Gravitational Wave Detectors and Spaceflight

I. What is a Gravitational Wave?

Gravitational radiation, or "gravitational waves", are ripples in spacetime. This requires some explanation. General relativity says essentially, "Mass-energy tells spacetime how to curve, spacetime tells mass-energy how to move." It is the first half of this equation that leads to gravitational waves. If I have a spring, and I pull it back and release it, it travels beyond its starting point a bit, finally slows down and returns to center, overshoots and moves almost to its pulled-back position, back to the center, and so on. This oscillation also occurs when I have moving matter (or energy) - spacetime curves in response to the matter's presence, but "overshoots" as it tries to restore to "flatness" after the matter moves on. This overshooting works exactly like the spring, so we get a "ripple" that propagates out into space. There are three very important considerations here: first, the body producing the wave must be moving in some way. No motion, no gravitational waves. Secondly, because the gravitational field is a spin-2 field (instead of spin-1 as, for example, is electromagnetic fields), you also only get radiation from the "quadrupole moment" (instead of from the dipole moment of EM radiation). This is a bit arcane, but the biggest effect is that spherically-symmetric objects (such as a single black hole) produce no gravitational waves. Finally, the amplitude of the gravitational wave depends upon the mass of the object involved, as well as the amount of motion involved - more mass, or faster orbits (for example) produce bigger (and more detectable) gravitational waves. Further, the amplitude of these waves die out as they propagate through space. Gravitational waves travel at light speed just as do EM waves (and for the same reason, essentially). Also note, that there are two polarizations for gravitational waves, a "plus" and a "cross" polarizations, named because the waves oscillate in two directions simultaneously, up/down and left/right for the plus (+) polarization and at 45-degree diagonals for the cross (X) polarization.

Gravitational waves are produced mainly by extremely massive binary stellar objects, such as binary neutron stars or binary black holes. While you produce gravitational waves just by waving your arms, the amplitude of these waves is far too small to detect. Normal solar systems produce gravitational waves when their planets orbit their primary, but again, these are incredibly tiny ripples. Even a binary black hole - which produces the most powerful gravitational waves we can imagine - requires measurements of distances of about 1/1000 the diameter of a proton. Solar system objects would be even smaller. Shown here are the gravitational waves produced by the head-on collision of two black holes.

One other quick comment: gravitational waves have frequencies just as do EM waves. These frequencies depend upon the mass, composition, and motion (type and velocity) of the system producing the waves. This is why we care about them in the first place since they are the only known way to probe the interior of a neutron star, for example.

In summary:

Gravitational waves are produced by extremely massive, non-symmetric, moving systems.
Gravitational waves propagate at light speed and decay as they propagate.
Gravitational waves have different frequencies, just as EM waves do.
Gravitational waves have two polarization modes.

II. How Are Gravitational Waves Detected?

We've talked about the fact that gravitational waves are ripples in spacetime, but what measurable effect do they have on us? When spacetime distorts, distances between two objects change. For the plus (+) polarization, the ripple squeezes you left/right and it stretches you up/down, then stretches you left/right and it squeezes you up/down, and so on. The frequency and amplitudes of these oscillations are all the information we get from gravitational waves.

There are three types of gravitational wave detectors:

Cylindrical bar detector
Ground-based laser interferometry
Space-based laser interferometry

The cylindrical bar detector was invented by Joseph Weber (with whom I had the pleasure of discussing this device not too long ago) here at UMaryland in the seventies. It works by mounting stress sensors along the surface of the bar and detecting the change in the stress along the surface of the bar. The detector is mainly an experiment - it is nowhere near sensitive enough to do much scientific work with. Joe got lots of results, but the trucks passing on Adelphi Road produced as strong vibrations as the gravitational waves coming in. Normally one uses two detectors and cross-references them in order to find "coincidences". Joe's system produced coincidences, but none that seem to correspond to any known source, so the jury is still out on that one.

The first ground-based laser interferometer is now under construction at two sites in the United States. Called LIGO (Laser Interferometry Gravitational Observatory), it works by measuring the distance between three free-hanging weights separated by a distance of about three miles. The three weights form an "L", thus allowing both the left/right and up/down components to be measured. (As a side note, you should know that no gravitational wave detector can detect more than one polarization of waves. This is true of EM antennas as well, of course.) A laser is reflected off of the weights (in order to minimize effects on the beam, it is enclosed in underground vacuum tunnels) and the return beams are then allowed to produce an interference pattern. Tiny shifts in the positions of the weights produce measurable changes in the interference pattern. This pattern then gives the desired information about the wave. LIGO is a marvel of precision optics and engineering, by the way. If they ever open it up to tours, it'd be well worth the look. LIGO Interferometer Diagram

It should be noted here that a single gravitational wave detector is essentially non-directional. With two detectors we can narrow down the position of the source to, say, 30-40 degrees in the sky, we then ask our radio astronomers to point their telescopes in the general direction of the source and see if they see anything that matches. Normally, highly energetic objects such has black holes and neutron stars (pulsars) are very easily detectable to radio (and sometimes optical) telescopes, but current (non-gravitational wave) methods have no way to probe these objects' structure. This is the use of gravitational wave detectors, not "finding things in space". If we have three detectors separated by 300-4500 km, or better yet, four (forming a tetrahedron of maximum volume), we can then pinpoint the right ascension and declination or the source (but not, of course, the distance to the source). This however, rwquires a planet-wide network or a space-based system, as described below.

Note that just getting the amplitude and frequency patterns of the wave (called its spectrum) does not tell us anything about the system producing those waves directly. In order to interpret the data, we must find a solution of Einstein's equation (which is actually a coupled system of 10 second-order partial differential equations involving several hundred variables) which produces these waveforms. The mass configuration which is the solution to the equation will tell us the information we desire to know. This end of the project (for the binary neutron star case) is what I do for a living, incidentally. The equations are far too complicated to solve analytically, so we must turn to numerical methods. To date, however, no one has been able to solve even the simplest binary black hole or neutron star configurations. Currently, there is not enough computing power on the planet to solve the black hole case. It is hoped that with the advent of teraflop computers and better memory systems, more progress can be made. (NB: This is something of a scandal, by the way. The Binary Black Hole Grand Challenge is a multi-million dollar collaboration of some of the best minds in numerical relativity. They almost certainly are not going to succeed in producing numerical waveforms by the time the challenge runs out. We hope to do somewhat better with the neutron star case.)

The third system is a variation on the first. The ESA has proposed LISA, a space-based version of LIGO. Here, though, the masses are separated by a large distance (perhaps a 1/10 of an AU?) and the interferometer follows Earth in its orbit. This detector will be much more sensitive than ground-based detectors if it can be made to work. LISA is still very much in the design stages at this point, but the principle is the same as LIGO.

In summary:

We detect gravitational waves by measuring the squeezing and stretching of objects as the wave passes by.
Even for the strongest source, the amount of stretching is less than 1/1000 the diameter of a proton.
Gravitational wave detectors are essentially non-directional. You receive the wave and the information on what's producing it, but you cannot identify where the source is, except only crudely. In general, you can detect nothing with a gravitational wave detector that you cannot more easily detect with an EM telescope (unless, of course, your source is not producing EM radiation - an important point since if it's moving it can't help but produce gravitational waves).
There are three main types of gravitational wave detectors, the best of which use laser interferometry and very long baselines.

III. Gravitational Wave Detectors for Spaceflight

A. Technological Assumptions

Right now, we are very nearly able to use gravitational wave detectors as probes of compact-mass systems. A space-based interferometer (such as the LISA detector) is even more sensitive. So, it is not too unreasonable to postulate that spacecraft may one day be equipped with gravitational wave sensors. How could those sensors be used? I will make the assumption that all our advancements in technology should generally be in the area of improvements rather truly new physics. Specifically:

1. I assume computers have evolved to the speed at which they can all reliably solve Einstein's equations in a matter of a couple of days (note that even with teraflop machines - which we don't have yet - it takes over a year to generate even one solution). It is possible computers will be able to do it in less time, but even to reduce the time to days is a major quantum leap in computing technology. However, it is likely that scientists employed by the military will be working continuously to produce waveforms from solutions to Einstein's equations for a wide variety of possible sources. These comparison waveforms would be placed in an on-board "catalog" in the ship's computer. The sensor operator, with the assistance of the computer, compares the observed waveform to the pre-determined waveforms in the catalog and makes a tenative identification based on that comparison. Using this catalog, the time to process the waveform is reduced to seconds, rather than days, but a cost: the ship is no longer absolutely certain what is going on "out there", since it is unlikely the observed waveform will exactly match any predetermined waveform. For truly new situations (for example, the mapping of a new solar system), the catalog will not be able to come up with an acceptable match and the full 2-day procedure must be followed.

2. I assume that detector sensitivity has improved to the point that planets can be reliably detected by means of gravitational waves and by a single ship. Essentially, we assume that a single shipboard detector has roughly the equivalent sensitivity of today's 4 km long LIGO detector.

3. Even with the sensitivities postulated, a single ship will not be able to tell more than the general direction of a planetary body or ship (i.e., port/starboard and fore.aft and up/down). The reason is, as my previous article indicated, directionality for gravitational wave detectors is more a function of baseline than sensitivity. Two ships could narrow the bearing down to within a 30-40 degree cone. Three or four widely-separated ships can triangulate to get the approximate (for three ships) or exact (for four ships) bearing to the source. This task would require a great deal of coordination and would probably require several minutes to pinpoint the source's bearing accurately.

B. Uses of Gravitational Wave Detectors

Gravitational wave detectors on a single ship are of little use to military ships, unless they could somehow detect the effects of a ship in motion (such as a black hole power source?). So what good are gravitational wave detectors? Suppose you are exploring a new solar system and somewhere in the "middle" you stop and do a grav scan (you would have a devil of a time doing it with your own drive running). You could tell how many planets are present and what their orbital periods are. Using Kepler's Laws (assuming these planets aren't orbiting a black hole or some such), you can determine the semimajor axis of their orbits (and you can get things like eccentricity as well directly from the waveform). Presto, you have just mapped the system. No, you don't know exactly where every planet is located at this instant, but you now have a good idea of the orbit of each. If you can find the planet to get its position at some known time, you can predict its position for all time. You log the data, and now future ships will know where to find each planet as they enter the system based on the current time and the known orbits.

Essentially, gravitational wave detectors are best suited and are primarily intended for navigation and survey (both astrometry and astronomy). I therefore find it completely reasonable that they be considered navigation scanners and generally only appear on survey-type ships. That's not to say that they can't be stretched to be of some use to military operations, as we have mentioned. If the gravitational wave detector is sensitive enough (and I really don't see this happening in the near future) we can know if there is a ship "out there", how many are present, and some idea of what it's doing (is it orbiting - stronger waves - or moving in a straight line - weaker waves?). It is possible to set up automated satellites to run continuous surveys, but by the time this information is relayed to humans (even with ultrafast computers, due to the light travel time) the position information is already seriously out of date so that the satellites provide little more information (but a tiny bit more) than the individual ships can get themselves. If the ships themselves are operating in cooperative mode to triangulate, they could conceivably follow the source and maintain a scan ..

The game effects can therefore be summarized as follows:

1. Grav scanners are essentially non-directional for a single ship, but can narrow the bearing target down to a 30-40 degree cone if two ships are working together, to an approximate (about 3 degree cone) if thre ships are working together, and an exact bearing if four ships are working together.

2. If the detector is sensitive enough or if the ship uses a compact mass for power, single-ship grav scanners provide information on the presence (i.e., "something is out there"), number of ships, and perhaps some indication of what the ship is doing, but not where it is doing it.

3. Grav scanners are primarily used in solar system mapping. They are a quick, efficient means of determining most of the orbital parameters of the solar system's planets. All that remains is to go out and find the actual positions at some known time (using optical telescopes) and we have the data we need - so we move on to the next system.

4. Grav scanners have a limited, but important military potential. Your first indication that an encroachment upon your space has occurred will likely be gravitational waves from the intruder's drive (subject to the same technology stretches mentioned in 2). At that point, you know you must start scanning for EM (radio, optical, and other) emission to locate the bogey or attempt to triangulate with fellow ships.

(Back to the Main Page)