Zero, a hypothetical planet, has a mass of 5.8 ×10 23 kg, a radius of 2.1 ×10 6

Question

Zero, a hypothetical planet, has a mass of 5.8 ×1023 kg, a radius of 2.1 ×106 m, and no atmosphere. A 4.4 kg space probe isto be launched vertically from itssurface. (a) If the probe is launchedwith an initial kinetic energy of 7.2 ×107 J, what will be its kinetic energy when it is2.9 × 106 m from the center ofZero? (b) If the probe is to achieve amaximum distance of 5.9 × 106 m from thecenter of Zero, with what initial kinetic energy must it belaunched from the surface of Zero?

(a)

Number

Units

(b)

Number

Units

(a)

Number

Units

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 = 7.2 × 107J and
   r2 = 2.9 × 106 J
   then we get that
   K2 = K1 + G M m [(1 /r2) - (1 / r1)]
         = ......... J
(b)
   in this case
   K2 = 0
   r2 = 5.9 × 106 m
   K1 = K2 + G M m [(1 /r1) - (1 / r2)]
         = .........J

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