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Chapter 13: Q. 14 (page 353)
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?
(a) The mass of planet Z is
(b) The free-fall acceleration above Planet Z’s north pole is
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While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet’s radius every 230 min. What are the (a) mass and (b) radius of Planet Physics?
A 55,000 kg space capsule is in a 28,000-km-diameter circular orbit around the moon. A brief but intense firing of its engine in the forward direction suddenly decreases its speed by 50%. This
causes the space capsule to go into an elliptical orbit. What are the space capsule’s (a) maximum and (b) minimum distances from the center of the moon in its new orbit?
Hint: You will need to use two conservation laws.
Two Jupiter-size planets are released from rest 1.0 x 1011m apart. What are their speeds as they crash together?
A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes earth years to complete one orbit around the star. Vega’s mass is times the sun’s mass. What is the radius of the planet’s orbit? Give your answer as a multiple of the radius of the earth’s orbit.
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.
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