Tides
Tides are the periodic rise and fall of sea levels caused primarily by the gravitational pull of the Moon — and to a lesser extent the Sun — on Earth's oceans. As Earth rotates, most coastal locations experience two high tides and two low tides every 24 hours 50 minutes. The difference between high and low water is called the tidal range, which varies from less than a metre in some enclosed seas to over 16 metres in the Bay of Fundy, Canada.
How Tides Are Caused
The Moon exerts a gravitational force on every part of Earth, but the force is stronger on the side of Earth closest to the Moon (shorter distance) than on the far side (longer distance). This differential gravitational pull — called the tidal force — stretches Earth's oceans into an elongated shape, creating two tidal bulges: one facing the Moon (stronger pull) and one facing away (the residual or "inertial" bulge). As Earth rotates under these fixed bulges, a coastal observer passes through high tide → low tide → high tide → low tide roughly every 24 hours 50 minutes.
The Sun's Tidal Influence
Although the Sun is 27 million times more massive than the Moon, it is also 390 times farther away. Because tidal force scales as 1/r³ (not 1/r²), the Sun's tidal effect on Earth is only about 46% of the Moon's. The Sun's tides combine with the Moon's to produce spring tides and neap tides.
Spring Tides and Neap Tides
| Tide Type | Configuration | Moon Phase | Tidal Range | Occurs |
|---|---|---|---|---|
| Spring Tide | Sun–Earth–Moon aligned (syzygy) | New Moon or Full Moon | Largest (~140% of mean) | Every ~14.8 days |
| Neap Tide | Moon at 90° to Sun–Earth line (quadrature) | First or Third Quarter | Smallest (~60% of mean) | Every ~14.8 days |
Types of Tidal Pattern
Semidiurnal
Two nearly equal high tides and two low tides per day. Period: 12h 25 min. Common along the Atlantic coasts of Europe and North America.
Diurnal
One high tide and one low tide per day. Period: 24h 50 min. Occurs in the Gulf of Mexico and some Pacific coast areas.
Mixed Semidiurnal
Two unequal high tides and two unequal low tides per day. Common along the Pacific coasts of North America. Both diurnal and semidiurnal components present.
Key Tidal Formulas
Solved Examples
Example 1 — Tidal Force Ratio: Moon vs Sun
Given: MMoon = 7.35 × 10²² kg, MSun = 1.99 × 10³⁰ kg, dMoon = 3.84 × 10⁸ m, dSun = 1.50 × 10¹¹ m
Tidal force ∝ M/d³, so ratio:
FMoon/FSun = (MMoon/dMoon³) / (MSun/dSun³)
= (7.35×10²² / (3.84×10⁸)³) / (1.99×10³⁰ / (1.50×10¹¹)³)
= (1.30×10⁻³) / (5.89×10⁻⁴) ≈ 2.17
Result: Moon's tidal force is ~2.17× stronger than Sun's → Moon dominates tides.
Example 2 — Time Between Tides
Given: Earth's rotation period = 24h, Moon's orbital period = 27.3 days
Moon advances: 360°/27.3 = 13.2° per day relative to stars
Earth must rotate extra: 13.2°/360° × 24h = 0.883h = 53 min extra per day
High-to-high tide period: (24h + 53min)/2 = 12h 26.5 min (matches observed 12h 25 min M2 period)
Practice Questions
- Why are there two high tides per day rather than one, even though Earth has only one Moon?
- Calculate the ratio of the Moon's tidal force to its gravitational force on Earth's surface.
- Spring tides occur at New Moon AND Full Moon. Why do tidal bulges align with the Sun at Full Moon when the Moon is on the opposite side of Earth?
- The Bay of Fundy has a tidal range of up to 16 m. Name two reasons why some locations experience much larger tides than others.
- If Earth's rotation slowed so a day equalled one month, how many tides would a coastal location experience per day?
- Why does a semidiurnal tidal cycle have a period of 12h 25 min rather than exactly 12h?
Frequently Asked Questions
Why does the far side of Earth have a high tide too?
The far-side bulge arises because the Moon's gravity is weaker there than at Earth's center. Earth's center accelerates toward the Moon faster than the far-side ocean does, so the ocean on the far side is effectively "left behind" — forming a bulge. This is the tidal (differential gravity) effect, not centrifugal force.
What is the difference between spring and neap tides?
Spring tides occur when the Sun, Earth, and Moon are aligned (syzygy) at New or Full Moon. The Sun's and Moon's tidal forces add together, producing the largest tidal range (~40% above mean). Neap tides occur when the Moon is at 90° (quadrature) at quarter phases — the Sun's and Moon's forces partially cancel, giving the smallest tidal range (~40% below mean).
Why does the Moon cause bigger tides than the Sun despite the Sun's greater mass?
Tidal force depends on the difference in gravity across Earth's diameter, which is proportional to mass/distance³. Although the Sun is 27 million times more massive than the Moon, it is 390 times farther away. Since (390)³ ≈ 59 million and 27 million/59 million ≈ 0.46, the Sun's tidal effect is only about 46% of the Moon's — making the Moon the dominant tidal force.
Do tides occur on land too?
Yes — Earth's solid crust flexes about 20–30 cm each tidal cycle (called "Earth tides" or "body tides"). The oceans show much larger tides because water flows freely. The atmosphere also has its own tidal variations, though these are dominated by solar heating rather than gravitational tides.
What is tidal locking and is the Moon tidally locked to Earth?
Yes — the Moon is tidally locked to Earth, meaning its rotation period equals its orbital period (both ~27.3 days). This is why we always see the same face of the Moon. Earth's tidal forces on the early Moon gradually slowed its rotation over millions of years until it synchronized. Earth's rotation is also slowly being braked by tidal friction — days are lengthening by about 1.4 milliseconds per century.