Consider two particles: p at the origin (0,0,0) € R³ with mass M > 0, and q at the point/position vector = (x, y, z) = R³ with mass m > 0. Let G be the universal gravitational constant. (We will assume the MKS system of units.) The force = (7) felt by the particle q due to its gravitational interaction with particle p is: GMm 7 (7) = - ||7||³| ·7, for all 7 = (x, y, z) € R³\{♂} . Also consider the function f R³\{0} →→R given by GMm "या f(x, y, z) := = for all 7 = (x, y, z) € R³\{0} . " Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. (1) Using our derivative rules from Calculus 1 and/or 2, calculate the gradient of f, Vƒ(x, y, z). (2) Prove/calculate that Vƒ(x, y, z) = F(x, y, z). (3) Calculate the magnitude of the vector ₹(7).
Consider two particles: p at the origin (0,0,0) € R³ with mass M > 0, and q at the point/position vector = (x, y, z) = R³ with mass m > 0. Let G be the universal gravitational constant. (We will assume the MKS system of units.) The force = (7) felt by the particle q due to its gravitational interaction with particle p is: GMm 7 (7) = - ||7||³| ·7, for all 7 = (x, y, z) € R³\{♂} . Also consider the function f R³\{0} →→R given by GMm "या f(x, y, z) := = for all 7 = (x, y, z) € R³\{0} . " Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. (1) Using our derivative rules from Calculus 1 and/or 2, calculate the gradient of f, Vƒ(x, y, z). (2) Prove/calculate that Vƒ(x, y, z) = F(x, y, z). (3) Calculate the magnitude of the vector ₹(7).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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