The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?
Escape velocity of Planet Y is 14140 m/sec
Escape velocity of planet X, is 10000 m/sDensity of planet Y is twice the density of planet X => ρx = 2ρy
Radius of planet Y is equal to the radius of planet X => Rx = Ry
We can calculate escape velocity as
Where G = universal gravitational constant, M = mass of the planet r = radius of the planet
The escape velocity of planet X is
And for plant Y is
Now get the ratio and substitute values given
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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