CHAPTER 5 | GRAVITY 87
they would collide in about two weeks except that they are orbit-
ing around their common center of mass. Th e ocean tides are
caused by the accelerations Earth and its oceans feel as they orbit
around that center of mass.
A Common Misconception holds that the moon’s
eff ect on tides means that the moon has an affi nity for water—
including the water in your body—and, according to some people,
that’s how the moon aff ects you. Th at’s not true. If the moon’s grav-
ity aff ected only water, then there would be only one tidal bulge,
the one facing the moon. As you know, the moon’s gravity acts on
the rock of Earth as well as on water, and that produces the tidal
bulge in the oceans on the far side of Earth. In fact, small tidal
bulges occur in the rocky bulk of Earth as it is deformed by the
moon’s gravity, and although you don’t notice it, as Earth rotates, its
mountains and plains rise and fall by a few centimeters. Th e moon
has no special affi nity for water, and, because your body is so much
smaller than Earth, any tides the moon raises in your body are
immeasurably small. Ocean tides are large because oceans are large.
You can see dramatic evidence of tides if you watch the
ocean shore for a few hours. As Earth rotates on its axis, the tidal
bulges remain fi xed with respect to the moon. As the turning
Earth carries you and your beach into a tidal bulge, the ocean
water deepens, and the tide crawls up the sand. Th e tide does not
so much “come in” as you are carried into the tidal bulge. Later,
when Earth’s rotation carries you out of the bulge, the ocean
becomes shallower, and the tide falls. Because there are two
bulges on opposite sides of Earth, the tides rise and fall twice a
day on an ideal coast.
In reality, the tidal cycle at any given location can be quite
complex because it is aff ected by the latitude of the site, shape of
the shore, winds, and so on. Tides in the Bay of Fundy (New
Brunswick, Canada), for example, occur twice a day and can
exceed 40 feet. In contrast, the northern coast of the Gulf of
Mexico has only one tidal cycle a day of roughly 1 foot.
Gravity is universal, so the sun also produces tides on Earth.
Th e sun is roughly 27 million times more massive than the moon,
but it lies almost 400 times farther from Earth. Tides on Earth
caused by the sun are less than half as high as those caused by the
moon. Twice a month, at new moon and at full moon, the moon
and sun produce tidal bulges that add together and produce
extreme tidal changes; high tide is exceptionally high, and low
tide is exceptionally low. Such tides are called spring tides. Here
the word spring does not refer to the season of the year but to the
rapid welling up of water. At fi rst- and third-quarter moons, the
sun and moon pull at right angles to each other, and the sun’s
tides cancel out some of the moon’s tides. Th ese less-extreme tides
are called neap tides, and they do not rise very high or fall very
low. Th e word neap comes from an obscure Old English word,
nep, that seems to have meant “lacking power to advance.” Spring
tides and neap tides are illustrated in Figure 5-8.
Galileo tried to understand tides, but it was not until
Newton described gravity that astronomers could analyze tidalHere M is just the total mass of the system in kilograms. For a
planet orbiting the sun, you can use the mass of the sun for M,
because the mass of the planet is negligible compared to the mass
of the sun. (In a later chapter, you will apply this formula to two
stars orbiting each other, and then the mass M will be the sum of
the two masses.) For a circular orbit, r equals the semimajor axis
a, so this formula is a general version of Kepler’s third law, P^2
a^3. In Kepler’s version, you used astronomical units (AU) and
years, but in Newton’s version of the formula, you should use
units of meters, seconds, and kilograms. G, of course, is the
gravitational constant.
Th is is a powerful formula. Astronomers use it to calculate
the masses of bodies by observing orbital motion. If, for example,
you observed a moon orbiting a planet and you could measure
the size of the moon’s orbit, r, and its orbital period, P, you could
use this formula to solve for M, the total mass of the planet plus
the moon. Th ere is no other way to fi nd masses of objects in the
universe, and, in later chapters, you will see this formula used
over and over to fi nd the masses of stars, galaxies, and planets.
Th is discussion is a good illustration of the power of
Newton’s work. By carefully defi ning motion and gravity and by
giving them mathematical expression, Newton was able to derive
new truths, among them Newton’s version of Kepler’s third law.
His work transformed the mysterious wanderings of the planets
into understandable motions that follow simple rules. In fact, his
discovery of gravity explained something else that had mystifi ed
philosophers for millennia—the ebb and fl ow of the oceans.
Tides and Tidal Forces
Newton understood that gravity is mutual—Earth attracts the
moon, and the moon attracts Earth—and that means the moon’s
gravity can explain the ocean tides.
Tides are caused by small diff erences in gravitational forces.
For example, Earth’s gravity attracts your body downward with a
force equal to your weight. Th e moon is less massive and more
distant, so it attracts your body with a force that is a tiny percent
of your weight. You don’t notice that little force, but Earth’s
oceans respond dramatically.
Th e side of Earth that faces the moon is about 4000 miles
closer to the moon than is the center of Earth. Consequently, the
moon’s gravity, tiny though it is at the distance of Earth, is just a
bit stronger when it acts on the near side of Earth than on the
center. It pulls on the oceans on the near side of Earth a bit more
strongly than on Earth’s center, and the oceans respond by fl ow-
ing into a bulge of water on the side of Earth facing the moon.
Th ere is also a bulge on the side of Earth that faces away from the
moon because the moon pulls more strongly on Earth’s center
than on the far side. Th us the moon pulls Earth away from the
oceans, which fl ow into a bulge away from the moon as shown
at the top of ■ Figure 5-8.
You might wonder: If Earth and moon accelerate toward
each other, why don’t they smash together? Th e answer is that