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Chapter 05 - Gravity and Motion
CHAPTER 5
GRAVITY AND MOTION
CHAPTER OUTLINE AND LECTURE NOTES
1. Force and Motion Before Newton
As was the case with Copernicus, I think it is important to show that Newton, as great a genius
as he was, built his ideas on those of his predecessors and contemporaries. You may wonder
why the illustration of David Scott dropping a feather and a hammer on the Moon is a drawing
rather than a photograph. The reason is that the only recording of the event that I have found is
an extremely fuzzy videotape in which it is nearly impossible to tell what is going on.
Individual frames are also very fuzzy.
2. Planetary Motion Before Newton
My students always seem to have trouble with the concept of a central force being responsible
for circular motion. I’ve found that repeating Robert Hooke’s famous but very simple
demonstration often helps.
3. Isaac Newton
Figure 5.8, illustrating Newton’s thought experiment on orbital motion, is taken almost directly
from Principia. This thought experiment was a key step in the analysis that led Newton to
conclude that gravity was responsible for the motions of the Moon and planets.
4. Orbital Energy and Speed
5. Tides
Tidal forces and tides are introduced and explained in this section. The effect of tides on the
rotation of the Earth and the orbit of the Moon are discussed in the chapter on the Moon
(Chapter 9).
KEY TERMS
acceleration — The rate of change of velocity. An acceleration may involve a change of speed,
direction of motion, or both.
acceleration of gravity — The acceleration of body, equal to 9.8 meters per second per
second(m/s2), due to the force of gravity near the surface of the Earth.
angular momentum — The momentum of a body associated with its rotation or revolution. For a
body in a circular orbit, angular momentum is the product of orbital distance, orbital speed, and
mass. When two bodies collide or interact, angular momentum is conserved.
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Chapter 05 - Gravity and Motion
central force — A force directed at the center of motion of a body. Gravity is the central force that
accounts for the orbital motion of solar system bodies.
centripetal acceleration — The acceleration toward the center of motion that causes the path of an
orbiting body to continually bend away from a straight line path.
centripetal force — The central force that produces centripetal acceleration.
circle — A curve on which all points are equidistant from the center.
circular speed — The speed for which an orbiting body has a circular orbit rather than an elliptical
one.
conic section — One of four kinds of curves (circle, ellipse, hyperbola, and parabola) that can be
formed by slicing a right circular cone with a plane.
ellipse — A closed, elongated curve describing the shape of the orbit that one body follows about
another.
escape velocity — The speed that an object must have to achieve a parabolic trajectory and escape
from its parent body.
force — A push or a pull.
gravitational potential energy — The energy stored in a body subject to the gravitational attraction
of another body. As the body falls, its gravitational potential energy decreases and is converted
into kinetic energy.
gravity — The force of attraction between two bodies generated by their masses.
hyperbola — A curved path that does not close on itself. A body moving with a speed greater than
escape velocity follows a hyperbola.
inertia — The tendency of a body at rest to remain at rest and a body in motion to remain in motion
at a constant speed and in a constant direction.
inertial motion — Motion in a straight line at constant speed followed by a body when there are no
unbalanced forces acting on it.
kinetic energy — Energy of motion. Kinetic energy is given by one half the product of a body’s
mass and the square of its speed.
mass — A measure of the amount of matter a body contains. Mass is also a measure of the inertia
of a body.
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Chapter 05 - Gravity and Motion
momentum — A quantity, equal to the product of a body’s mass and velocity, used to describe the
motion of the body. When two bodies collide or otherwise interact, the sum of their momenta is
conserved.
neap tide — An unusually low high tide and unusually high low tide that occur when the tidal
forces of the Sun and Moon act at right angles to one another.
parabola — A geometric curve followed by a body that moves with a speed exactly equal to escape
velocity.
spring tide — An unusually high, high tide and unusually low, low tide that occur when the tidal
forces of the Sun and Moon are aligned. This occurs at full moon and new moon.
tidal force — The differences in gravity in a body being attracted by another body.
tides — Distortions in a body’s shape resulting from tidal forces.
vector — A quantity that has both direction and magnitude. Velocity is a vector, whereas speed is
not.
velocity — A physical quantity that gives the speed of a body and the direction in which it is
moving.
weight — The gravitational force exerted on a body by the Earth (or another astronomical object).
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. Advocates of the impetus theory said that there was a constant force acting on the body. Galileo
said that there was no force acting on the body.
2. It would follow a circular orbit.
3. It accelerates because the direction of its motion changes constantly as it orbits.
4. The body will accelerate to the right.
5. There are several methods. One would be to remove a shoe and throw it horizontally. The
person would experience a force in the opposite direction as the shoe is thrown, would
accelerate briefly, and then glide to the shore.
6. The speed would be less than escape velocity, so the path of the satellite would be an ellipse.
7. The Earth is 80 times as massive as the Moon. This more than compensates for the fact that the
Moon is 1/4 the size of the Earth.
8. When the two accelerations add (2 + 1), they are three times stronger than when they work
against each other (2 1).
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Chapter 05 - Gravity and Motion
Problems
1. 5.0 m/s2
2. It would triple.
3. The acceleration of A is 1/4 the acceleration of B.
4. 20 N upward
5. 2 m/s2 to the south
6. 4.5 m/s2
7. The mass of A is 1/20 the mass of B.
8. 0.4 m/s toward the south celestial pole
9. The force would be the same.
10. 2.0 × 1022 N
11. It becomes four times as great.
12. It would become 1/4 as large.
13. 490 N
14. 30.4 N
15. 8.3 km/s
16. The period would double.
17. 0.32 as massive as the Sun
18. 22.3 years
19. 0.7 km/s, 67 km/s
20. 30 km/s
21. 7.6 km/s
22. 1.3 km/s
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