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R2GW

From IFPA wiki
  1. The gravitational wave signal GW170817 lasted for approximately 100 seconds starting from a frequency of 24 hertz. Assuming that the masses of the merging compact objects are within a factor 2 of each other, find a range for the total mass of the system.
  2. Consider a pulsar, and assume that it is an irregular ellipsoid. Assume that at [math]\displaystyle{ t=0 }[/math] its quadrupole tensor is [math]\displaystyle{ Q_{ij}=diag(Q_1,Q_2,Q_3) }[/math] and that it is rotating around [math]\displaystyle{ x_3 }[/math]. Calculate the amplitude of the gravitational wave tensor as a function of [math]\displaystyle{ Q=Q_!+Q_2,\ Q_3 }[/math] and of the excentricity [math]\displaystyle{ \epsilon=|Q_1-Q_2|/Q_3 }[/math]. What is the luminosity of the emitted waves?
  3. What is the power of the gravitational waves emitted by the Earth as it goes around the Sun?
  4. The Einstein telescope aims at measuring waves of frequencies larger than 2 Hz. How long would the signal of problem 1 last if it started at 2 Hz? How long would last a black hole merger for 20 solar-mass black holes? How far could each of these systems be to have an amplitude [math]\displaystyle{ h\approx 10^{-22} }[/math] at 2 Hz?

Solutions 2020

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