**Problem Statement:**Determine the orbital speed, in meters per second (m/s), of a satellite that circles the Earth with a period of \(2.20 \times 10^4\) seconds. The mass of the Earth is \(5.97 \times 10^{24}\) kilograms.**Answer:**\[ \text{Orbital Speed} = \, \_\_\_\_ \, \text{m/s} \]**Explanation:**To solve for the orbital speed of the satellite, we use the formula for the orbital speed \( v \):\[ v = \frac{2\pi r}{T} \]where:- \( r \) is the orbital radius,- \( T \) is the orbital period.To find the orbital radius \( r \), use the formula for gravitational force:\[ F = \frac{G M m}{r^2} \]and set it equal to the centripetal force:\[ F = \frac{m v^2}{r} \]From these equations, you can derive the orbital speed without needing the satellite's mass \( m \):\[ v = \sqrt{\frac{G M}{r}} \]Given data:- \( T = 2.20 \times 10^4 \) s- \( M = 5.97 \times 10^{24} \) kg- \( G = 6.674 \times 10^{-11} \, \text{m}^3/\text{kg}\cdot\text{s}^2 \) (Universal gravitational constant)The orbital speed can be calculated once \( r \) is determined from the period using Kepler's Third Law or through manipulation of the centripetal force formula.**Note:**This problem doesn’t directly provide the orbital radius. To completely solve for \( v \), additional calculations involving \( r \) and understanding of the relationship between \( r \) and \( T \) are necessary.

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Answered: Determine the orbital speed, in m/s, of…

Determine the orbital speed, in m/s, of a satellite that circles the Earth with a period of 2.20 x 104 s. The mass of the Earth is 5.97 x 1024 kg. m/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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