Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 8, Problem 43P
To determine
An expression for the orbital period of three identical stars with orbital motion.
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The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B,
and C. The table provides the mass of each body in the system, as well as their spatial coordinates (x, y) in their initial and final
positions. The spatial coordinates of the bodies are given in Astronomical Units (AU).
Initital Position
Body
S
A
B
с
Mass (kg)
mg = 2.3863 × 10³⁰
mA = 2.1957 × 1028
mB = 6.2841 × 1026
mc = 7.8063 × 1027
The initial velocity of the center of mass of the system is zero.
Find the magnitude ds of the star's displacement from the origin in its final position.
C
S (0,0)
(0,0)
(0.4815, 0)
(0.4373, 1.3397)
(0, 1.6711)
A
Final Position
(xs, ys)
(0, -0.4913)
B
(-1.6007, 0)
(-0.8443,-0.7481)
B
●
С.
S
A
Chapter 13, Problem 055
In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radii a and periods T are as follows
(a) Io has a mean orbital radius of 4.22 x 108 m and a period of 1.77 days. Find the mass of Jupiter from this information.
(b) Europa has a mean orbital radius of 6.71 x 108 m and a period of 3.55 days. Find the mass of Jupiter from this information.
(c) Ganymede has a mean orbital radius of 10.7 x 108 m and a period of 7.16 days. Find the mass of Jupiter from this information.
(d) Callisto has a mean orbital radius of 18.8 x 108 m and a period of 16.7 days. Find the mass of Jupiter from this information.
Units
(a) Number
Units
(b) Number
Units
(c) Number
Units
(d) Number
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Chapter 13, Problem 011
In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M form an equilateral triangle, and a fourth
sphere of mass mą is at the center of the triangle. The net gravitational force on that central sphere from the three other
spheres is zero. (a) What is the value of mass M? (b) If we double the value of m4, what then is the magnitude of the
net gravitational force on the central sphere?
M
(a) Number
Units
(b) Number
Units
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Chapter 8 Solutions
Essential University Physics (3rd Edition)
Ch. 8.2 - Suppose the distance between two objects is cut in...Ch. 8.3 - Suppose the paths in Fig. 8.8 are the paths of...Ch. 8.4 - Prob. 8.3GICh. 8 - What do Newtons apple and the Moon have in common?Ch. 8 - Prob. 2FTDCh. 8 - When you stand on Earth, the distance between you...Ch. 8 - The force of gravity on an object is proportional...Ch. 8 - A friend who knows nothing about physics asks what...Ch. 8 - Could you put a satellite in an orbit that keeps...Ch. 8 - Why are satellites generally launched eastward and...
Ch. 8 - Given Earths mass, the Moons distance and orbital...Ch. 8 - How should a satellite be launched so that its...Ch. 8 - Does the gravitational force of the Sun do work on...Ch. 8 - Space explorers land on a planet with the same...Ch. 8 - Use data for the Moons orbit from Appendix E to...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Two identical lead spheres with their centers 14...Ch. 8 - Whats the approximate value of the gravitational...Ch. 8 - A sensitive gravimeter is carried to the top of...Ch. 8 - Prob. 18ECh. 8 - Find the speed of a satellite in geostationary...Ch. 8 - Marss orbit has a diameter 1.52 times that of...Ch. 8 - Calculate the orbital period for Jupiters moon Io,...Ch. 8 - An astronaut hits a golf ball horizontally from...Ch. 8 - The Mars Reconnaissance Orbiter circles the red...Ch. 8 - Earths distance from the Sun varies from 147 Gm at...Ch. 8 - Prob. 25ECh. 8 - A rocket is launched vertically upward from Earths...Ch. 8 - What vertical launch speed is necessary to get a...Ch. 8 - Find the energy necessary to put 1 kg, initially...Ch. 8 - Whats the total mechanical energy associated with...Ch. 8 - Prob. 30ECh. 8 - Determine escape speeds from (a) Jupiters moon...Ch. 8 - Prob. 32ECh. 8 - The gravitational acceleration at a planets...Ch. 8 - One of the longest-standing athletic records is...Ch. 8 - Prob. 35PCh. 8 - If youre standing on the ground 15 m directly...Ch. 8 - Given the Moons orbital radius of 384,400 km and...Ch. 8 - Equation 7.9 relates force to the derivative of...Ch. 8 - During the Apollo Moon landings, one astronaut...Ch. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Youre preparing an exhibit for the Golf Hall of...Ch. 8 - Prob. 43PCh. 8 - Satellites A and B are in circular orbits, with A...Ch. 8 - The asteroid that exploded over Chelyabinsk,...Ch. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Neglecting air resistance, to what height would...Ch. 8 - Show that an object released from rest very far...Ch. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - Two meteoroids are 160,000 km from Earths center...Ch. 8 - Two rockets are launched from Earths surface, one...Ch. 8 - Prob. 58PCh. 8 - A missiles trajectory takes it to a maximum...Ch. 8 - Prob. 60PCh. 8 - Mercurys orbital speed varies from 38.8 km/s at...Ch. 8 - Prob. 62PCh. 8 - Two satellites are in geostationary orbit but in...Ch. 8 - Prob. 64PCh. 8 - Prob. 65PCh. 8 - We derived Equation 8.4 on the assumption that the...Ch. 8 - Prob. 67PCh. 8 - As a member of the 2040 Olympic committee, youre...Ch. 8 - The Olympic Committee is keeping you busy! Youre...Ch. 8 - Tidal forces are proportional to the variation in...Ch. 8 - Spacecraft that study the Sun are often placed at...Ch. 8 - Prob. 72PPCh. 8 - Prob. 73PPCh. 8 - Prob. 74PPCh. 8 - The Global Positioning System (GPS) uses a...
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- Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)arrow_forwardThree objects of equal mass m1 = m2 = m3 = 1.15 kg are located on the vertices of an equilateral triangle of length d = 3.40 m. A fourth mass m4 = 15.5 kg is at the center of the triangle. What is the net gravitational force on the mass m1 that is at the origin? Express your answer in vector form. Fnet?arrow_forwardA satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.02 × 104 m/s. The mass of the planet is M = 5.94 × 1024 kg. The mass of the satellite is m = 4.7 × 103 kg. Enter an expression for the magnitude of the gravitional force F in terms of M,R,m and the gravitional constant G. Enter an expression for the radius in terms of G,M and R. Enter an expression for the gravational potetial energy PE in terms of G,M,m and R. Enter an expresssion for the centripal acceleration of the satellite ac in terms of the speed of the satellite v, and r.arrow_forward
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