What is the ratio of the sun’s gravitational force on the moon to
the earth’s gravitational force on the moon?
The ratio of the sun’s gravitational force on the moon to the earth’s gravitational force on the moon is 2.26.
Mass of moon:
Gravitational constant Mass of earth: Distance from earth to moon: Mass of sun: Distance from sun to moon:
The gravitational force is calculated by
Use this to calculate gravitational force of sun on moon
And gravitational force on earth on moon is
Now find the ratio
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, meaningthat 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 vp = Cuq, where C is a constant. The exponents p and q are not necessarily integers. Define x = log u and y = log v. Findan 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.
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