In Tides you saw how the Moon raises two bulges of ocean, giving most coasts two high tides a day. The Sun raises tides too. Whether its tides add to the Moon's or work against them depends on the phase of the Moon.
Why it works
Tides come from the difference in gravity across Earth (see how gravity depends on distance). The side of Earth facing the Moon is pulled a little more than Earth's center, and the far side a little less, so Earth is stretched along the Earth–Moon line. That difference falls off as $M/d^3$, faster than gravity itself. The Sun is 27 million times more massive than the Moon but 390 times farther away: $2.7 \times 10^7 \div 390^3 \approx 0.46$. So the Sun's tides are a little under half as strong as the Moon's. When the Sun, Earth and Moon line up (new and full moon) the two pairs of bulges line up and add. At the quarter moons, the Sun's bulges sit at right angles to the Moon's and partly cancel them.
Key idea
Spring tides (the largest range) come at new and full moon, when the Sun's and Moon's tides add. Neap tides (the smallest range) come at first and third quarter, when they partly cancel. Each comes about every two weeks, all year round.
Worked examples
Worked example: Spring and neap
On one coast the Moon alone would make a tidal range of $2.0$ m and the Sun alone $0.92$ m. Find the spring and neap ranges.
- Spring (lined up, they add): $2.0 + 0.92 = 2.92$ m.
- Neap (at right angles, the Sun's tide works against the Moon's): $2.0 - 0.92 = 1.08$ m.
Answer: About $2.9$ m at spring tide and $1.1$ m at neap tide.
Worked example: How often?
How many days pass between spring tides, and from a spring tide to the next neap tide?
- Spring tides come at new moon and again at full moon: half of $29.53$ days, about $14.8$ days apart.
- Neap tides fall halfway between, at the quarters: about $7.4$ days after each spring tide.
Answer: About $14.8$ days; about $7.4$ days.
Common mistake
The word "spring" in spring tide has nothing to do with the season. It comes from the water springing up. Spring tides happen twice every month, in January as much as in April. Check: new moon happens about every 29.5 days, all year, and each one brings a spring tide.
Real tides also depend on coastline shapes and ocean basins, which is why tide tables for each harbor come from local measurements (NOAA publishes them for U.S. coasts).