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A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.4 × 107 m. The mass of the planet is M = 4.4 × 1024 kg. Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite.  F =    Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R.  ac =    Express the speed v in terms of G, M and R.  v = Calculate the numerical value of v, in m/s.  v =

A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.4 × 107 m. The mass of the planet is M = 4.4 × 1024 kg. Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite.  F =    Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R.  ac =    Express the speed v in terms of G, M and R.  v = Calculate the numerical value of v, in m/s.  v =

College Physics
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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 A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from the center of the planet is R = 1.4 × 107 m. The mass of the planet is M = 4.4 × 1024 kg.

Express the magnitude of the gravitational force F in terms of M, R, the gravitational constant G, and the mass m of the satellite. 
F =

 

 Express the magnitude of the centripetal acceleration ac of the satellite in terms of the speed of the satellite v, and R. 
ac = 

 

Express the speed v in terms of G, M and R. 
v =
Calculate the numerical value of v, in m/s. 
v =

 

The diagram illustrates the concept of circular motion, commonly encountered in orbital mechanics. - **Central Object**: The shaded circle represents a celestial body, such as a planet. - **Orbiting Object**: A smaller object, indicated with a dot and small icon resembling a satellite, is shown in orbit around the central body. - **Velocity (V)**: An arrow labeled "V" is tangent to the orbit, indicating the direction of the satellite's velocity. This demonstrates that the satellite is in circular motion, moving perpendicular to the radius of the orbit at any point. - **Radius (R)**: A dashed line labeled "R" extends from the center of the larger body to the orbiting satellite, representing the radius of the circular path. - **Orbit Path**: A dashed circle outlines the orbit, illustrating the satellite's path around the larger body. This diagram is a simplified representation to explain how objects travel in circular orbits due to gravitational forces.
Transcribed Image Text:The diagram illustrates the concept of circular motion, commonly encountered in orbital mechanics. - **Central Object**: The shaded circle represents a celestial body, such as a planet. - **Orbiting Object**: A smaller object, indicated with a dot and small icon resembling a satellite, is shown in orbit around the central body. - **Velocity (V)**: An arrow labeled "V" is tangent to the orbit, indicating the direction of the satellite's velocity. This demonstrates that the satellite is in circular motion, moving perpendicular to the radius of the orbit at any point. - **Radius (R)**: A dashed line labeled "R" extends from the center of the larger body to the orbiting satellite, representing the radius of the circular path. - **Orbit Path**: A dashed circle outlines the orbit, illustrating the satellite's path around the larger body. This diagram is a simplified representation to explain how objects travel in circular orbits due to gravitational forces.
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