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I'm sure you've all seen the diagrams and/or 3D visualizations of gravity; the ball sitting on a piece of fabric which makes it sink down. They've also started using it in the videos that explain gravitational waves. Two objects will be circling each other on the fabric and will emit waves.

I know this is an oversimplification of what's going on, but it is quite misleading and has left me a little bit puzzled as to why gravitational waves are infact the size of protons, not the size of planets like the videos suggest.

So I guess my question is, why are they in fact so small, and why can't we detect them from astral bodies in our solar system that we can actually detect a physical force from?

Qmechanic
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Varrick
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Actually the wavelengths often are the sizes of planets. If the period of something moving at $c = 3\times10^5\ \mathrm{km/s}$ is $1\ \mathrm{s}$ (similar to the recent LIGO discovery), its wavelength is $\lambda = 3\times10^5\ \mathrm{km}$. Other phenomena could well produce waves with wavelengths larger than the solar system.

What is small is the amplitude of the waves. The recently detected waves had amplitudes of $10^{-21}$. This means that they stretched spatial lengths by one part in a thousand billion billion. LIGO in particular has interferometer arms that are a few thousand meters in length, so these arms were stretched by a few parts in a billion billion.

Think about light. There is wavelength -- radio waves are meters long, visible waves are hundreds of nanometers long, and gamma rays are fractions of a nanometer long -- and there is intensity. Even if your eyes are optimized for detecting visible light, they can't see sources that are too faint.

The wavelengths of gravitational waves are set by the typical scales in the system generating them. For example, with inspiraling stellar mass black holes, the system is a bit smaller than Earth. The reason gravitational waves are weaker in amplitude than electromagnetic waves is usually given as gravity being an intrinsically weaker force, or equivalently as most matter being very highly charged (it's mostly protons and electrons) while not very massive (it takes a lot of matter to have a noticeable gravitational effect).