Zero, a hypothetical planet, has a mass of 4.1 ×10 23 kg, a radius of 2.9 × 10 6

Question

Zero, a hypothetical planet, has a mass of 4.1 ×1023 kg, a radius of 2.9 × 106 m, andno atmosphere. A 2.3 kg space probe is to be launched verticallyfrom its surface. (a) If the probe is launchedwith an initial kinetic energy of 5.5 × 107 J,what will be its kinetic energy when it is 4.2 ×106 m from the center of Zero? (b) Ifthe probe is to achieve a maximum distance of 7.3 ×106 m from the center of Zero, with what initial kineticenergy must it be launched from the surface of Zero?

(a)

Number

Units

(b)

Number

Units

Chapter 13, Problem 38

Explanation / Answer

   the energy conservation for the situation isgiven by    K1 + U1 =K2 + U2    K1 - (G m M / r1) =K2 - (G m M / r2) (a)    if K1 = 5.5 ×107 J and    K2 = 4.2 ×106 J    then we get that    K2 = K1 + G M m [(1 /r2) - (1 / r1)]          = .........J (b)    in this case    K2 = 0    r2 = 7.3 × 106m    K1 = K2 + G M m [(1 /r1) - (1 / r2)]          = .........J    K1 - (G m M / r1) =K2 - (G m M / r2) (a)    if K1 = 5.5 ×107 J and    K2 = 4.2 ×106 J    then we get that    K2 = K1 + G M m [(1 /r2) - (1 / r1)]          = .........J (b)    in this case    K2 = 0    r2 = 7.3 × 106m    K1 = K2 + G M m [(1 /r1) - (1 / r2)]          = .........J          = .........J

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