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Chapter 13: Q. 18 (page 353)
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?
The minimum speed that the probe needs to escape the solar system is
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How much energy would be required to move the earth into a circular orbit with a radius larger than its current radius?
The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?
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 鈥渃orrect鈥� 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 鈥渂est-fit鈥� line in Figure 13.17 to find the mass of the sun.
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.
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.
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