Chapter 13, Problem 58EAP

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^qwhere 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.