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International Space Station (ISS) plan to snag a cable for removal

The International Space Station is in a nearly circular orbit at an altitude of 398.00 km above the surface of the earth.

A maintenance crew is about to arrive on the space shuttle that is also in a circular in the same orbital plane as the ISS, but with an altitude of 398.10km.

The crew has come to remove a faulty 125 m cable electrical cable, one end of which is attached to the ISS and the other end of it is floating free in space.

The plan is for the shuttle to snag the free end just as the moment that the shuttle, the ISS, and the center of earth all lie along the same line. The cable will then break free from the ISS when it becomes taut.

How long after the free end is caught by the space shuttle will it detach from from the ISS? Give answer in minutes.

c) If the shuttle misses catching the cable, show that the crew must wait a time:

t=(like almost equal)=T^2/(bigdeltaT)

before they have a second chance. What is the numerical value of t and explain whether it would be worth to wait.

Solution Preview

Because, the difference in the orbits radii of shuttle and ISS = 0.1 km = 100 m

The leght of the cable = 125 m

Radius of the orbit of the ISS r1 = Re+398 km = 3200+398
= 3598 km = 3598000 m
Radius of the orbit of the shuttle r2 = Re+398.1 km = 3200+398.1
= 3598.1 km = 3598100 m
difference of orbits delta(r) = 100 m

For 3598 km, 100 m is a very small distance. Therefore the disance travelled along the track can be ...

Solution Summary

With complete calculations and explanations, the problems are solved.