Zero, a hypothetical planet, has a mass of 4.2 Times 10^23 kg, a radius of 3.5 T
ID: 1477015 • Letter: Z
Question
Zero, a hypothetical planet, has a mass of 4.2 Times 10^23 kg, a radius of 3.5 Times 10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface, If the probe is launched with an initial kinetic energy of 5.0 Times 10^7 J, what will be its kinetic energy when it is 4.0 Times 10^6 m from the center of Zero? If the probe is to achieve a maximum distance of 8.0 Times 10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?Explanation / Answer
a)
use conservation of energy:
initial kinetic energy + initial potential energy = final kinetic energy + final kinetic energy
5*10^7 - G*M*m/R = final kinetic energy - G*M*m/r
5*10^7 - (6.673*10^-11)*(4.2*10^23)*10/(3.5*10^6) = final kinetic energy - (6.673*10^-11)*(4.2*10^23)*10/(4*10^6)
5*10^7 - 8*10^7 = final kinetic energy - 7*10^7
final kinetic energy = 4*10^7 J
Answer: 4*10^7 J
b)
use conservation of energy:
initial kinetic energy + initial potential energy = final kinetic energy + final kinetic energy
initial kinetic energy - G*M*m/R = 0 - G*M*m/r
initial kinetic energy - (6.673*10^-11)*(4.2*10^23)*10/(3.5*10^6) =- (6.673*10^-11)*(4.2*10^23)*10/(8*10^6)
initial kinetic energy - 8*10^7 = -3.5*10^7
initial kinetic energy = 4.5*10^7
Answer: 4.5*10^7 J
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