Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 19: Tides

Key Ideas:

Tides are caused by the difference between the Moon's gravitational pull on the near and far sides of the Earth
Tidal Effects:: Tidal Locking of the Moon's Rotation; Tidal Braking slowing the Earth's Rotation; Lunar Recession (increasing size of the Moon's orbit)

Seashore Astronomy

Tides are familiar to those living near the sea:: Sea level is highest twice a day at "high tide"; Sea level is lowest twice a day at "low tide"
Timing of Tides is governed by the Moon: Time between successive high tides: 12 hours, 25 minutes; Time between successive moonrises: 24 hours, 50 minutes, exactly twice the high-tide interval.
Tides are caused by the gravitational pull of the Moon.

Differential Gravity

The Moon is 12,740 km closer to the near side of the Earth than to the far side: Result is a 7% stronger pull on the near side of the Earth
The net front-to-back differential force: Stretches Earth along the Moon-Earth line; Squeezes Earth at right angles to this line
Results in 2 tidal bulges, so 2 tides per day

Land and Sea Tides

How big is the Tidal Bulge of the Earth?
Rock is stiff and resists tidal deformation: "Body Tides" on Earth are only 30 cm high
Water is fluid and flows more easily with gravity:: Ocean tides are 1 meter high on the open sea; Near the shore, tidal flows and seafloor shape can result in much larger local tides.
Canada's Bay of Fundy has 12 meter tides

Sun Tides

The Sun also raises tides on earth: The differential gravity force between the day and night sides is about half that due to the Moon
Highest High Tides are Spring Tides:: When the Sun and Moon are lined up; Occur at New Moon and Full Moon
Lowest High Tides are Neap Tides:: When the Sun and Moon are at right angles; Occur at First and Last Quarter Moon

Tidal Locking of the Moon

The Earth raises body tides on the Moon: Earth is more massive, so the tides are stronger
Constant squeezing and stretching in a rapidly rotating Moon would generate heat:: Energy gets taken from the Moon's rotation; The Moon slows down until its rotation and orbit periods are the same, stopping the squeezing.
Result: Moon is Tidally Locked to the Earth: Always keeps the same face toward the Earth

Tidal Braking of the Earth

The Earth rotates faster than the Moon orbits
Friction between the oceans and seafloor drag the ocean tidal bulges in the direction of rotation (eastware): Ocean Tides lead the Moon by about 10 degrees
Friction also robs energy from Earth's rotation: Slows the Earth down a tiny bit; Day is getting longer by 0.0023 sec/century
This effect is called Tidal Braking

Lunar Recession

The Moon feels a slight forward gravitational tug from the ocean tidal bulge: Results in a net acceleration of the Moon; Moves it outward into a slightly larger orbit
Lunar Recession: Increase in average Moon-Earth distance by about 3.8 cm per year; Measured by Doppler Laser Ranging

The Once and Future Moon

Tidal Braking and Lunar Recession are coupled:: Rotational energy from the Earth is transferred to the Moon as orbital energy; The Earth rotates slower and the Moon moves further away
After a few Billion years: The Moon will be ~50% farther away; Lunar Sidereal Month will be ~47 days long; Earth's rotation period will be 47 days
Earth and Moon get locked in a Tidal Resonance

Dynamical Evolution

Tidal phenomena are extremely important throughout the Solar System
We see examples of:: Tidal Resonances determining rotation periods (Moon and Mercury); Tidal Locking (Pluto and Charon); Tidally-induced Heating (Io around Jupiter and Triton around Neptune)
Tides are essential to understanding the dynamical evolution of the Solar System

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.