Zero, a hypothetical planet, has a mass of 4.0 1023 kg, a radius of 3.0 multipli

Question

Zero, a hypothetical planet, has a mass of 4.0 1023 kg, a radius of 3.0 multiplied by 106 m, and no atmosphere. A 15 kg space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial kinetic energy of 5.0 multiplied by 107 J, what will be its kinetic energy when it is 4.0 multiplied by 106 m from the center of Zero?

Explanation / Answer

Mass of the planet = M = 4 x 10^23 kg Radius of the planet = R = 3 x 10^6 m Universal gravitational constant = G = 6.673 x 10^-11 => Acceleratiion due to gravity on planet zero = g = G*M/R^2 = (6.673 x 10^-11)*(4 x 10^23)/(3 x 10^6)^2 = 2.97 m/sec^2 Now conserving the total energy at the surface of the planet and at the given point we get KE1 + PE1 = KE2 + PE2 => (5 x 10^7) + m.g.H1 = K.E2 + m.g.H2 m = 15 kg H1 = 3 x 10^6 H2 = 4 x 10^6 =>(5 x 10^7) + 15*2.97*3 x 10^6 = K.E2 + 15*2.97*4 x 10^6 =>(5 x 10^7) + (13.365 x 10^7) = K.E2 + (17.82 x 10^7) => K.E2 = 5.45 x 10^6 J

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