4. In the movie \'\'Gravity\'\' two astronauts travel from the space shuttle at

Question

4. In the movie ''Gravity'' two astronauts travel from the space shuttle at the Hubble Space Telescope's (HST) orbit, to the International Space Station (ISS) using only the propulsion of a Manned Maneuvering Unit (MMU), a jet-pack. The The MMU is designed to give a single astronaut a maximum total change in velocity of 25 m/s. The height of the HST's orbit is 554 km above tile surface of the Earth. The height of the ISS's orbit is 413 km above the surface of the Earth. The orbits can be treated as circular. (They very nearly are.) What is the (total mechanical) energy difference between a pair of circular orbits at those heights for a pair of astronauts, each of mass 125 kg? Is it possible for the MMU to provide enough change in kinetic energy for two astronauts to achieve this change in energy? actual fact the energy required to transition between these two orbits will be much higher. Two orbi rent radius but the same angular inclination can be transitioned using a Hohmann transfer maneuv er, the orbits are also not a the same inclination. The HST is at inclination 28.5 degree and the ISS rl at 52 degree from the equatorial orbit. Transitioning between orbits at different inclinations involves

Explanation / Answer

Energy difference = GM(2m) / d1 - GM(2m) / d2

= 6.67 x 10-11x 5.97x 10^24 x 2 x 125 x 10-3 [ 1/413 - 1/554 ]

= 1.028 x 10^10 J

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energy diff = change in K.E.

1.028 x 10^10 = (2 x 125)v^2 /2

v = 9066.87 m/s

No

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