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Chapter 13: Q. 2 (page 353)
What is the ratio of the sun鈥檚 gravitational force on the moon to
the earth鈥檚 gravitational force on the moon?
The ratio of the sun鈥檚 gravitational force on the moon to the earth鈥檚 gravitational force on the moon is 2.26.
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What is the ratio of the sun鈥檚 gravitational force on you to the
earth鈥檚 gravitational force on you?
FIGURE P13.35 shows three masses. What are the magnitude and the direction of the net gravitational force on (a) the 20.0 kg mass and (b) the 5.0 kg mass? Give the direction as an angle cw or ccw from the y-axis.
The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 108 m/s. Astronomers have determined
that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.
a. Assuming the orbit is circular, what is the period of the solar
system鈥檚 orbit? Give your answer in years.
b. Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?
c. The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?
d. Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?
Astronomers have spent many years trying to determine how many stars there are in the Milky Way. The number of stars seems to be only about 10% of what you found in part d. In other words,
about 90% of the mass of the galaxy appears to be in some form other than stars. This is called the dark matter of the universe. No one knows what the dark matter is. This is one of the outstanding scientific questions of our day.
FIGURE P13.57 shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter. Find an exact expression for the orbital period T. Hint: Each planet feels two forces.
Planet Z is in diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827"
(a) What is the mass of Planet Z?
(b) What is the free-fall accelerationabove Planet Z鈥檚 north pole?
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