I published this post some years ago (archived version), but for unilateral decision of the online publisher, it is deleted, so I decide to recover it now.

We all known the story of the

*little green men*: in 1967

**Jocelyn Bell**and

**Antony Hewish**discovered a strange, regular cosmic signal, a periodic

*bep*. They consulted

**Fred Hoyle**, astronomers and sci-fi writer, and he understood that the signal was emitted by a neutrons' star, a pulsar. An italian research team, composed by

**Matteo Luca Ruggiero**,

**Emiliano Capolongo**,

**Angelo Tartaglia**, published the following paper,

*Pulsars as celestial beacons to detect the motion of the Earth*(arXiv). In their paper, researchers propose to apply some relativistic mathematical tools to calculate Earth position using pulsars signals.

First of all, for every pulsars we must define the following 4-vector: \[f^\mu = \frac{1}{cT} (1, \hat n)\] where $\hat n$ is the versor of the direction of propagation of pulsar signals.

To each spacetime events we can define the following 4-vector: \[r^\mu = (ct, \vec x)\] and using $f$ and $r$, we can construct the following scalar function: \[X(r) = f^\mu r_\mu = f \cdot r\] Now, if we have $N$ pulsars, we can construct $N$ scalar functions: \[X_{(N)}(r) = f^\mu_{(N)} r_\mu = f \cdot r\] So, starting from the following symmetric matrix \[\eta_{(M)(N)} = f_{(M)} \cdot f_{(N)}\] it could be possible calculate an object's position using pulsars' 4-vectors: \[r = \sum_a X_{(a)} f^{(a)}\] where $X_{(a)}$ is a phase who corresponds to the coordinates in null frame.

The only problem is now the measure of these phases.

Researchers proposed a metod (I don't try to describe you) that they numerically tested. The most important thing is that reasearchers show the possibility to use pulsars to detect the position of a celestial body.

Ruggiero M.L., Capolongo E. & Tartaglia A. (2011). Pulsars as celestial beacons to detect the motion of the Earth, International Journal of Modern Physics D, 20 (06) 1025-1038. DOI: 10.1142/S0218271811019256

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