(Problem 13.1.1) Escape! . Vc а) A projectile on a planet of radius Rand mass M is sent directly upward with a speed v. Using energy conservation, find the critical initial speed v, such that as the projectile reaches an infinite range it has exactly zero m. final speed, and therefore does not return. This critical velocity as defined is called the escape velocity. Neglect atmospheric effects and planetary rotation. R M b) Apply your expression for the escape velocity to our own planet Earth (M=6x1024kg, R=6,378km, G= 6.67408x10-11m³/kg s²). Compare the escape velocity to the speed of sound, vs = 343 m/s. c) Consider what radius the Earth would need to be such that the escape velocity is exactly the speed of light, c = 3x10® m/s.

(Problem 13.1.1) Escape! . Vc а) A projectile on a planet of radius Rand mass M is sent directly upward with a speed v. Using energy conservation, find the critical initial speed v, such that as the projectile reaches an infinite range it has exactly zero m. final speed, and therefore does not return. This critical velocity as defined is called the escape velocity. Neglect atmospheric effects and planetary rotation. R M b) Apply your expression for the escape velocity to our own planet Earth (M=6x1024kg, R=6,378km, G= 6.67408x10-11m³/kg s²). Compare the escape velocity to the speed of sound, vs = 343 m/s. c) Consider what radius the Earth would need to be such that the escape velocity is exactly the speed of light, c = 3x10® m/s.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.17P

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