Zero, a hypothetical planet, has a mass of 4.6 times 1023 kg, a radius of 3.2 ti

Question

Zero, a hypothetical planet, has a mass of 4.6 times 1023 kg, a radius of 3.2 times 106 m, and no atmosphere. A 11 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 107 J, what will be its kinetic energy when it is 4.0 times 106 m from the center of Zero? If the probe is to achieve a maximum distance of 8.0 times 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Explanation / Answer

E1 = KE1 + PE1 = 5*10^7 + G*M*m/R

E2 = KE2+PE2 = KE2 + G*M*m/r


E2 = E1

KE2 - G*M*m/r = 5*10^7 + G*M*m/R

KE2 = 5*10^7 + G*M*m/R - G*M*m/r

KE2 = 5*10^7 + ((6.67*10^-11*4.6*10^23*11)*((1/3.2*10^6)-(1/4*10^6)))

KE2 = 21.094e+18 J

b) KE3 = GMM/r = (6.67*10^-11*4.6*10^23*11)*((1/(8*10^6))= 42.188e+6 J

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