Tides, Tidal Friction, and Synchronous Rotation. Why do tides occur?

Tides, Tidal Friction, and Synchronous Rotation

• Why do tides occur?

• Why do tides occur?• They are caused by the

gravity of the Moon

gravity of the Moon• But how?

gravity of the Moon• This is how:

The Universal Law of Gravitation

The strength of gravity decreases with distance

gravity of the Moon• So the Moon pulls harder on

the nearer side

the nearer side• This stretches the Earth out,

making two tidal bulges on opposite sides

• The Moon goes around the Earth slower than the Earth rotates

• So any point on Earth should have two high tides and two low tides each day

• But they aren’t exactly 12 hours apart

• Why?

• It’s because the Moon orbits around the Earth

• So at a given location, the Earth has to go through more than one sidereal rotation to get back to the same tide

• It also depends on the shape of the coast and the shape of the bottom

• The tidal bulge in mid-ocean is only about 2 meters

• But tidal heights vary from place to place

• Locally, the tide at the beach varies about 4 feet from low to high

• Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge

• But elsewhere, the variation can be much greater

• For example, the Bay of Fundy

• This is high tide there

• This is high tide there• This is low tide

• This is high tide there• This is low tide• The tides can vary by as

much as 40 feet!

• This is due to the shape of the bay

• The natural frequency with which waves want to slosh back and forth in the bay

• The natural frequency with which waves want to slosh back and forth in the bay – like in a bath tub

• The natural frequency with which waves want to slosh back and forth in the bay – like in a bath tub – matches the time it takes for the tide to roll in

• So the sloshing amplifies the tides and leads to the huge variation in water height between low and high tides

• The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon

• Occasionally the Sun and the Moon work together to produce unusually extreme tides

• When the Sun, Earth, and Moon are in a line there is a “spring tide”

• When they form a right angle there is a “neap tide”

• When should these occur?

• In fact, the tidal bulge is not lined up with the Earth and Moon• This is due to “tidal friction”• As the Earth rotates through the tidal bulges, it pulls them ahead• So they run slightly “ahead” of the Earth-Moon line• If the Earth didn’t rotate faster than the Moon orbits, the bulges would

be on the Earth-Moon line

• This tidal friction slows down Earth's rotation • Length of day increases ~2 ms per century (1 s per 50,000 y)

• It also pulls the Moon ahead in its orbit• This increases orbital energy• And moves the Moon away from the Earth by ~4 cm per year • So the Moon is ~1 m farther away than when Apollo 11 landed

• Knowing what you know about conservation of angular momentum, how will this affect the angular momentum of the system consisting of the Earth and the Moon?

• The angular momentum lost by the Earth is gained by the Moon

• The Earth’s rotation is slowed ever so slightly by this process

• The Earth’s rotation is slowed ever so slightly by this process• But the Earth’s tidal force causes a tidal bulge on the Moon, too

• The Earth’s rotation is slowed ever so slightly by this process• But the Earth’s tidal force causes a tidal bulge on the Moon, too• And the Moon’s rotation has been affected much more, because the

Moon is much smaller

• Over time, the Moon’s rotation has slowed until its rate matches its orbital period

• It is now in “synchronous rotation” with its orbit

• It is now in “synchronous rotation” with its orbit• This is why it always shows the same face to us

• It is now in “synchronous rotation” with its orbit• This is why it always shows the same face to us• Well, almost the same face

• It is now in “synchronous rotation” with its orbit• This is why it always shows the same face to us• Well, almost the same face…these are called “librations”

• There are many other examples of this sort of rotational “locking”

• There are many other examples of this sort of rotational “locking”• Some are truly synchronous:

• the Moon

• the Moon• Pluto and its moon Charon

END OF LECTURE 09 JUN 2008

• Others somewhat different:

• Others somewhat different:• Mercury’s 2:3::orbital:rotational resonance with the Sun

Tides, Tidal Friction, and Synchronous Rotation. Why do tides occur?

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