Questions: Tidal Equilibrium Theory and Tidal Mechanics

Question 1

Most people understand why there is a tidal bulge on the side of Earth facing the Moon (the Moon pulls that water toward it). Why is there also a tidal bulge on the opposite side of Earth, away from the Moon?

• A. Earth's rotation generates centrifugal force that flings water outward on the far side
• B. On the far side, the Moon's gravity is weaker than average, so that water is effectively left behind as Earth's center is pulled more strongly toward the Moon
• C. The Sun creates the far-side bulge while the Moon creates the near-side bulge
• D. The far-side bulge is a pressure wave reflected from the near-side bulge through Earth's rigid interior

Answer: (B)

Tides arise from the differential in gravity across Earth's diameter — not from gravity itself. The Moon pulls the near-side ocean stronger than Earth's center, and pulls Earth's center stronger than the far-side ocean. From Earth's reference frame, the far-side ocean is 'left behind' as Earth accelerates toward the Moon. The result is two bulges — one pulled toward the Moon, one left behind — which is why most coastlines experience two high tides per day. Option A (centrifugal force) is a common misconception; rotation alone cannot explain why both bulges track the Earth-Moon line.

Question 2

The Sun is 27 million times more massive than the Moon, yet the Moon produces tides roughly twice as large as the Sun's. Why?

• A. The Moon orbits closer to sea level and therefore exerts tidal force more directly on surface water
• B. The tide-generating force falls off with the cube of distance — not the square — so the Moon's proximity more than compensates for the Sun's greater mass
• C. The Sun's light and radiation counteract its gravitational pull on the oceans
• D. The Moon orbits in the same plane as Earth's equator, maximizing its tidal effect

Answer: (B)

This is the key quantitative insight of tidal mechanics. Gravitational force itself falls off as the square of distance (inverse square law). But the tide-generating force — the differential in gravity across Earth's diameter — falls off with the cube of distance. This means proximity matters enormously more for tides than for gravity. The Sun is about 390 times farther from Earth than the Moon. Although the Sun is 27 million times more massive, the cube of 390 (about 59 million) overcomes that mass advantage, leaving the Moon with roughly twice the Sun's tidal effect.

Question 3

Spring tides — the largest tidal ranges — occur when the Moon is at its closest orbital point to Earth (perigee), maximizing its gravitational pull on the oceans.

• T. True
• F. False

Answer: False

Spring tides are caused by the alignment of the Sun, Earth, and Moon — at new moon and full moon — not by the Moon's orbital distance. When the Sun and Moon are aligned, their tidal bulges reinforce each other, producing larger combined tides. When the Moon is at perigee (closest approach), tides are also somewhat larger (called perigean tides), but that is a separate effect. The spring-neap cycle is driven purely by the angular relationship between the Sun and Moon as seen from Earth, repeating every ~14.8 days as the Moon orbits.

Question 4

Equilibrium tidal theory predicts that most locations on Earth should experience two high tides and two low tides each lunar day (approximately 24 hours and 50 minutes).

• T. True
• F. False

Answer: True

In the equilibrium model, two tidal bulges remain fixed along the Earth-Moon line while Earth rotates beneath them. Any point on the equator therefore passes through both bulges — two high tides — and the two troughs between them — two low tides — per lunar day. This semi-diurnal pattern dominates at most coastlines worldwide. The 50-minute offset from a solar day arises because the Moon advances in its orbit, so Earth must rotate slightly more than 360° to return to the same Moon-relative position.

Question 5

Why do tides arise from the differential in gravitational force across Earth's diameter, rather than from the Moon's gravity simply pulling the ocean toward it?

Model answer: If the Moon's gravity pulled uniformly on all of Earth, it would accelerate the entire planet — ocean, land, and core — equally, and no tides would form. What creates tides is the variation in the Moon's pull: stronger on the near side, average at the center, weaker on the far side. This differential stretches the ocean into an elongated shape. On the near side, water is pulled more strongly than Earth's center; on the far side, water is pulled less strongly and is effectively left behind. The tide-generating force is this difference — not the Moon's gravity itself.

This differential origin is why the tide-generating force falls off with the cube of distance rather than the square. Gravity (the average pull) falls as 1/r². The differential across Earth's diameter is proportional to the change in gravity over distance d, which scales as d/r³ — one additional power of distance in the denominator. This is why distance matters so much more for tides than for ordinary gravity, and why the Moon dominates tides despite being far less massive than the Sun.