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Consider two particles: p at the origin (0,0,0) E R³ with mass M > 0, and q at the point/position vector 7=(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 F (7) felt by the particle q due to its gravitational interaction with particle p is: GMm ||7|3 = 7 (7) = =- , for all 7 = (x, y, z) = R³\{J} . Also consider the function f: R³\{} → R given by GMm f(x, y, z) := "या Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. late the for all 7 = (x, y, z) = R³\{7} . E " of the vector F(7). (4) Calculate the direction of the vector (5) Assume that is the total force on the particle q. Calculate the instantaneous acceleration, d, of the particle q when it is at the point 7=(x, y, z).

Consider two particles: p at the origin (0,0,0) E R³ with mass M > 0, and q at the point/position vector 7=(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 F (7) felt by the particle q due to its gravitational interaction with particle p is: GMm ||7|3 = 7 (7) = =- , for all 7 = (x, y, z) = R³\{J} . Also consider the function f: R³\{} → R given by GMm f(x, y, z) := "या Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. late the for all 7 = (x, y, z) = R³\{7} . E " of the vector F(7). (4) Calculate the direction of the vector (5) Assume that is the total force on the particle q. Calculate the instantaneous acceleration, d, of the particle q when it is at the point 7=(x, y, z).

Question
Consider two particles: p at the origin (0,0,0) = R³ with mass M > 0, and q at the point/position vector 7 = (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 F = F (7) felt by the particle q due to its gravitational interaction with particle p is: GMm 7(7)= == 7, for all 7 = (x, y, z) € R³\{0} . 17 Also consider the function ƒ : R³\{♂} → R given by GMm f(x, y, z) := TT , for all 7 = (x, y, z) € R³\{0} . Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. 2, calculate the (3) Calculat cade of the vector (4) Calculate the direction of the vector ₹(7). (5) Assume that is the total force on the particle q. Calculate the instantaneous acceleration, d, of the particle q when it is at the point 7 = (x, y, z).
Transcribed Image Text:Consider two particles: p at the origin (0,0,0) = R³ with mass M > 0, and q at the point/position vector 7 = (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 F = F (7) felt by the particle q due to its gravitational interaction with particle p is: GMm 7(7)= == 7, for all 7 = (x, y, z) € R³\{0} . 17 Also consider the function ƒ : R³\{♂} → R given by GMm f(x, y, z) := TT , for all 7 = (x, y, z) € R³\{0} . Fix an arbitrary point/position vector = (x, y, z) in R³\{♂}. 2, calculate the (3) Calculat cade of the vector (4) Calculate the direction of the vector ₹(7). (5) Assume that is the total force on the particle q. Calculate the instantaneous acceleration, d, of the particle q when it is at the point 7 = (x, y, z).
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