Tidal Theory: Moon's Influence

• Tidal theory starts with a spherical Earth uniformly covered with water for simplicity.
• The effects of the moon and sun are considered separately, then combined.
• Tides result from gravitational effects within the Earth-Moon-Sun system and the movements of these bodies.

Effect of the Moon

• Tides are influenced by the gravitational attraction between the Earth and the Moon.
• Centrifugal forces also play a role, resulting from the revolution of the Earth and Moon around a common center located about 810 miles (1500 km) beneath the Earth's surface.
• Gravitational and centrifugal forces are balanced, preventing the Earth and Moon from colliding or drifting apart.
• The Earth-Moon system is in equilibrium.
• Centrifugal force is constant across the Earth's surface, acting parallel to the line joining the centers of the Earth and Moon.
• Gravitational force varies, being stronger for particles nearer the Moon.
• The combination of gravitational and centrifugal forces causes water to flow towards points on Earth's surface nearest and farthest from the Moon.
• This flow leads to higher water levels at these points and lower levels where the water flows from.
• The outward force at the nearest and farthest points is minimal.
• The true tide arises from near-horizontal forces that cause the water flow.
• As the Earth rotates, each point experiences two high tides and two low tides daily.
• The tilt of the Earth's axis causes the high and low tides to have unequal levels.

Effect of the Sun

• The sun affects the tides
• The sun's mass is much greater than the moon's.
• The sun's effect on tides is about 46 percent as strong as the moon's due to its distance.
• Tides are a result of combined lunar and solar influences.

Spring and Neap Tides

• Spring tides occur when the moon and sun are aligned with the observer's meridian.
• At the new moon, the forces of the moon and sun combine, creating a spring tide.
• Spring tides also occur at the full moon, about 14.5 days later, when the moon and sun are in opposition and their forces align.
• Neap tides occur about seven days after spring tides, when the moon is in quadrature.
• During neap tides, the high water due to the moon coincides with the low water due to the sun, resulting in a smaller tidal range.
• The range at neap tides is expressed as (M2 - S2).
• Neap tides occur when the gravitational forces of the Moon and Sun are perpendicular to each other.

Tidal Range Example

• If the moon produces a tide range of 14 meters and the sun produces a range of 6 meters:
• At spring tides (M2 + S2) = (14 + 6) = 20 meters.
• At neap tides (M2 - S2) = (14 - 6) = 8 meters.
• The phase inequality of heights, caused by the moon's phase, is the 12 meter difference.

Lunar Day

• The mean lunar day is about 50 minutes longer than the solar day.
• The interval between high water on one day and the corresponding high water on the next day is about 24 hours and 50 minutes.
• The interval between high water and the next low water is about 6 hours and 12 minutes.