# Problem: Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was 2.87x106 km from the earth and traveling at 1.20x104 km/hr relative to the earth.(a) At this time, what was the spacecraft's kinetic energy relative to the earth?(b) What was the potential energy of the earth-spacecraft system?

###### FREE Expert Solution

(a)

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

v = 1.20 × 104 km/hr (1hr/60min)(1min/60s)(1000m/1km) = 3.333 × 103 m/s

KE = (1/2)(629)(3.333 × 103) = 3.49 × 109

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Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was 2.87x106 km from the earth and traveling at 1.20x104 km/hr relative to the earth.

(a) At this time, what was the spacecraft's kinetic energy relative to the earth?
(b) What was the potential energy of the earth-spacecraft system?