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|We're in a galaxy?|
What does it look like?
INTRODUCTION. This is another cosmological project that would, on the surface, seem dauntingly difficult, but in reality it isn't all that difficult at all. You should go back to familiarize yourself with the project on whether the universe is lumpy. Much of the data you will need can be gleened from those observations.
Since you have already determined that the universe is lumpy, and that one of those lumps is very close by - or possibly that we are even inside a lump, you must hypothesize about what shapes might be assumed by our local lump - our local galaxy. It might look like a glob (left of the title) or like something more drawn out in either a line or perhaps appearing that way because you are looking sideways at something flat and spread out (right of the title).
The glob. Yes, that is a proper astronomical term because one class of galaxies are called globular galaxies. If you determine that our local galaxy looks like a roundish glob in the sky, you know that it must be either something spherical or it is a disk, which you are observing from either above or below.
The line or something flat. If you see something vaguely like the righthand figure, you must now determine whether it is like a long line of stars - sort of a hotdog-shaped cluster of stars, or whether it is something flat.
The trick of determining the shape is in being able to take a look in the opposite direction, but how do you get the look out the other side of the earth and see anything? Afterall, the bright sun is over there - so that an email friend living on the other side of the world couldn't help you! So what can you do? The answer is: "wait 6 months."
After six months, when the earth has gone exactly halfway round its orbit, you can look into the night sky in the opposite direction from which you first viewed our galaxy. If you don't see any lumpiness, that means that the galaxy was totally, or almost totally out in that first direction and thus would be either a line or a disk seen from on top. However, if you do see some sort of aggregation in this second view also, then you can draw one of two conclusions. If your first view was of a globular galaxy, then the aggregation of stars you see must be those that lie a little further from the center of that galaxy that you do. And if you first view was of some sort of swath of stars, and you see a swath also in your second view, your galaxy must be a huge moderately thin sheet of stars and you are in it somewhere.
Determining whether the sheet of stars is in a square or a circle is a matter for more advanced studies. Supposing you had unlimited earth-bound telescopic equipment, how could you tell if the galaxy was a disk or a square?
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