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Chapter 34: Q15CQ (page 1237)
What are gravitational waves, and have they yet been observed either directly or indirectly?
LIGO discovered gravitational waves in 2016, which are periodic disruptions in the gravitational field (space-time).
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(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some\({\rm{10 Gly}}\)away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than\({\rm{0}}{\rm{.9c}}\).
A section of superconducting wire carries a current of\({\rm{100 A}}\)and requires\({\rm{1}}{\rm{.00 L}}\)of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is\({\rm{\$ 0}}{\rm{.30}}\)per litre, and that electric energy costs\({\rm{\$ 0}}{\rm{.10}}\)per KW·h. What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?
(a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of\({\rm{1}}{{\rm{0}}^{{\rm{ - 43}}}}{\rm{ s}}\). (b) Compare this energy with the\({\rm{1}}{{\rm{0}}^{{\rm{19}}}}{\rm{ GeV}}\)unification-of-forces energy and discuss why they are similar.
Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other tests that could be made of gravity at large distances, such as observing the motions of neighbouring galaxies?
Distances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in the galaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be any correction necessary to compensate for the red shift of the galaxy (all distant galaxies have significant red shifts)? Discuss possible causes of uncertainties in these measurements.
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