We’ve seen some remarkable feats of celestial navigation lately, not the least of which has been the flyby of comet Hartley 2 by the EPOXI mission. But as we continue our push out into the Solar System, we’re going to run into the natural limits of our navigation methods. The Deep Space Network can track a spacecraft from the ground and achieve the kind of phenomenal accuracy that can thread a Cassini probe through a gap in the rings of Saturn. But positional errors grow with distance, and can mount up to 4 kilometers per AU of distance from the Earth.

To go beyond the Solar System, we’ll need a method that works independently, without the need for ground station assistance. Pulsar navigation is one way around the problem. Imagine a spacecraft equipped with a radio telescope that can determine its position by analyzing the signals from distant pulsars. These super-dense remnants of stellar explosions emit a beam of electromagnetic radiation that is extremely regular, and as we’ve seen in these pages before, that offers a navigational opportunity, especially when we’re dealing with millisecond pulsars.

Scientists have been studying how to use pulsars for navigation since the objects were first discovered and several proposals have surfaced that are based on measuring the time of arrival of pulses or the phase difference between pulses, all in reference to the Solar System barycenter, the center of mass for all orbiting objects in the system. But a new paper from Angelo Tartaglia (INFN, Torino) and colleagues takes a look at an operational approach for defining a what they call an ‘autonomous relativistic positioning and navigation system’:

We assume that a user is equipped with a receiver that can count pulses from a set of sources whose periods and positions in the sky are known; then, reckoning the periodic electromagnetic signals coming from (at least) four sources and measuring the proper time intervals between successive arrivals of the signals allow to localize the user, within an accuracy controlled by the precision of the clock he is equipped with.

Moreover, the spacecraft determines its own position solely by reference to the signals it receives, which no longer have to flow from Earth:

This system can allow autopositioning with respect to an arbitrary event in spacetime and three directions in space, so that it could be used for space navigation and positioning in the Solar System and beyond. In practice the initial event of the self-positioning process is used as the origin of the reference, and the axes are oriented according to the positions of the distant sources; all subsequent positions will be given in that frame.

Hence the term ‘autonomous’ to describe the system. Marissa Cevallos did a terrific job on the pulsar navigation story in a recent online post, talking to the researchers involved and noting a key problem of conventional spacecraft navigation: We can use Doppler shift to calculate a spacecraft’s position, but we lack accuracy when it comes to generating a three-dimensional view of the vehicle’s trajectory. What pulsars could provide would be an ability to place the spacecraft in that three dimensional frame, as the Italian team was able to demonstrate through computer simulations using software that worked with artificial signals to test the method.

This is celestial navigation of a kind that conjures up sailing ships deep in southern seas in the 18th Century, using the stars to fix their position. We know, of course, that neither stars nor pulsars are fixed in the sky, but the regularity of pulsars is such a huge advantage that we can adjust for long-term movement. What is more problematic is the weakness of the pulsar signal, which could demand the use of a large radio telescope aboard the spacecraft. That will remain an issue for work outside the Solar System, but in the inner System, the Italian team wonders whether we could combine pulsars signals with those of local transmitters. From the paper:

For the use in the Solar system, one could for instance think to lay down regular pulse emitters on the surface of some celestial bodies: let us say the Earth, the Moon, Mars etc. The behaviour of the most relevant bodies is indeed pretty well known, so that we have at hands the time dependence of the direction cosines of the pulses: this is enough to apply the method and algorithm we have described and the final issue in this case would be the position within the Solar system. In principle the same can be done in the terrestrial environment: here the sources of pulses would be onboard satellites, just as it happens for GPS, but without the need of continuous intervention from the ground: again the key point is a very good knowledge of the motion of the sources in the reference frame one wants to use.

What’s fascinating about this work is that while it does not consider the numerous technological problems involved in building such a positioning system, it does define an autonomous method which fully moves the positioning frame from Earth to spacetime, in what the authors call a ‘truly relativistic viewpoint.’ The paper goes on:

The procedure is fully relativistic and allows position determination with respect to an arbitrary event in flat spacetime. Once a null frame has been defined, it turns out that the phases of the electromagnetic signals can be used to label an arbitrary event in spacetime. If the sources emit continuously and the phases can be determined with arbitrary precision at any event, it is straightforward to obtain the coordinates of the user and his worldline.

The spacecraft using these methods, then, is fully capable of navigating without help from the Earth. For nearby missions, emitters on inner system objects can supplement the observation of a single bright pulsar to produce the data necessary for the positional calculation, but deep space will demand multiple pulsars and the onboard capabilities of an X-ray telescope to acquire the needed signals. How we factor that into payload considerations is a matter for future engineering — right now the key task is to work out the feasibility of a pulsar navigation system that could one day guide us in interstellar flight.

The paper is Tartaglia et al., “A null frame for spacetime positioning by means of pulsating sources,” accepted for publication in Advances in Space Research (preprint). See also Ruggiero et al., “Pulsars as celestial beacons to detect the motion of the Earth” (preprint).

Related (and focused on the analysis of X-ray pulsar signals): Bernhardt et al., “Timing X-ray Pulsars with Application to Spacecraft Navigation,” to be published in the proceedings of High Time Resolution Astrophysics IV – The Era of Extremely Large Telescopes, held on May 5-7, 2010, Agios Nikolaos, Crete, Greece (preprint). Thanks to Mark Phelps for the pointer to this one.