Monday, September 3, 2018

The Sky


There are a lot of different entry points to learning astronomy.  Some people become interested because of science fiction, or the incredible images produced by space-based telescopes, or by an interest in the physics involved ... or, from standing outside at night looking up at the sky.  If you are brought to this interest by the last path, this might well be your starting point.

(As this is one of the possible starting points, some of the language in this section may assume that you are just beginning your trip through these astronomy pages.  If you are not starting here, and have been redirected here from somewhere else so that this language seems clumsy to you, at least know that there was some active thought that went into this.)

The study of the universe will involve shifting our point of view across tremendous distances, from the scale of atoms to that of clusters of galaxies.  One starting point is that of our ancestors thousands of years ago, standing on the ground looking up at the sky.  While this sounds simple, a way of describing what we see in the sky can be difficult.  We are looking at thousands of objects on what seems like the inside of a bowl, extended to a sphere, on which the position of an individual object depends on where on Earth we are, and the time we are looking at it.

This presents a challenge that is commonly answered using an armillary sphere such as the one below.

Building examples is beyond the scope of this work.  Even two-dimensional representations of three dimensional objects (especially those you will want to envision well enough to rotate in your mind) will be challenging, some we will work up to something like the thing below:



                If you don’t have experience working with the celestial sphere, it will be helpful to work through the steps by which it is constructed.  After all, our final display contains a lot of information.  Let us start by considering the stars visible on a clear, moonless night. There certainly are a lot of them, there being about six thousand stars visible to the eye spread across the entirety of the sky.  

Now: imagine yourself looking at stars.



Clearly this diagram is wrong.  

That image almost certainly doesn’t look like you, and there are millions of people who could be reading this for whom the diagram, crude as it is, still manages to be different in major ways from themselves.  Before we move on to the obvious stuff that I’ve missed, I’d like to take a moment to defend this weak version of you, and to explain why I’m going to rely on diagrams even at some times when I could produce a photograph. [Link to come]


Even more importantly, the Earth isn’t there.  What does the Earth around you look like?  As far as this goes, we really don’t care.  This is another instance in which an insistence on being exact would only make the situation far more complicated and confused than it really needed to be.  Drawing in hills and holes and houses would camouflage where the similarities between different areas are far more teachable than getting the shape of the neighbor’s roof right. 






Where does the effect of the Earth come in?  Consider the following diagram of a person standing on the Earth:





 Again, that diagram is extremely wrong.  Clearly, the person is actually much, MUCH larger than a person, but now have another benefit of using a sketch instead of a photograph.  We can start from a point that is obviously wrong, and then start moving toward a more correct view.  Doing this, we can look for patterns that appear as circumstances change and extend those patterns to mimic the real world in a useful way.  Looking at our starting image, we see that the mini-Earth blocks some of the stars.  Let’s make the mini-Earth larger and see what changes.


The larger mini-Earth blocks more stars.  If we look at these two diagrams, and perhaps keep making drawings with the Earth as a larger and larger circle, we can predict that by the time that the sketch of the Earth reaches the size of the Earth, then the lines showing the part of the sky that is blocked is a single straight line.  Thus, I can now draw the visible sky as it is drawn below, with half of stars visible, and half of the stars blocked.

Now we are able to add the stars.  When we stand in a room with other people, a step in any direction changes your view of where people are in relation to each other.  If you are at the center of a larger room, taking one step results in a lesser effect. All these stars are so far away from the Earth to be essentially infinitely far away, and therefore we can treat them as basically fixed to the sphere of the sky.  
At this moment, we stand inside the celestial sphere with half of the sky blocked. We are not done, because the Earth rotates.  The Earth spins around an axis, but it carries us, the air around us, any little things that we toss up into the air at the same rate.  This motion is so universal to our experience that when we look out at the rest of the universe, it appears that we are standing still and the universe is moving around us.  (This illusion took a long time to overcome in our understanding of the universe [Link to come].)

If we were standing at one of the poles (I will use the North Pole just because most people live in the Northern Hemisphere), then we would feel ourselves to be at the top of the spinning Earth, and the stars in the sky would be spinning about us.  A star directly about us (and there is one very close to that [Link To Come] - at least at currently [Link To Come]) would stay in that place, and every other star would trace a circle around the sky, always staying at the same altitude [Link to Come] above the horizon.  Should we take one step away from the pole (which is honestly not a place humans are well-adapted to live), this view would change.

Were we to walk to the equator, we would see one pole on one horizon and the other pole on the opposite horizon.  The stars would no longer be tracing constant circles in the sky, but each star would be above the horizon for half of the day, rising in the east and setting in the west.  If we imagine walking from the equator to the pole, our view of the rotating sky would change from the second situation to the first.



We are able to get something positive out of the illusion of the sky’s motion.  The point in the sky directly above one of the poles, the point which would appear to not move if we were standing at a pole looking straight up, is the point on this imaginary sphere straight out from the Earth’s axis.  We can define these points as the North and South Celestial Poles.  On the celestial sphere, this provides one of the axes on which we can define an object’s position on the celestial sphere.  On the diagram, we can note these points, and define the Celestial Equator as the great circle exactly hallway between the poles.  We can define the position of a celestial object by the angle made by a line from the center to the object and the plane of the Celestial Equator, and that's handled here [Link to come] for convenience's sake.
  



Were we to move to a latitude of 10˚ north of the equator, the point on the sky where the Earth’s axis passing through the Earth’s North Pole strikes the sky (The North Celestial Pole, or NCP) will be 10˚ above the horizon, and this will keep tracking until we reach the pole at a latitude of 90˚ north, and 90˚ above the equator.  This means that from any latitude (I’ll use the Greek letter lambda – [Argh! How do I do this in Blogger?] – to denote this angle in diagrams) the North Celestial Pole will be that angle above the horizon.

Stars close to the pole in the sky will always be visible above the horizon.  Often, a circle will be added in to denote this mark.  Any star inside this circle will always be above the horizon, and can be observed any time, any clear night. We have to pay for this; there will be an equally sized area around the other pole that will be invisible to us at every point during the year.

The next complication is that the Earth's rotation is tilted by 23.5˚ to the Earth's orbit

This means that the path of the Sun in the sky (over the day and over the year) is tilted to the Earth’s orbit, and that will carry the Moon and the planets with it.  That accounts for the remaining set of circles, but that topic has enough interest to deserve its own page. [Link to come]

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