3.6 Flying Out of the Solar System
181
(2) Positioning and Timing by Using Fourteen Pulsars
At the middle of the left side in Fig. 3.6, a radial pattern with fifteen lines emanating
from the same origin is shown in a polar coordinate system. There are fourteen radial
lines with a string of binary numbers, representing the positions of fourteen pulsars
relative to the Sun. With the hydrogen spin-flip transition frequency as the unit, the
binary numbers at the end of each radial line stand for the period of corresponding
pulsar, with 10 significant figures in the decimal notation. There is a tick mark near
the end of each line, and the length from the origin to the tick mark stands for
the relative distance of the pulsar, while that from the tick mark to the line’s end
gives the Z coordinate perpendicular to the Galactic plane. Because the earth-pulsar
distance is not accurately known, the radial lines are shown with breaks. According
to the actually-observed pulsars, it could be determined whether the Z coordinates
are positive or negative. The fifteenth line extends to the far right, behind the human
figures. From the tick mark near the end of the fifteenth line, it may be shown that its
Z coordinate is zero, so the line indicates the Sun’s relative distance to the center of
the Galactic System. In an astronomical interpretation, the two most-likely origins
would be the home star of the launch civilization and the center of the Galactic
System. The reconstruction of pulsar periods will indicate that the origin of polar
coordinates is not the Galactic center.
The relevant parameters of the fourteen selected pulsars, including the PSR
number, binary period, decimal period, second’s period, azimuth and distance, are
listed in Table 3.2, where the azimuth is accounted in the clockwise direction and the
line from the Sun to the Galactic center regarded as the azimuth of zero; the distance
between the Sun and the Galactic center is with a unit of 100. The fourteen pulsars
were selected to be distributed as evenly as possible in Galactic longitude, with the
shortest period, the greatest longevity and the highest luminosity, to well receive and
use their radiation signals in the far future. For any position and time solution, the
fourteen pulsars would be able to provide enough redundancy, but also to allow for
the good possibility that pulsar’s emissions are highly beamed and that not all pulsars
are visible at all view angles. If the gold-anodized aluminum plate is intercepted by
the extraterrestrial civilization with the same or more advanced technical levels as
mankind on the Earth, which have also kept the historical observation records of the
pulsars, the launch epoch of the Pioneer can be derived from the properties of the
pulsars’ periods changing over time. Even if the glitches of pulsars occur and are not
recoded, the launch epoch may be calculated with an error range of 100−1000 years.
With triangulation, only three pulsars need to be observed to determine the earth’s
position of launching the spacecraft. Fortuitously, two of the pulsars are very near
the Earth. If either is correctly identified, it can be used to place the position of our
solar system in the Galactic System to approximately 20 parsecs, thereby specifying
our location to approximately 1 in 1000 stars [11].
It should be pointed out that the listed period of one of the pulsars in Table 3.2
is misleading. At the time when the plaque was designed, pulsar “B1240–64” (now
know as J1243–6423) had a known period of 0.388 s, only with the three significant
digits, in the then astronomical community. Unfortunately, to be useful on the Pioneer
181
(2) Positioning and Timing by Using Fourteen Pulsars
At the middle of the left side in Fig. 3.6, a radial pattern with fifteen lines emanating
from the same origin is shown in a polar coordinate system. There are fourteen radial
lines with a string of binary numbers, representing the positions of fourteen pulsars
relative to the Sun. With the hydrogen spin-flip transition frequency as the unit, the
binary numbers at the end of each radial line stand for the period of corresponding
pulsar, with 10 significant figures in the decimal notation. There is a tick mark near
the end of each line, and the length from the origin to the tick mark stands for
the relative distance of the pulsar, while that from the tick mark to the line’s end
gives the Z coordinate perpendicular to the Galactic plane. Because the earth-pulsar
distance is not accurately known, the radial lines are shown with breaks. According
to the actually-observed pulsars, it could be determined whether the Z coordinates
are positive or negative. The fifteenth line extends to the far right, behind the human
figures. From the tick mark near the end of the fifteenth line, it may be shown that its
Z coordinate is zero, so the line indicates the Sun’s relative distance to the center of
the Galactic System. In an astronomical interpretation, the two most-likely origins
would be the home star of the launch civilization and the center of the Galactic
System. The reconstruction of pulsar periods will indicate that the origin of polar
coordinates is not the Galactic center.
The relevant parameters of the fourteen selected pulsars, including the PSR
number, binary period, decimal period, second’s period, azimuth and distance, are
listed in Table 3.2, where the azimuth is accounted in the clockwise direction and the
line from the Sun to the Galactic center regarded as the azimuth of zero; the distance
between the Sun and the Galactic center is with a unit of 100. The fourteen pulsars
were selected to be distributed as evenly as possible in Galactic longitude, with the
shortest period, the greatest longevity and the highest luminosity, to well receive and
use their radiation signals in the far future. For any position and time solution, the
fourteen pulsars would be able to provide enough redundancy, but also to allow for
the good possibility that pulsar’s emissions are highly beamed and that not all pulsars
are visible at all view angles. If the gold-anodized aluminum plate is intercepted by
the extraterrestrial civilization with the same or more advanced technical levels as
mankind on the Earth, which have also kept the historical observation records of the
pulsars, the launch epoch of the Pioneer can be derived from the properties of the
pulsars’ periods changing over time. Even if the glitches of pulsars occur and are not
recoded, the launch epoch may be calculated with an error range of 100−1000 years.
With triangulation, only three pulsars need to be observed to determine the earth’s
position of launching the spacecraft. Fortuitously, two of the pulsars are very near
the Earth. If either is correctly identified, it can be used to place the position of our
solar system in the Galactic System to approximately 20 parsecs, thereby specifying
our location to approximately 1 in 1000 stars [11].
It should be pointed out that the listed period of one of the pulsars in Table 3.2
is misleading. At the time when the plaque was designed, pulsar “B1240–64” (now
know as J1243–6423) had a known period of 0.388 s, only with the three significant
digits, in the then astronomical community. Unfortunately, to be useful on the Pioneer