Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 10, Problem 79P
To determine
ToShow: The Kepler’s second law follows directly from the law of conservation of
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The Moon orbits the Earth such that the same side alwaysfaces the Earth. Determine the ratio of the Moon’s spinangular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as aparticle orbiting the Earth.)
Kepler’s second law is a consequence of conservation of angular momentum. Angular momentum equals the (transverse speed of the planet) x(mass of the planet) x (distance from the sun). The transverse speed isthe amount of the planet’s orbital velocity that is in the direction perpendicular to the line between the planet and the Sun. If the distancedecreases, then the speed must increase to compensate; if the distanceincreases, then the speed decreases.(a) Using this information derive an expression for how much greatera planet’s velocity is at perihelion compared to aphelion. Hint: Atperihelion and aphelion all the planets orbital velocity is perpendicularto the line between the planet and the Sun.(b) If Mars has an orbital speed of 25 km/s at perihelion, what is itsorbital speed at aphelion?(c) What is the ratio between the kinetic energy at perihelion and aphelion?
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in Figure. Consider the mass and radius of thec Earth are ME 5.97 x 10 kg and R: = 6.38
x10° m, respectively. Assume that the axial and orbital axis of rotations are parallel to cach
other.
%3D
Earth
North Pole
(d) How much encrgy is needed to stop the Earth's rotation about its axis after the collision?
(e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly
shifted so that it touches the cquator?
Chapter 10 Solutions
Physics for Scientists and Engineers
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