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Astronomy 161
An Introduction to Solar System Astronomy
Prof. Scott Gaudi

Lecture 20: Tides

Key Ideas

Tides are caused by differences in the gravitational pulls of the Moon and Sun between near and far sides of the Earth.

Tidal Effects:

Seashore Astronomy

Ocean Tides are a familiar phenomenon to those who make their homes near the sea:

People near the sea quickly notice that the timing of the tides was governed by the motions of the Moon:

This folk intuition is correct: Tides are in fact caused primarily by the gravitational pull of the Moon.

Differential Gravity

The gravitational force exerted by the Moon on the near and far sides of the Earth is different: This causes a net front-to-back differential gravitational force felt by the Earth:

The net result is 2 tidal bulges on opposite sides of the Earth, and so 2 tides per day as the Earth rotates through the Earth-Moon line.

Land and Sea Tides

How big is the Tidal Bulge of the Earth?

The main body of the Earth is made of rock, which is stiff and resists deformation by tides.

The oceans are made of water which is fluid and flows easily in response to the tidal forces:

The most extreme ocean tides are experienced in Canada's Bay of Fundy between Nova Scotia and New Brunswick, where the shape of the bay leads to average high tides of 12 meters compared to low tide, and maximum high tides of up to 17 to 18 meters!

Sun Tides

Gravity is a universal force, so tides are raised between any two bodies.

The Sun also raises tides on the Earth:

The Sun and Moon work together to give different kinds of tides and different times of a Lunar Month.

The highest High Tides are the Spring Tides:

The lowest High Tides are the Neap Tides:

Tidal Locking of the Moon

Similarly, the Earth raises tides on the Moon If the Moon were rotating faster than its orbit, the constant stretching and squeezing of the Moon by Earth tides would have generated heat. The end result is that the Moon is Tidally Locked to the Earth.

This is why the Moon always keeps the same face towards the Earth, as we saw back in Lecture 8.

Because the rotation and orbit periods are the same, we say that the Moon is locked in a 1:1 Tidal Resonance with the Earth.

Tidal Braking of the Earth

The Earth rotates faster than the Moon orbits the Earth (24 hours compared to 27 days).

There is therefore friction between the ocean and the seabed as the Earth turns out from underneath the ocean tidal bulges.

The friction from the ocean tides robs the Earth of rotational energy, acting like brake pads.

This effect is known as Tidal Braking

Lunar Recession

Another effect of the Tidal Braking is that the extra mass in the ocean bulges leading the Moon causes a small net forward tug.

This effect is known as Lunar Recession

The Lunar Recession rate is measurable using Laser Ranging experiments that use retroreflector arrays left on the Moon by the Apollo missions (Apollo 11, 14, and 15), and two Soviet landers (Lunakhod 1 and 2). Telescopes on Earth bounce laser beams off the reflector arrays and measure the distance to the Moon to millimeter precision.

The Once and Future Moon

Lunar Recession and Tidal Braking of the Earth's rotation are coupled: the rotational energy being taken from the Earth in braking is effectively being transferred, via tides, to the Moon. This extra energy lifts it into a higher orbit.

As a result:

After a few Billion Years, this adds up until: The Earth & Moon will be locked together in a 1:1 Tidal Resonance, and always keep the same face towards each other.

Dynamical Evolution

Tidal phenomena are extremely important throughout the Solar System.

In the remainder of the class, we will often encounter examples of tides playing a role in the dynamics of planets and their moons.

Some examples:

Tides are essential to understanding the dynamical evolution of the Solar System.
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