Fundamentals of Physics, Volume 1, Chapter 1-20
Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
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Chapter 44, Problem 43P

SSM Suppose that the radius of the Sun were increased to 5.90 × 1012 m (the average radius of the orbit of Pluto), that the density of this expanded Sun were uniform, and that the planets revolved within this tenuous object. (a) Calculate Earth’s orbital speed in this new configuration. (b) What is the ratio of the orbital speed calculated in (a) to Earth’s present orbital speed of 29.8 km/s? Assume that the radius of Earth’s orbit remains unchanged. (c) What would be Earth’s new period of revolution? (The Sun’s mass remains unchanged.)

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An object of mass mm is launched from a planet of mass MM and radius RR.  a) Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r=∞.  b) Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M=2.73×1023kg and R=86.2×103km.
Suppose that a planet were discovered between the Sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury. What would be the orbital period of such a planet? (Such a planet was once postulated, in part to explain the precession of Mercury's orbit. It was even given the name Vulcan, although we now have no evidence that it actually exists. Mercury's precession has been explained by general relativity.)
An object of mass m is launched from a planet of mass M and radius R. a)Derive and enter an expression for the minimum launch speed needed for the object to escape gravity, i.e. to be able to just reach r = ∞.  b)Calculate this minimum launch speed (called the escape speed), in meters per second, for a planet of mass M = 6 × 1023 kg and R = 76 × 104 km.
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