Chapter 13, Problem 036 Zero, a hypothetical planet, has a mass of 5.0 x 10 23 k

Question

Chapter 13, Problem 036

Zero, a hypothetical planet, has a mass of 5.0 x 1023 kg, a radius of 2.9 x 106 m, and no atmosphere. A 10 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 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

Explanation / Answer

Then solve

G *m *M

Put values

= 6.674 * 10^-11 * 10 * 5 * 10^23

= 3.337 kg m^3 / s^2

At the surface (r=2.9*10^6 m), then, F = 39.6N
and Ep = F*r = 11.4*10^7 J

At r1= 4*10^6m, F = 20.85 N
and Ep = 8.34 *10^7 J
from the ground, delta Ep = 3.06 * 10^7 J case 1

At r2= 8*10^6 m , F = 5.21 N
and Ep = 4.16 * 10^7 J
from the ground, delta Ep = 7.22 * 10^7 J case 2

case 1 delta Ep = delta Ek = 3.06 * 10^7 J = 5*10^7 J - Ek

Then solving
Ek = 1.94 * 10^7 J ....... Answer

case 2 Ep = Ek = 7.22*10^7 J ........ Answer

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