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Chapter 13: Q.42 - Excercises And Problems (page 355)
An object of mass is dropped from height above a planet of mass and radius Find an expression for the object’s speed as it hits the ground.
the expression for object's speed is
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You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.
a. What is the planet’s radius?
b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?
An astronaut circling the earth at an altitude of is horrified to discover that a cloud of space debris is moving in the exact same orbit as his spacecraft, but in the opposite direction. The astronaut detects the debris when it is away. How much time does he have to fire his rockets and change orbits?
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’s north pole?
Figure 13.17 showed a graph of log T versus log r for the planetary data given in Table 13.2. Such a graph is called a log-log graph. The scales in Figure 13.17 are logarithmic, not linear, meaning
that each division along the axis corresponds to a factor of 10 increase in the value. Strictly speaking, the “correct” labels on the y-axis should be 7, 8, 9, and 10 because these are the logarithms of 107...... 1010.
a. Consider two quantities u and v that are related by the expression vp = Cuq, where C is a constant. The exponents p and q are not necessarily integers. Define x = log u and y = log v. Find
an expression for y in terms of x.
b. What shape will a graph of y versus x have? Explain.
c. What slope will a graph of y versus x have? Explain.
d. Use the experimentally determined “best-fit” line in Figure 13.17 to find the mass of the sun.
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’s 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.
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