Frequency of Gravitational Waves: Limit & Possibilities

[DaveC426913]

TL;DR

Can gravitational waves theoretically have any wavelength, even ultra long?

A question elsewhere got me thinking about the frequencies/wavelengths of gravitational waves.

The most obvious source of gravitational waves we are finding is from merging black holes, so presumably the orbital period will directly determine the frequency of those waves, yes? So the frequency's upper bound in this case is determined only by how short of period gets before they merge.

Can frequencies get very low? Can you have a gravitational wave whose wavelength is, like, the radius of the solar system? It would have a period of about 5.5 light hours, varying sinusoidally over that time.

Is there any phenomena that could produce such a long wavelength of gravitational waves?

 

[Dale]

Summary:: Can gravitational waves theoretically have any wavelength, even ultra long?

Is there any phenomena that could produce such a long wavelength of gravitational waves?

The Earth produces gravitational waves with a wavelength of one light-year. Other planets produce even longer wavelength waves

 

[DaveC426913]

Of course.I over thunk it.

This render is of two bodies of comparable mass, but it works just fine with Earth-Sun:

https://www.physicsforums.com/attachments/299520

 

[PeterDonis]

The Earth produces gravitational waves with a wavelength of one light-year. Other planets produce even longer wavelength waves

Theoretically, the solar system itself, orbiting the center of our galaxy, is emitting gravitational waves with wavelengths of hundreds of millions of light years.

 

[Orodruin]

The Earth produces gravitational waves with a wavelength of one light-year.

Half a light year to be nitpicking. The period of gravitational waves emitted by a binary system is half the period of the system’s orbit.

 

[DaveC426913]

Half a light year to be nitpicking. The period of gravitational waves emitted by a binary system is half the period of the system’s orbit.

I've been tying myself in knots trying to figure out the wavelengths/frequencies. I keep thinking it's half, then double, then giving up. But this is an additional wrinkle.

Is it half the period because it's one crest per body?

So, if the two bodies were to vary widely in their mass, would the amplitude of successive wave peaks alternate between high and low?

Which suggests that @Dale is technically correct. Earth, in-and-of-itself, would produce a wave with a period of one light year. So would the Sun, and the two waves - each with period of 1ly - would be interleaved - 180 degrees out of phase. Yes?

 

[PeterDonis]

Is it half the period because it's one crest per body?

No. The GWs are not produced by either body separately. They are produced by the two-body system as a whole. There is no way to split up the GW into a part that comes from one body and a part that comes from the other.

 

[Dale]

Half a light year to be nitpicking. The period of gravitational waves emitted by a binary system is half the period of the system’s orbit.

Oh, that is interesting. I didn’t know that.

I guess that means that the quadrupole moment is the same after half an orbit. So if the system is two unequal point masses, do you know what is the lowest moment which requires a full orbit to be the same again?

 

[Orodruin]

To add to what Peter said, in the close to flat case, the source of the gravitational waves is the system’s quadrupole moment (or rather, its second derivative). The quadrupole period is half the period of the binary and therefore that is the period of the generated wave. A spherical body in itself has zero quadrupole moment

 

[PeterDonis]

the source of the gravitational waves is the system’s quadrupole moment (or rather, its second derivative)

Isn't it actually the third time derivative?

 

[Orodruin]

wavelengths/frequencies. I keep thinking it's half, then double

Well, wavelength is half, frequency double.

 

[DaveC426913]

Well, wavelength is half, frequency double.

If i did it correctly before the wrinkle, then Pluto's GW frequency will be 1 over (248 Earth years in seconds). The wrinkle means i double that.

The wavelength will be 5.5 light hours, halved.

 

[Orodruin]

The wavelength will be 5.5 light hours, halved.

No, the speed of the GW is the speed of light so wavelength is the speed of light/frequency. If you have frequency in years^-1, wavelength is the inverse of that in light years. Making the wavelength generated by the Sun-Pluto system 124 light years.

 

[Orodruin]

Some years back, I had a couple of bachelor students writing their bachelor thesis on gravitational waves from the solar system. You may find it to be of interest.
http://kth.diva-portal.org/smash/get/diva2:1120371/FULLTEXT01.pdf

 

[phinds]

Some years back, I had a couple of bachelor students writing their bachelor thesis on gravitational waves from the solar system. You may find it to be of interest.
http://kth.diva-portal.org/smash/get/diva2:1120371/FULLTEXT01.pdf

Hilarious acknowledgments. You must have had a good relationship with them for them to be comfortable writing that.

 

[Orodruin]

Hilarious acknowledgments. You must have had a good relationship with them for them to be comfortable writing that.

I did not even remember that. I can get a bit carried away with the correction pen. Who here would have guessed?