Astronomy 161:
An Introduction to Solar System Astronomy

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 in the Earth-Moon System:

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: Tidal Bulges
[Click on the image to view full size (6.1k GIF)] (Graphic by R. Pogge)

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:

High and Low Tides
[Click on the image to view full size (16k GIF)] (Graphic by R. Pogge)

Some of the most extreme ocean tides on Earth are observed in Canada's Bay of Fundy between Nova Scotia and New Brunswick. Here the shape of the bay leads to average high tides of 12 meters compared to low tide, with 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.

Spring Tides:

Spring Tide (Graphic by R. Pogge)

Neap Tides:

Neap Tide (Graphic by R. Pogge)

Tidal Locking of the Moon

Similarly, the Earth raises tides on the Moon The early Moon rotated much faster: The end result is that the Moon got Tidally Locked in Synchronous Rotation.

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.

Tidal Braking in the Earth and Moon
[Click on the image to view full size (18k GIF)] (Graphic by R. Pogge)

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

This effect is known as Tidal Braking

The process of tidal braking is made complicated by the fact that the interior of the Earth is semi-molten, and the actual rate of change of the rotation rate is very complicated. Tidal braking is one of the most important components of the Length-of-Day change, but not the only process at work.

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 rate of lunar recession quoted is the present-day measured rate. However, please use caution if using this number to extrapolate back into the past or forward into the future, as the rate depends on a number of factor that make the actual recession rate over long periods of time non-linear.

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 many Billions of years, this could potentially add up until: The Earth & Moon would then be locked together in a 1:1 Tidal Resonance, and always keep the same face towards each other.

Once the Earth and Moon are tidally locked, further tidal evolution should stop. However, remember that the Earth and Moon orbit the Sun, and so tidal effects from the Sun will come into play, and continue to evolve the Earth-Moon system dynamically. The details are quite complicated, and beyond the scope of this course (and, to be fair, even the experts argue among themselves about the details - it is a difficult problem!).

The time required for the Moon and Earth to get into perfect tidal synchronization is actually longer than the time remaining in the Sun's life. Thus other changes will occur in the Earth-Moon system that somewhat obviate these effects, so they are shown for illustration only. The main point to carry away is that, all other things being equal, it takes a very long time for a well-separated system like the Earth and Moon to tidally lock.

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.

Updated: 2010 October 11, Todd A. Thompson
Copyright Richard W. Pogge, All Rights Reserved.