Foucault's Pendulum is used to determine the latitude of the location of the Pendulum. Such pendulum oscilates through the same plane so, as the Earth rotate around its axis, it seems, to an observer, that the pendulum is rotating the plane it oscilates in as time goes on. By measuring the period of this apparent rotation of the plane, one is able to determine the latitude of the pendulum's location, as the period is T = 24h / sinα, with α being the latitude. So a pendulum like this seems to be useless to determine the position of the Island. But here is what I think: the center of mass is a particular point of a system of particles defined as the average of their position weighted by their masses. Moreover, the center of mass (CM) makes possible to consider the Earth as a particle with all the mass concentrated in the said point. This way, considering an object on Earth's surface, we can consider the Gravitational Force acting on that object to be directed to the CM (not considering any gravimetric anomaly).
Now, let's suppose the Island is moving through Space. This can hypothetically cause the center of mass to change it's position.
A pendulum will oscilates only through one plane, that means the plane NEVER changes. But, if the CM moves, the Pendulum will probably correct its oscillation following the new gravitational force coming from the new CM. So the pendulum, while oscilating in the very same plane, can have a correction in its direction.
So as the CM changes its position we would see the Pendulum rotating around a different axis (as seen by an observer on Earth). If we position the pendulum on a map that takes into account such aspects, the pendulum could hypothetically indicate the actual position of the Island.
Of course this theory has some unclear aspects, as any other theory:
- With the Island moving, the CM of the Earth would change in an imperceptible way, because the mass of the Island is negligible in relation to Earth's mass.
- Even if the CM moves considerably, why nobody on Earth seems to notice this too (as there is more than Mrs Hawking's pendulum in the world)?
Anyway, as seen in episode 502, Mrs Hawking seems to have found the actual position of the Island. I tried to enhance a screencap of the map she used.
As you can see, the lines converge in a point just above the Equator: we can see French Polynesia and Kiribati to the South and Hawaii to the North. So every grid of that map is 30° x 30°. Considering this piece of information, I think we could approximate the location of the Island to the coordinates:
0° - 5° N, 160° - 165° W
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2 comments:
Hi Q,
Looking at your enhanced photo of Mrs Hawkins map, I would have to agree with your coordinates. I like your explanation, I just agree that center of mass of the island is just too small in relation to the Earth's center of mass. What's odder is that this pendulum is not located on the island. A person would have to be at the same latitude as the pendulum to realize their latitude. I believe this is much more than a Foucault's Pendulum, although it may use certain functions of one.
I was impressed by your enhanced version of the map. My only question is are you sure thats Hawaii and not the Kingman reef? Also, just left of the where the map says Equator (above the equater line), it seems like it reads Kiritimati, Frech Polynsia.
Great job, and like I said, I agree with your coodinates.
Last night's show was a great show for screen caps. Its going to take a little while to digest though.
Mike
Hi Mike,
I have to be honest, I actually hadn't enough time and knowledge to elaborate a theory better than this one. Anyway, I was rather surprised about how this theory could make sense. If it wasn't for the fact that the mass of the Island is too small, I think it could be right - I'm actually hoping that TPTB used their artistic licence :). And, or it is this, or something related to the electromagnetism of the Island. Or something I didn't thought about, of course...
As for your question, I have to answer yes, I'm pretty sure it is Hawaii. On the upper part of the map there's a dotted line. The Tropics (of Cancer and of Capricorn) are usually marked with those kind of dotted lines, and looking at any Pacific Ocean map, you can clearly see that the State of Hawaii is just south of the Tropic of Cancer. Moreover, the scale seems right with Hawaii there, and not Kingman reef.
You are right about Kiritimati (Christmas) Island. Moreover it would seem that the Island is now near that Island and probably even nearer to another island, Jarvis Island (well, that's what Wikipedia says, as Google Earth has another island under that name...).
Great episode last night, I have to agree. A lot of screen-capturing and mapping wait for me as well, but probably next week. Probably.
Good luck with your update!
Q.
P.S.: I just noticed an unforgivable and horrible mistake... It's actually 160° - 165° West, not East as I wrote more than once... Sorry XD
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