### Gravitational Work Calculation**Problem Statement:**If the gravitational force between two objects of mass \( M \) and \( m \), separated by a distance \( r \), has a magnitude \( \frac{GMm}{r^2} \), where \( G = 6.67 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2} \), then the work required to increase the separation from a distance \( r_1 \) to a distance \( r_2 \) is given by:\[GMm \left( \frac{1}{r_1} - \frac{1}{r_2} \right)\]**Task:**Compute the work required to move a 1500-kg satellite from an orbit 1000 km above the surface of Earth to an orbit 1500 km above the surface of Earth. Assume that Earth is a sphere with a radius \( R_e = 6.37 \times 10^6 \) m and mass \( M_e = 5.98 \times 10^{24} \) kg. Treat the satellite as a point mass.*(Write your answer in scientific notation with two decimal places.)***Given Answer:**\[W = 1.47 \times 10^7 \, \text{J}\]**Feedback:**The given answer is marked as incorrect.---**Explanation of Concepts:**To solve this problem, you need to use the gravitational work formula and substitute the appropriate values:1. **Identify \( r_1 \) and \( r_2 \):** - \( r_1 = R_e + 1000 \times 10^3 \) - \( r_2 = R_e + 1500 \times 10^3 \)2. **Insert these values into the work formula:** \[ W = GMm \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]3. **Calculate using the given constants:** - \( G = 6.67 \times 10^{-11} \, \text{m}^3\text{kg}^{-1}\text{s}^{-2} \) - \( M = 5.98 \

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If the gravitational force between two objects of mass M and m, separated by a distancer, has magnitude GMm where G = 6.67 × 10¬|" m’kg¯'s¯2, then the work required to increase the separation from a distance r¡ to a distance r2 is GMm(r,' – r,"). Compute the work required to move a 1500-kg satellite from an orbit 1000 km above the surface of Earth to an orbit 1500 km above the surface of Earth. Assume that Earth is a sphere of radius R. = 6.37 × 10° m and mass M. = 5.98 × 1024 kg. Treat the satellite as a point mass. (Write your answer in scientific notation with two decimal places.) 1.47 x10" J W = Incorrect

If the gravitational force between two objects of mass M and m, separated by a distancer, has magnitude GMm where G = 6.67 × 10¬|" m’kg¯'s¯2, then the work required to increase the separation from a distance r¡ to a distance r2 is GMm(r,' – r,"). Compute the work required to move a 1500-kg satellite from an orbit 1000 km above the surface of Earth to an orbit 1500 km above the surface of Earth. Assume that Earth is a sphere of radius R. = 6.37 × 10° m and mass M. = 5.98 × 1024 kg. Treat the satellite as a point mass. (Write your answer in scientific notation with two decimal places.) 1.47 x10" J W = Incorrect

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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