia.

Tides originate in the fact that the force of gravity decreases with distance from a massive body. The Moon exerts a force on the Earth, and Earth responds by accelerating toward the Moon; however, the waters on the side facing then Moon, being closer to the Moon, accelerate more and fall ahead of Earth. Similarly, Earth itself accelerates more than the waters on the far side and falls ahead of these waters. Thus two aqueous bulges are produced, one on the side of Earth facing the Moon, and one on the side facing away from the Moon.

moonphasesAs Earth rotates on its axis beneath these two bulges, the rise and fall of the oceans results. If Earth had not rigidity, the entire planet would flex freely in the same fashion, the ocean bottoms would rise and fall too, and there would be virtually no water tides. The very existence of the tides indicates that on a time scale of several hours, our planet displays considerable rigidity.

Although the Sun exerts a gravitational force 180 times as strong as does the Moon on Earth, because the Moon is so much closer, the variation in Moon’s force across Earth’s diameter is about 2.2 times larger than the variation in the Sun’s force. As noted above, it is this variation that produces tides, thus the pair of bulges raised by the Moon are considerably larger than the pair of tidal bulges raised by the Sun.

When these tidal bulges get in and out of step variations in the height of tides are noted – combining in step to produce “spring” tides (no connection with the season) when the Moon is new or full, and out of step to produce “neap” tides when the Moon is at first or last quarter.

Another factor having a substantial influence on tidal ranges is the elliptical shape of the Moon’s orbit. Although the Moon is only 9 to 14% closer at its close point to Earth (perigee) than at its far point (apogee), because the variation in its gravitational force varies inversely as the cube of its distance (the force itself varies inversely as the square of the distance), the Moon’s tidal influence is 30 to 48% greater at perigee than at apogee. In the Bay of Fundy the perigee-apogee influence is greater than the spring-neap influence. Although the variation of the Moon’s distance is not readily apparent to observers viewing the Moon directly, to observers near the shores of Minas Basin, the three to six metre increase in the vertical tidal range makes it obvious when the Moon is near perigee, clear skies or cloudy!