Gravitational Waves

Adelante! Adelante las naves! (Cristoforo Colombo)
Tullio

I just learned that spacecraft Doppler tracking has also been used in an attempt to detect low-frequency gravitational waves. It's very similar to using the interferometers, where the spacecraft and the Earth are acting as the free test masses (like the mirrors in the LIGOs) but instead of measuring a change in distance between the test masses caused by a gravitational wave, the Doppler tracking measures a change in the relative velocity between the spacecraft and Earth. Here's an article I just ran across (from November 2001) that tells about the effort that went into the Cassini-Hugygens mission to improve the sensitivity an order of magnitude beyond previous spacecraft missions:NASA Spacecraft to Hunt for Elusive Gravity Ripples

Doppler tracking is still not as sensitive as the LIGOs, but the much greater distance between the test masses (hundreds of millions of miles compared to 4 kilometer arms in the interferometers) means that it's sensitive to gravitational waves having much longer wavelengths than those that could be detected by the interferometers, so the efforts complement each other.

For anyone interested in the nitty-gritty physics of using Doppler tracking for trying to detect gravitational waves, I found this: Low-frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking. Section 8, an update, is about the LISA (Laser Interferometer Space Antenna); I thought it was ingenious obtaining “extra� gravitational wave data from spacecraft that have other primary missions, but it's easy to see why it's far better to have a full-time mission using sciencecraft dedicated specifically to the effort.

I had not read much about advanced LIGO, so that was a very informative read.

Thanks for posting it! :)

Join the club! Incidentally linear is a key word here, so do read on ...... :-)

Yup, it's a fascinating connection. Mass ( or energy ) bends space, and mass moves according to that.

Ah, now that's a real head banger! :-)

The 'pure' answer is yes : in that the wave itself has energy ( = mass ), it causes altered movement by it's passage, that altered movement could create waves, which themselves have energy ( = mass ), would could interact with the original incoming wave, which .......... etc Arggh!!!

The 'self' energy of the field is what makes solving Einstein's tensor equation ( 16 factors with 10 of them independent ) such a bitch. Photons ( at ordinary energies ) will not interfere with each other's passage, hence a light beam can be shone across another light beam and neither will be upset. If several photons arrive at a point they add, a linear superposition with phase adjustments. [ At higher energies coupling with other fields can occur and, say, an electron/positron pair might result ..... ]

Thus solving these gravity equations is non-linear. There's a few groups ( numerical relativists ) who use computers to approximate black hole mergers for instance. For LIGO, out here in detection land a long way away from the sources, approximations are made that:

- space is otherwise basically flat ( Minkowski metric )
- perturbations are small & linear
- distinct disturbances add like electromagnetic waves do

even though strictly speaking that's not true. But hey, the higher order terms should be small right?

The wavelengths that LIGO is sensitive to .... :-)
Seriously, the 'sweet spot' for the IFO's is ~200Hz but it's broadband also - hence our task units are working upwards through the frequencies. As the waves go at the speed of light ( 3 x 10^8 m/sec ) then 200Hz corresponds to a wavelength of = 3 x 10^8 / 200 ~ 1.5 x 10^6 m ~ 1.5 x 10^3 km. It's worth noting that the interferometers are of the order of 4km long and hence they 'sample' only a small part of the wavefront with a single circuit of the arms. You could liken this to a small boat being raised and lowered by the passage of a very long ocean 'swell'.

Oh, and just to be annoying, the 'waves' we are discussing are transverse to the direction of propagation. This means that if one were to go through my chest, going 'square-on' travelling from my front to my back, then it is my width from shoulder tip to shoulder tip and my length from head to toe that will alternately stretch and contract. My shoulders separate while I get shorter and they scrunch closer when I get taller. But my dimensions from breastbone to backbone are unaltered!

Cheers, Mike.