Shortly after the news of the discovery of gravity waves, my physics professor explained the significance of the discovery by comparing it to a medical X-ray machine. He said that gravity waves can be used to detect objects that cannot be seen using telescopes. Therefore, could gravity wave detectors be used to confirm the existence of the theorized ninth planet? Even though it doesn't have a high enough albedo to be seen, it would still be detectable gravitationally, wouldn't it?


No, they can't.

Gravity waves from a small, simple object moving slowly are very, very faint, to the point of being undetectable with current (or foreseeable) technology.

The waves that have been detected come from the merger (a very fast movement in the last orbits) of two black holes (two very big masses). And they were just detected over the noise level.

Do not confuse that with the possibility to detect the gravitational influence of such a planet over other bodies. That is how Neptune and Pluto were detected, indeed.

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  • $\begingroup$ In fact the gravitational influence was also key to the prediction of a nineth planet. Good answer! $\endgroup$ – Jaywalker Feb 16 '16 at 20:54
  • $\begingroup$ The strain(On the LIGO detector arms) due to g-waves from the binary black hole merger was 10^(-21). Theoretically what would be the strain due to g-waves from a average planet ? $\endgroup$ – Naveen Feb 17 '16 at 18:49

The maths on Wikipedia give a way of calculating the the amplitude of graviational waves.

One detail is that for the waves to be detected by a ligo apparatus, one needs to be far enough from the source of the waves. The distance required depends on the frequency. For planet 9, if it has orbit of 10000 years, one would need to be more than $2500\pi$ light years distant. That is nearly 10000 light years away. This value is "R"

Then we can use the formula: $$h_{+} =-\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{4m_1 m_2}{r}$$

using the above value of R, the known values of the gravitation constant and speed of light, and the masses of the sun and a hypothesised value for the mass and semi-major axis of planet 9.

That gives a strain of $10^{-32}$. That is far far far below what is detectable. It also would have a frequency of 10000 years or so. So you would be trying to detect an oscillation comparable to the plank length, you would need at least 10000 years of observation, and your detector has to be built on the other side of the galaxy.

Not possible.

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