# Pulsars to detect Earth's motion


by @ulaulaman about #astronomy #pulsars #mathematics #earth

I published this post some years ago ([archived version](https://web.archive.org/web/20101129170833/http://sciencebackstage.blogosfere.it/2010/11/pulsars-to-detect-earths-motion.html)), but for unilateral decision of the online publisher, it is deleted, so I decide to recover it now.

![](https://cdn.hashnode.com/res/hashnode/image/upload/v1743071386041/43971463-26c9-42a3-a330-885aa20c0408.jpeg)  
_A Pulsar's Hand_ **P. Slane** _et. al_ ([Apod](http://apod.nasa.gov/apod/ap100501.html))

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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](http://www.technologyreview.com/blog/arxiv/25972/) the following paper, _Pulsars as celestial beacons to detect the motion of the Earth_ ([arXiv](http://arxiv.org/abs/1011.0065)). 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.

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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](http://dx.doi.org/10.1142%2FS0218271811019256)