I just started to learn general theory of relativity by Hartle's gravity textbook. In a section on gravitational wave I encountered following statement 'Gravitational waves are hard to detect due to weak coupling of matter' and refers to this equation $$\frac{F_{grav}}{F_{elec}}\approx10^{-36}$$ There is another statement 'Gravitational waves are detected by its effect on the orbits of bodies emitting the radiation'. I am unable to understand both statements. As per my knowledge as gravitational waves travels through space and time it stretch the space results in increase in distance between two test masses. So what both statements wants to tell us.
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2$\begingroup$ I'm not sure what you're trying to ask. Gravitational waves are very weak, and our best detectors can only detect waves from extremely intense events, like black hole mergers. Before LIGO successfully detected any waves, we had some indirect evidence of gravitational waves, through the changing period of binary neutron stars. $\endgroup$– PM 2RingCommented Feb 1, 2021 at 13:35
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$\begingroup$ Yes I was asking before LIGO detected gravitational waves please can you refer me where I can study about changing period of binary neutron stars and also tell me. Does gravitational waves affect the bodies who produces it(in this case binary neutron star? $\endgroup$– Nikhil PathakCommented Feb 2, 2021 at 8:18
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$\begingroup$ See en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary $\endgroup$– PM 2RingCommented Feb 2, 2021 at 10:11
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2 Answers
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First, gravitational waves that we do have available for observations are, thankfully, not that much intense. Their sources are rather powerful (like, radiating few solar masses for half a second for a stellar black hole binary), but they are also far away and the inverse squares law kicks in pretty well. A billion light years is quite a distance.
The light output of a supernova may be of comparable order of magnitude, but both our eyes and our telescopes are impressively sensitive to light. We can detect ~10 photons in few hours and pinpoint them to an miliarcsecond-sized area in the sky. Then, depending on other circumstaces, we may call them an asteroid, a star, a galaxy or a supernova.
We don't have anything comparable for the gravitational waves (at least, for now). All we can do about them is to detect some movement of a rather distant to each other objects and somehow distinguish that movement from movements imposed by other known forces. The more distant objects we have (up to the scale of the gravitational wave length), the more movement the gravitational waves create (and the less control we have over the external forces).
LIGO interferometers detect atomic nucleus-sized movements over 4km distance (an impressive feat itself) and then have to filter out e.g. people walking around the detectors.
Second, the universe presents us more or less bright gravitational events in the kilohertz range (and probably below). Higher-frequency waves would be somewhat easier to detect because of their shorter wavelengths, but the black holes simply refuse to orbit each other faster. 1kHz wave has wavelength comparable to several Earth's diameters and we are still unable to build Earth-sized detectors. Our 4km detectors catch only a very small part of the possible signal.
Just like with electromagnetic waves, for best results, the receiving antenna has to be of a size comparable to 1/4 of the wavelength. We have 4km instead ot ~10000km here.
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I can try to tell you why gravitational waves are (experimentally) hard to detect. If you want to detect them, you do so nowadays in Laser Physics experiments (e. g. at LIGO in the US or at Virgo in Europe). For this, huge mirrors are used. If know gravitational waves are in the interferometers, the amount by which the mirrors are shifted due to gravitational waves is very very small, thus making it very hard to detect them. In fact, one needs to make sure that the very small distance that the mirrors are shifted does not e. g. come from Brownian motion on the mirror surfaces.
I know that I didn't directly answer your two questions, but I hope this still clarifies at least a bit why gravitational waves are hard to detect.