Solved: Figure 13.17 showed a graph of log T versus log r

Chapter 13, Problem 13.85

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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 ,c,1010 . a. Consider two quantities u and v that are related by the expression v p = 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