# Tides & Roche Limit Explorer - Tidal Force, Spring Tides, Tidal Locking

> Explore tides: tidal force field and bulge, spring and neap tides, M2/S2/K1/O1 tide curves, an animated Roche-limit breakup and lunar recession vs day length.

- URL: https://qilingtools.com/en/physics/tides
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Look down on Earth from above the North Pole and see how the tidal accelerations from the Moon and Sun pull the oceans into two bulges. Spin the Earth to see why there are two high tides a day, and why tides are larger at new and full moon than at the quarters. The other tabs build tide curves of any type from the M2, S2, K1, O1 and other constituents, animate a satellite being torn into a ring inside the Roche limit, and use angular-momentum conservation to turn the Moon's recession rate into a change in day length and a tidal-locking timescale.

## How to use

1. On the Tidal force tab set the lunar phase, Earth–Moon distance and latitude (or pick a date), then press Spin the Earth to watch the tide at the observer
2. On the Tide curve tab choose a semidiurnal, mixed or diurnal preset, edit amplitudes and phase lags, and read the form factor and the times of high and low water
3. On the Roche limit tab pick Earth–Moon, Saturn's rings, Shoemaker–Levy 9 and more, compare the rigid and fluid limits, and press Run to watch a breakup
4. On the Tidal locking tab enter a recession rate to get the day lengthening per century, past day lengths and locking times

## Features

- Real tidal-acceleration vector field and exaggerated equilibrium bulge, with the Sun and Moon toggled separately
- Equilibrium tide height by latitude and declination, a 48-hour curve and a date-based lunar phase
- Harmonic synthesis of 8 major constituents, tide-type form factor and automatic high and low waters
- Rigid and fluid Roche limits with an animation of fragments shearing into a ring
- Earth–Moon angular momentum: recession rate vs day length, compared with Devonian corals and other evidence
- Order-of-magnitude tidal-locking timescales with adjustable Q and k₂

## FAQ

### Why are there two high tides a day?

Tides come not from the Moon's gravity itself but from how it varies across the Earth. Water on the near side is pulled toward the Moon more strongly than Earth's centre is. Water on the far side is pulled less strongly, so it lags behind the centre and bulges outward too. The Earth has a bulge on each side, and as it turns a location passes through both, giving a high tide about every 12 hours 25 minutes. The extra 25 minutes come from the Moon moving along its orbit.

### What causes spring and neap tides?

The Sun's tidal force is about 0.46 times the Moon's. At new and full moon the Sun, Moon and Earth line up, the bulges add, and the range is largest: spring tides. At first and last quarter they are 90° apart and partly cancel, giving the smallest range: neap tides. In equilibrium theory the spring range at the equator is about 2.7 times the neap range. The cycle repeats every 14.77 days, which is the beat period between the S₂ and M₂ constituents.

### Why do some places get only one high tide a day?

When the Moon or Sun is north or south of the equator, the two bulges are unequal at a given latitude, which adds once-daily constituents K₁ and O₁. In some basins resonance boosts the diurnal part and suppresses the semidiurnal one, for example in the Gulf of Tonkin and the Gulf of Mexico, so there is a single high tide a day. The form factor F = (K₁+O₁)/(M₂+S₂) classifies tides: below 0.25 semidiurnal, above 3 diurnal, mixed in between.

### What is the Roche limit, and why are Saturn's rings there?

Close to a massive body, tides stretch a satellite by pulling its near and far sides apart. When that stretch beats the satellite's own gravity, a body held together only by gravity breaks up. This critical distance is the Roche limit: about 2.44R(ρM/ρm)^(1/3) for a fluid or rubble-pile satellite, and about 1.26R(ρM/ρm)^(1/3) for a rigid body with internal strength. Most of Saturn's main rings lie inside the fluid Roche limit for ice, so the material cannot gather into a moon. Comet Shoemaker–Levy 9 was torn into more than 20 pieces when it passed Jupiter in 1992, and hit the planet two years later.

### Is the Moon really moving away from Earth?

Yes. Lunar laser ranging shows the Moon receding by about 3.8 cm a year. Earth spins faster than the Moon orbits, so the tidal bulge is carried ahead of the Moon. Its pull drags the Moon forward and enlarges the orbit, while the reaction slows Earth's spin. By angular-momentum conservation, 3.8 cm a year corresponds to the day getting about 2 ms longer per century, consistent with the roughly 2.3 ms tidal contribution inferred from ancient eclipse records. Devonian coral growth bands show about 400 days per year, which also points to shorter days in the past.

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