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Unformatted text preview: 1101 Chapter 11 Gravity Conceptual Problems 1 • [SSM] True or false: ( a ) For Kepler’s law of equal areas to be valid, the force of gravity must vary inversely with the square of the distance between a given planet and the Sun. ( b ) The planet closest to the Sun has the shortest orbital period. ( c ) Venus’s orbital speed is larger than the orbital speed of Earth. ( d ) The orbital period of a planet allows accurate determination of that planet’s mass. ( a ) False. Kepler’s law of equal areas is a consequence of the fact that the gravitational force acts along the line joining two bodies but is independent of the manner in which the force varies with distance. ( b ) True. The periods of the planets vary with the three-halves power of their distances from the Sun. So the shorter the distance from the Sun, the shorter the period of the planet’s motion. ( c ) True. Setting up a proportion involving the orbital speeds of the two planets in terms of their orbital periods and mean distances from the Sun (see Table 11-1) shows that Earth Venus 17 . 1 v v = . ( d ) False. The orbital period of a planet is independent of the planet’s mass. 2 • If the mass of a small Earth-orbiting satellite is doubled, the radius of its orbit can remain constant if the speed of the satellite ( a ) increases by a factor of 8, ( b ) increases by a factor of 2, ( c ) does not change, ( d ) is reduced by a factor of 8, ( e ) is reduced by a factor of 2. Determine the Concept We can apply Newton’s second law and the law of gravity to the satellite to obtain an expression for its speed as a function of the radius of its orbit. Apply Newton’s second law to the satellite to obtain: ∑ = = r v m r GMm F 2 2 radial where M is the mass of the object the satellite is orbiting and m is the mass of the satellite. Chapter 11 1102 Solving for v yields: r GM v = Thus the speed of the satellite is independent of its mass and ) ( c is correct. 3 • [SSM] During what season in the northern hemisphere does Earth attain its maximum orbital speed about the Sun? What season is related to its minimum orbital speed? Hint: Earth is at perihelion in early January. Determine the Concept Earth is closest to the Sun during winter in the northern hemisphere. This is the time of fastest orbital speed. Summer would be the time for minimum orbital speed. 4 • Haley’s comet is in a highly elliptical orbit about the Sun with a period of about 76 y. Its last closest approach to the Sun occurred in 1987. In what years of the twentieth century was it traveling at its fastest or slowest orbital speed about the Sun? Determine the Concept Haley’s comet was traveling at its fastest orbital speed in 1987, and at its slowest orbital speed 38 years previously in 1949. 5 • Venus has no natural satellites. However artificial satellites have been placed in orbit around it. To use one of their orbits to determine the mass of Venus, what orbital parameters would you have to measure? How would you then use them to do the mass calculation?...
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