Question

1.

a) Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 600 km (or even higher) above the surface. Io has a mass of 8.94×1022 kg and a radius of 1815 km . Ignore any variation in gravity over the 600 km range of the debris.

How high would this material go on earth if it were ejected with the same speed as on Io?

b) Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass 629 kg) was 2.87×10⁶km from the earth and traveling at 1.20×10⁴km/h relative to the earth.

i) At this time, what was the spacecraft's kinetic energy relative to the earth?

ii) What was the potential energy of the earth-spacecraft system?

Answer 1