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Chapter 13: Q. 4 (page 353)
How far away from the earth must an orbiting spacecraft be for the astronauts inside to be weightless? Explain.
It must be at half the radius of earth (R/2)
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A rocket is launched straight up from the earth’s surface at a speed of What is its speed when it is very far away from the earth?
FIGURE CP13.72 shows a particle of mass m at distance x from the center of a very thin cylinder of mass M and length L. The particle is outside the cylinder, so x > L/2.
a. Calculate the gravitational potential energy of these two masses.
b. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on m when it is at position x.
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 vp = 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.
In , NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of and a radius of
a. What is the speed of a satellite orbiting above the surface?
b. What is the escape speed from the asteroid?
The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of earth years. What are the asteroid’s orbital radius and speed?
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