Download PhysicsSG-Gravitation-91109R

Physics Study Guide:
2009-2010
Gravitation and Astronomy
Topics
 Newton’s law of gravity
 Kepler’s laws of planetary motion
 Circular orbits of planets and satellites
 A brief introduction to astronomy
AP Learning Objectives
I. NEWTONIAN MECHANICS

F. Gravitation
4. Newton’s law of gravity
Students should know Newton’s Law of Universal Gravitation, so they can:

Determine the force that one spherically symmetrical mass exerts on another.

Determine the strength of the gravitational field at a specified point outside a spherically
symmetrical mass.
5. Orbits of planets and satellites
Students should understand the motion of an object in orbit under the influence of gravitational
forces, so they can:
For a circular orbit:

Recognize that the motion does not depend on the object’s mass; describe qualitatively how
the velocity, period of revolution, and centripetal acceleration depend on the radius of orbit;
and derive expressions for the velocity and period of revolution in such an orbit.

Derive Kepler’s Third Law for the case of circular orbits.
Readings
 Glencoe Physics
Chapter 8: Universal Gravitation

Section 8-1: Motion in the Heavens and on Earth [p. 176–184]

Section 8-2: Using the Law of Universal Gravitation [p. 185–192]
 Cracking the AP Physics B Exam (2008 Edition)
Chapter 6: Newton’s Law of Gravitation [p. 99-109]
 Halliday, Resnick, and Walker (5th ed)
Chapter 14: Gravitation

Sections 14-1 to 14-2, 14-4 to 14-5, 14-7
Video
 The Mechanical Universe “Kepler’s Laws” (18:04 minutes)
(High School Adaptation: Lesson #113)
On the Web
 University of Colorado: Physics Education Technology (PhET)
http://phet.colorado.edu/new/index.php

Motion Simulations: My Solar System
Build your own solar system of heavenly bodies and watch the gravitational ballet. With this
orbital simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and
then see them orbit each other.
Data

Useful Gravitational and Astronomical Data:

Universal gravitational constant (‘big G”): G = 6.67 X 10-11 Nm2/kg2

Variation of the Earth’s acceleration due to gravity with height above the ground

Useful astronomical data

Some distances from Earth

The sun, Earth, and the moon

Some properties of the planets (plus Pluto)
PhysicsSG-Gravitation-91109R
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Physics Study Guide:
2009-2010
Gravitation and Astronomy
Problems
Newton’s Law of Gravity
Practice Problems
1. Two balls have their centers 2.00 meters apart. One ball has a mass of 8.00 kg. The other
has a mass of 6.0 kg. What is the gravitational force between them?
Answer: 8.0 X 10-10 N
[Zitzewitz, Glencoe Physics: Principles and Problems, 1999, p. 195 / 35]
2. The centers of a 10.0 kg lead ball and a 100.0 g lead ball are separated by 10.0 cm.
a) What gravitational force does each exert on the other?
b) What is the ratio of this gravitational force to the weight of the 100 g ball?
Answers: a) 6.67 X 10-9 N; b) 6.81 X 10-9
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 2]
3. Assume that you have a mass of 50.0 kg and the Earth has a mass of 5.98 X 10 24 kg. The
radius of the Earth is 6.37 X 106 meters.
a) What is the force of gravitational attraction between you and the Earth?
b) Is this force equal to your weight?
Answers: a) 489 N; b) Yes
[Zitzewitz, Glencoe Physics: Principles and Problems, 1999, p. 195 / 37 (modified)]
4. What is the ratio of the sun’s gravitational force on the moon to the Earth’s gravitational
force on the moon?
Answer: 2.16
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 4]
Challenge Problems
5. a) What is the acceleration due to gravity at the surface of the sun?
b) What is the sun’s acceleration due to gravity at the distance of the Earth?
Answers: a) 274 m/sec2; b) 5.90 X 10-3 m/sec2
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 8]
6. A sensitive gravimeter at a mountain observatory finds that the acceleration due to gravity
is 0.0075 m/sec2 less than at sea level. What is the observatory’s altitude? Use g = 9.80
m/sec2 for the acceleration due to gravity at sea level.
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 11 (modified)]
Kepler’s Third Law and the Orbits of Planets and Satellites
Practice Problems
7. Jupiter is 5.2 times farther from the sun than Earth is. Find Jupiter’s orbital period in Earth
years.
Answer: 12 years
[Zitzewitz, Glencoe Physics: Principles and Problems, 1999, p. 195 / 31]
8. A satellite orbits the sun with a period of 1.0 days. What is the radius of its orbit?
Answer: 2.93 X 109 meters
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 20]
9. Mars has a small moon, Phobos, that orbits with a period of 7 hours, 39 minutes. The radius
of Phobos’s orbit is 9.4 X 106 meters. What is the mass of Mars?
Answer: 6.48 X 1023 kg
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 366 / 52]
10. A geosynchronous satellite is one that appears to remain over one spot on Earth. Assume
that a geosynchronous satellite has an orbital radius of 4.23 X 107 meters.
a) Calculate its linear speed in orbit.
b) Calculate its period.
Answers: a) 3070 m/sec; b) 24.1 hours
[Zitzewitz, Glencoe Physics: Principles and Problems, 1999, p. 195 / 50]
PhysicsSG-Gravitation-91109R
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Physics Study Guide:
2009-2010
Gravitation and Astronomy
Challenge Problems
11. On July 19, 1969, Apollo 11’s orbit around the moon was adjusted to an average orbit of
111 km. The radius of the moon is 1785 km, and the mass of the moon is 7.34 X 10 22 kg.
a) How many minutes did Apollo 11 take to orbit the moon once?
b) At what velocity did it orbit the moon?
Answers: a) 123 minutes; b) 1610 m/sec
[Zitzewitz, Glencoe Physics: Principles and Problems, 1999, p. 195 / 55]
12. What is the speed and altitude of a geosynchronous satellite orbiting Mars? Mars rotates
on its axis once every 24.8 hours.
Answer: v = 1.44 X 103 m/sec; Altitude = 1.72 X 107 meters
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 364 / 24]
13. Extrasolar Planets
Astronomers using the most advanced telescopes have only recently seen evidence of planets
orbiting nearby stars. These are called extrasolar planets. Suppose a planet is observed to
have a 1200 day period as it orbits a star at the same distance that Jupiter is from the sun.
What is the mass of the star in solar masses? [notes: 1) 1 solar mass is defined to be the
mass of the sun (1.99 X 1030 kg); 2) “day” means earth days]
Answer: a) 13.0 solar masses
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 359 / Example 12.5]
Multitopic Problem
Challenge Problem
14. The Neutron Star
Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The
explosion blows away the outer layers of the star. According to Newton’s third law, the forces
that push the outer layers away have reaction forces that are inwardly directed on the core of
the star. These forces compress the core and can cause the core to undergo a gravitational
collapse. The gravitational forces keep pulling all the matter together tighter and tighter,
crushing the atoms out of existence. Under these extreme conditions, the protons and
electrons can be squeezed together to form neutrons. If the collapse is halted when the
neutrons all come into contact with each other, the result is an object called a neutron star, an
entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a
period of about one second and, as they do so, send out a pulse of electromagnetic waves
once a second. These stars were discovered in the 1960s and are called pulsars.
a) Consider a neutron star with a mass equal to the sun, a radius of 10.0 km, and a rotation
period of 1.00 seconds. What is the speed of a point on the equator of the star?
b) What is g at the surface of this neutron star?
c) A 1.00 kg mass has a weight on earth of 9.80 N. What would be its weight on the star?
d) How many revolutions per minute are made by a satellite orbiting 1.00 km above the
surface of the star?
e) What is the radius of a geosynchronous orbit about the neutron star?
Answers: a) 6.28 X 104 m/sec; b) 1.32 X 1012 m/sec2; c) 1.32 X 1012 N (equivalent to 1.49 X 108 Tons on Earth);
d) 95,400 rev/min; e) Rgeosynchronous orbit = 1.50 X 106 meters
[Knight, Physics for Scientists and Engineers: A Strategic Approach. p. 366-367 / 60]
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