Re: Fermi's Paradox and Seti

Terry Pilling wrote:

Aside about Sagan: Probably you know that Sagan designed a famous
plaque which was carried on the two Pioneer spacecraft and are now
headed out into the galaxy like a ``galactic message in a bottle''.
Well, on the plaque are some interesting and informative things,
in particular, a distance scale is set by the hydrogen atom, which
also sets a time duration scale in terms of the number of hyperfine
transitions of the hydrogen atom. A time duration which we know to
be 7.04024183647 x 10^-10 seconds and we can assume any other intelligence
would also know this. With this time scale Sagan listed a bunch of
pulsars along with their distance and periods of pulsation. For example,
the 7th pulsar listed is PSR 0531 in the crab nebula (M1)
[see: http://chandra.harvard.edu/photo/2002/0052/movies.html for
something I consider to be very cool! I even put a question on an
electrodynamics midterm exam last semester about the magnetic fields
generated by this thing.] Its rate is given on Sagan's plaque as
47057538 hyperfine transition periods. This is 33.1 ms. However, the pulsar
is slowing down at a rate of 10^-8 seconds per day! This means that since
the launch in 1972 the pulsars rate has slowed down and is now only 33.3 ms.
So any aliens getting our message (especially in a few million years!)
will have great difficulty triangulating our position (all of the pulsars
on the list are slowing down over time). In addition to this, the
pulsars are all moving through space! So by the time an alien
civilization gets the message the pulsars will all be in completely
different relative positions to the earth, making the message useless!

So I have an idea for an update of the plaque: We should list, in
addition to the pulsation periods, the decelerations of the pulsation
periods. The decelerations would allow them to find the pulsars (assuming
the decelerations are also constant) and the period data themselves will
allow them to figure out the travel time of the spacecraft since launch,
These will allow them to back trace the original positions of the
pulsars at time of launch (assuming they know the relative motions of
at least 4 pulsars) and thus finally triangulate our position at
time of launch. Then forward track our local motion to find our
position at the time of their discovery of the spacecraft!
Whew! Sounds complicated I know, but the original plaque, without
the deceleration data is impossible. As it stands now, the best
way for an alien to find the earth from a discovery of the pioneer
is to back track the spacecraft itself and forget the plaque altogether!

In the above, I say that one needs at least 4 pulsars to triangulate
the position of the earth. I read that somewhere but now I am not so sure.
Why can't one do it with fewer pulsar positions?
So on the plaque (http://en.wikipedia.org/wiki/Pioneer_plaque) there
is the distances to the pulsars from the earth and on my revised
version there would also be the deceleration data along with the
period data of the pulsars. So the problem is this:

----------
Problem:

Given the distances to the pulsars _today_, the periods, and the
decelerations of the periods, and assuming you can experimental
determine the trajectories through space of the pulsars, what is
the minimum number of pulsars needed at any time in the future so
that a triangulation of the earth's future position can be made?
----------

The way I was thinking about it is that you would need 4, first
determine the travel time of the probe since launch based on
the current periods of the pulsars given the decelerations. Then
track the pulsars back to their positions on the date of probe
launch. Then draw spheres centered on each pulsar with radius
equal to the distances given on the plaque. If there is a unique
point of intersection of these spheres, then you have found the
earth. In fact, even if there is a _discrete_ but finite number
of intersection points, or even a finite one-dimensional line of
intersection points (like a circle of relatively small radius),
then enterprizing aliens could find us. So the problem could be
restated (I think!) as `how many spheres does one need in 3
space so that their intersection is a `findable' set?' where
by `findable' I mean finite discrete set of points, or a
compact 1-dimensional manifold of points.

Anybody know how to solve this and what conditions are
necessary to guarantee a solution?


--
-Terry

---------------------------------------------------
Terry Pilling
Department of Physics
North Dakota State University

terry[at]member.ams.org
http://www.physics.ndsu.nodak.edu/people/index.html
---------------------------------------------------

.

Relevant Pages

  • Re: Fermis Paradox and Seti (was DNA)
    ... would intelligent aliens necessarily visit us? ... Well, on the plaque are some interesting and informative things, ... the launch in 1972 the pulsars rate has slowed down and is now only 33.3 ms. ... > faster than light travel just ISN'T possible?! ...
    (sci.physics.research)
  • Re: What practical jokes would you pull w/time machine?
    ... >>the idea that pulsars were narrow beams. ... see in an alien plaque or SETI message. ...
    (rec.arts.sf.science)