Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 1, Problem 75P
(a)
To determine
To find: The value of constants C and n.
(b)
To determine
To find: The radius of orbit for fifth satellite.
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Schwarzschild radius RS of a black hole is the maximum
distance from the black hole’s center at which light cannot escape its
gravitational field. The quantity RS (with dimensions of length) is
dependent on the mass of the black hole M, the speed of light c, and
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parameters, predict an equation for the Schwarzschild radius. Hint:
G has dimensions of [L3/MT2]
Kepler's Third Law of planetary motion states that the square of the period T of a planet (the time it takes for the planet to make a complete revolution about the sun) is directly proportional to the cube of its average distance d from the sun.
(a) Express Kepler's Third Law as an equation. (Use k for the constant of proportionality.)
(c) The planet Neptune is about 2.79 × 109 mi from the sun. Find the period of Neptune. (Round your answer to the nearest whole number of years.)
Kepler's third law states that for any object in a gravitational orbit,
P2∝a3P2∝a3
where PP is the orbital period of the object and aa is the average distance between the object and what it is orbiting.
In our Solar System, the natural units are distances measured in astronomical units (A.U.) and orbital periods measured in years. This can be seen for the Earth-Sun system which has an orbital period P=1P=1 year and an average distance a=1a=1 AU. Using these natural units in the Solar System, the proportionality becomes an equality, so for our Solar System:
(Pyears)2=(aA.U.)3(Pyears)2=(aA.U.)3 .
Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units.
Chapter 1 Solutions
Physics for Scientists and Engineers
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