Prof.
Clements Notes/Hints for Physics Courses
Chapter
6 Part 3 Open Stax College Physics or Most Introductory Physics
Courses
Tides,
Tidal Lock, Kepler's Laws of Planetary Motion, Miscellaneous Topics
Terms
you should know at the end of this unit: tide, tidal lock, Kepler's
Laws
Tides
Those
who live in Nebraska, or other landlocked states, have a handicap
when it comes to appreciating tides. Tides in the ocean cause the
water level to vary several feet (or more) depending on the location
of the Moon in the sky.
For
an Earth that is covered in water (no land) the average height
difference from low tide to high tide is about 3 feet. There are
locations on Earth where the shape of the ocean floor causes the
tides to vary by 60 feet. Also, the crust of the Earth flexes due to
tides about 8 inches twice a day. (Ref: Astronomy by Fix, 6th
ed. pages 94, 95)
The
tides are not caused by the Moon’s gravity lifting water off of the
surface of the Earth. One piece of evidence for this is that there
are two high tide locations around the Earth. One high tide location
is approximately underneath the Moon and the other is 180 degrees
around the Earth from this location. Water flows along the surface
of the Earth from approximately 90 degrees away from the direction to
the Moon to form the high tide region. Where the water is flowing
from becomes a low tide region.
The
Moon has more tide effect than the Sun because it is closer to the
Earth than the Sun. This leads to a larger difference in the Moon’s
force at various points on Earth compared to differences in the force
due to the Sun around the Earth
You
should watch some videos that explain the tides and ask your
instructor if you have questions.
Tides
Slow the Earth’s Rotation
Water
flowing on the Earth creates a friction force that slows down the
rotation of the Earth. The slow down is only 0.0016 seconds per
CENTURY but the effect is cumulative and noticeable over time.
Corals have daily growth rings and seasonal growth rings similar to
the annual growth rings of trees. The evidence indicates that the
Earth only needed 22 hours for one rotation about 400 million years
ago.
Also,
the locations of solar eclipses from computer predictions don’t
match the locations recorded by ancient cultures unless the slow down
of the Earth’s rotation is taken into account. The Moon’s shadow
comes to small area at the Earth (about 100 miles). The eclipse
track is often not parallel to the equator of the Earth. The Earth
spins and places observers into position to have the Moon’s shadow
sweep across the observer. If the spin rate was 24 hours in the
distant past the solar eclipses would have been seen from different
locations than what is recorded.
Tides
Enlarge the Moon’s Orbit
Astronomers
know that the size of the Moon’s orbit is increasing. Astronomers
measure the time for laser beams to return to Earth from the Moon.
Distance
= speed of light * round trip travel time/2
The
Earth-Moon system has angular momentum in it spin and revolution. As
the Earth slows down, the Moon must move to a larger distance from
the Earth to keep a constant value for the angular momentum. This is
a well confirmed law of physics.
Tidal
Lock
The
Moon always has one face towards the Earth because of an effect known
as tidal lock. The Earth creates tides in the crust of the Moon that
distort the Moon a little into an elongated shape rather than a
perfect sphere. The long axis of the elongated Moon points
approximately towards the Earth. If the Moon tries to rotate away
from this alignment the force of gravity of the Earth creates a
restoring force that brings the Moon back in line. You should make
your own sketch of this situation to convince yourself of these
statements.
Because
of tidal lock the Moon spins once on its axis for every orbit around
the Earth. This causes us (on Earth) to always see the same side of
the Moon.
Kepler’s
Laws of Planetary Motion
Ask
your instructor if you need to memorize Kepler’s Laws of planetary
motion. You should know that Newton was able to derive Kepler’s
Three Laws of planetary motion using the Law of Universal Gravitation
and calculus. A summary of the three laws: 1) The planets move on elliptical orbits around the Sun which is at one focus of the ellipse, 2) The planets move faster when they are closer to the Sun in their ellipse, 3) There is a relation between the size of the orbit and the period of the orbit.
You should be able to do the algebra of deriving
Kepler’s Third Law. Recall Fc = mV2 / r .
Here m is the mass of the planet and r is the size of the planet
orbit. Replace the V in the centripetal force equation with ( 2 pi r
/ T ) and substitute Newton's Law of Gravity (with the masses being
the planet and the Sun) for Fc. Simplify. You will now
have a relation between the orbit size, mass of the sun, and orbit
period. If you choose to use units of years for time and
Astronomical Units (AU) for distance, the relationship simplifies to
P2 = a3, where P is the period in years and
"a" is the semimajor axis of the planet's ellipse measured
in AUs.
Kepler’s
description that the planets traveled on ellipses with the Sun at one
focus simplified the model of the solar system. Before this, solar
system models that used circles had to have multiple circles to carry
the planets around in order to approximately match the observed
positions and motions of the planets. This was especially true for
the Ptolemaic, Earth-centered, model of the solar system.
Space
Debris
Man-made
objects have been put into orbit around the Earth since 1957. In the
process of putting satellites into orbit covers, small bolts, empty
rocket fuel containers, etc. also went into orbit. The debris in
space around the Earth is starting to become a problem. Some of the
debris has substantial mass and all of it has substantial speed. A
collision with an astronaut on a space walk or with a spacecraft
could be fatal. Occasionally the thrusters on the International
Space Station (ISS) are used to change the ISS orbit to prevent
possible collisions with this debris.
Copyright©
2017 by Greg Clements Permission is granted to reproduce this
document as long as 1) this copyright notice is included, 2) no
charge of any kind is made, and, 3) the use is for an educational
purpose. Editing of the document to suit your own class style and
purposes is allowed.
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