How-Tos

How Moon’s gravity causes tides, tidal forces

Imagine a family on their first vacation to a beach. They walk down a wide expanse of sand and set up their towels, picnic supplies, and beach umbrellas close to the water’s edge. A few hours later they need to rush all their stuff inland to avoid being drenched. What caused the tide to come in?

How Moon's gravity causes tides, tidal forces

How Moon Causes Tides

The Moon causes ocean tides on Earth. Specifically the difference in the Moon’s gravitational force acting on different locations on Earth causes tides.

The gravitational force between two objects depends on the distance between the objects. Earth is large enough that the location on Earth closest to the Moon is significantly closer than the location on Earth furthest from the Moon. Hence the lunar gravitational force is strongest on parts of Earth directly underneath the Moon. The lunar gravitational force is weakest on parts of Earth directly opposite the Moon. Physicists call this difference in gravitational force a tidal force or a tidal effect.

The tidal force acts on Earth’s oceans as well as on the solid Earth. The water in the oceans however flows more freely than the rock in Earth’s interior. The lunar tidal force therefore causes a double tidal bulge on the water in Earth’s oceans.

How Moon's gravity

Lunar gravity pulls water towards the side of Earth directly beneath the Moon. Simultaneously water, with less force pulling it, collects on the side of Earth directly opposite the Moon. These two bulges are the locations of the high tides.

As Earth spins on its axis, the tidal bulge migrates so that Earth experiences two high tides and two low tides each day. Earth’s rotation also creates a small time lag required for the water to flow into its new position. Hence the high tide bulge is not exactly underneath or opposite the Moon.

Because the Moon also orbits Earth high and low tides do not occur at the same time every day. The times vary as the Moon cycles through its phases.

Solar Tides and Lunar Phases

The Sun also exerts tidal forces on Earth. The Sun’s tidal effect is, however, weaker than the lunar effect because the Sun is much more distant than the Moon. Tidal forces depend much more strongly on distance than on mass, so the Sun’s much greater mass is less important than its larger distance.

Moon's gravity tides, tidal forces

During the full and new Moon phases, the Moon and Sun form a line with Earth. Hence during these lunar phases the Sun’s tidal effects add to the Moon’s tidal effects. High tides are higher during both the full Moon and the new Moon. These tides are called the spring tides.

During the first quarter and third quarter lunar phases, the Sun and Moon are at right angles as seen from Earth. Hence the solar tidal effect subtracts from the lunar tidal effect. High tides are not as high during the first and third quarter lunar phases. These tides are the neap tides.

Mathematics of Tidal Forces (Optional)

The gravitational force, F, between two masses, M and m, is given by Newton’s law of gravity:

F=GMm/r^2

Here G represents the universal gravitational constant and r is the distance between the two masses.

The tidal force is the difference in gravitational force at different distances and is found by using the calculus technique of taking the derivative of the gravitational force. The difference in the gravitational force is:

dF=-(2GMm/r^3)dr

Here dF represents the difference in gravitational force and dr is the difference in the distance. This difference in distance is usually the size of the object experiencing the tidal force.

Hence a larger object experiences greater tidal forces. The tidal force also gets smaller with the cube of the distance between the two objects. That is why the Sun’s tidal effect is less than the Moon’s.

Tidal Effects on Rock

Tidal forces act on Earth’s rocky and metallic interior as well as on water. While not flowing as easily as water, Earth’s interior does deform and flow a little. Friction from this deformation both slows Earth’s rotation and heats the interior. Similar tidal forces also heat the interiors of other worlds in the solar system, such as Jupiter’s volcanic moon, Io.

Tidal forces do more than cause ocean tides. Tidal effects act on other planets, on moons, and on stars.