Explanation 1) Concept: We can find the angular speed of a satellite at perihelion by using the law of conservation of angular momentum . Then putting the expression for the semi major axis in it from Kepler’s law of period, we can find the value of angular speed of a satellite at perihelion. 2) Formulae: i) I p ω p = I a ω a ii) T 2 = 4 π 2 G M a 3 3) Given: i. The period of the satellite is T = 8.00 × 10 4 s ii. The mass of the planet is M = 7.00 × 10 24 k g iii. The radius of elliptical orbit at aphelion is R a = 4.5 × 10 7 m iv. The angular speed of the satellite at aphelion is ω a = 7.158 × 10 - 5 r a d s 4) Calculations: The angular speed a satellite at perihelion: According to the law of conservation of angular momentum, I p ω p = I a ω a ω p = I a I p ω a … ( 1 ) According to the definition of the moment of inertia, I p = M R p 2 I a = M R a 2 Equation (1) becomes ω p = M R a 2 M R p 2 ω a ω p = R a 2 R p 2 ω a … ( 2 ) For the elliptical orbit, R a + R p = 2 a R p = 2 a - R a Equation (2) becomes ω p = R a 2 2 a - R a 2 ω a … ( 3 ) According to Kepler’s period law, the square of the period of any planet is proportional to the cube of the semi-major axis of its orbit

11th Edition

ISBN: 9781119573968

Author: David Halliday

Publisher: WILEY

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Chapter 13, Problem 82P

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The angular speed of a satellite at perihelion

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The angular speed of a satellite at perihelion

Solution Summary: The author explains how to find the angular speed of a satellite at perihelion by using the law of conservation of momentum and putting the expression for the semi major axis in it.

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The angular speed of a satellite at perihelion