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 v^p= Cu^q, 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.

Figure 13.17

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Period T (s) The best-fit straight line is log T= 1.500 logr – 9.264. 1010 Neptune Uranus 10°- Saturn Jupiter 10° Mars Earth Venus 107- 101 1012 1013 Distance from sun r (m)