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.