Jason Kendall's Introductory Astronomy Course

Adjunct faculty in Astronomy at CUNY Hunter (2015-2018) and William Paterson University (2011-2020)
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Angular Measurements and the Celestial Sphere

In this video, I talk about how we navigate our way around the sky using angular measurements, and I introduce the basics of the Equatorial Coordinate system.

Lecture Notes for This Video

Module 1: Foundations of Observational Astronomy: The Moon, the Seasons, and Mapping the Sky

  1. Navigating the Night Sky
  2. Angular Measurements and the Celestial Sphere
  3. The Celestial Sphere
  4. What Causes the Seasons?
  5. Lunar Phases and Months
  6. Lunar Eclipses
  7. What is a Solar Eclipse?
  8. Watching the Total Solar Eclipse of August 21, 2017
  9. Cosmic Distances using Parallax
  10. How do we know that the Earth is Round?
  11. How Big are the Sun and Moon?
  12. Geocentrism is False

Video Transcript

00:00:00:00 - 00:00:22:15
Now we're going to look at the positions of stars on the sky. We're going to look at angular separation and we're going to look at a new coordinate system, The equatorial coordinate system that helps us navigate on the celestial sphere. So let's start with this obvious picture of the night sky. This was done with a ten second exposure with a DSLR camera on a tripod.

00:00:22:17 - 00:00:50:23
And what we see is way off in the distance, mountains covered with snow and trees and things. So we know we're in a very dark location because it doesn't look like there's any ambient light. Notice above, we see stars and it's kind of supremely obvious to state. But the stars are in different places on the sky. And the way we distinguish one place for another from another is not with a physical distance between left and right on the sky.

00:00:51:00 - 00:01:12:00
We're pretending for now that the stars are printed on a dome, on the sky. And so they stay fixed on this dome. On the sky. And that's not a terrible way of thinking for this purpose. In fact, it's extremely useful. We know that the stars are not fixed on the dome, on the sky, but it's useful for this purpose.

00:01:12:05 - 00:01:36:26
And this is the basic concept of the celestial sphere. We need to remember that we're not using a yardstick or a tape measure to measure angular separation. We're simply looking at directions and we're saying we're going to make some kind of way of devising a direction on the sky. Also, obviously, we don't see the stars move with respect to each other.

00:01:36:27 - 00:02:00:19
Night after night, they rise and set maintaining the same patterns on the sky. So therefore, they're pretty reliable. Now we're going to do two things. We're going to learn how to measure angles on the sky, and we're going to find a good way to map them with a fixed coordinate system. Our next step is to look at the angular separation of the sky.

00:02:00:21 - 00:02:23:20
And if we have two directions, say, direction X and direction Y and you're looking at them, it doesn't matter how far a star is away on X or how far a star is away on Y. Now, they could be very far away or they could be very near. It doesn't matter. We don't care about the distance to the object for angular separation.

00:02:23:25 - 00:03:04:20
We only care that we're looking in one direction or another. And it is that angular separation that defines what we're talking about. So this angular separation is only on the sky and has nothing to do with the physical distance from any of these objects. Next, we can define angular measurement using a very simple tool. Our hand. So if you take your hand and arm's length and make a fist and you put your your your right hand of your fist at arm's length and close one eye and hold it up on a dark night where you can see many stars and put one star on the right hand side of your fist and one star on

00:03:04:20 - 00:03:31:02
the left hand side of your fist. Those stars will be roughly ten degrees apart. Also, you can use the ten degree idea to start the same thing. Look straight up towards the zenith. Hold your fist out and then put the right your thumb side of your fist at arm's length, straight up. And then it will take only nine fists to get to the horizon.

00:03:31:05 - 00:03:54:26
That's because the altitude of the zenith is 90 degrees. So it will take nine fists to come all the way to the horizon. For smaller, angular measurements, we can use our pinky held at arm's length. And you close one eye, hold your pinky at arm's length. And if there are two stars, one on your right hand side of your pinky and one on your left hand side of your pinky, then they're separated by about a degree.

00:03:54:28 - 00:04:21:20
Again, your hand can act as a ten degree thing for a fist. Your little finger is about one degree across. And for those inclined to use a piano and open octave, which is separate your thumb and pinky as far apart as you can, and then put those against the sky your pinky pointed far out to, let's say, your right handed and you point your right pinky all the way out in your left hand and your thumb all the way to the left and separate them as much as you can.

00:04:21:22 - 00:04:45:15
And that is about 15 degrees if you hold your hand at arm's length and close one eye. Now, we can make very small, angular measurements. But let's say you take your pinky and hold it out in arm's length. Guess what? Since your pinky is about a degree, the sun and the moon both are only about half the size of your pinky held at arm's length.

00:04:45:17 - 00:05:10:29
They're almost exactly the same size. And that's why we can have total solar eclipses. Anyway, let's go on. Angular measurement can then be broken down into smaller and smaller increments. We all know that there's 360 degrees in a circle, and therefore there are 36 fists all the way around, a circle held at arm's length. You could just use your arm back and forth and back and forth all the way around.

00:05:11:01 - 00:05:35:12
And we can also then say we can look at each pinky is a degree. So one of those degrees is going to be 360 pinkies all the way around, held at arm's length. We can now divide those things up into smaller and smaller angles. And we do do this because there are things that are very separated by very small angles in the sky.

00:05:35:14 - 00:05:56:24
Now, imagine that you took your finger, your pinky held at arm's length and the mark 60 little tick marks from the left side to the right side across your pinky nail, and then held that arm's length and close one eye and look at that. And those 60 evenly made markings across your pinky. Each would be one arc minute.

00:05:57:01 - 00:06:21:16
So there are 60 arc minutes in a degree, and that's a very tiny angular measurement. And that's why it's actually we call it an art by nuit, because it is an extremely minute measurement and you could in theory have each of those 60 tick marks that you had your cosmetologist paint very carefully on your pinky nail with a very fine tooth.

00:06:21:19 - 00:06:49:16
I guess 1a1 camel hair brush or something like that, a very fine brush with one hair. And then you put 60 tick works in between each of those tick marks on your pinky. So now you have 3600 tick marks across your pinky. Each one of those tick marks across your pinky would be one arc second. That is an incredibly, incredibly small angular measurement.

00:06:49:18 - 00:07:16:21
So there are 360 degrees in a circle. There are 60 arc minutes in as in a degree, and there are 60 arcseconds in an arc minute. So there are 3600 arc seconds in every degree. So a second, an arc second would be the second might be a new portion. So it is a second order minded thing. So these are really tiny angular measurements.

00:07:16:24 - 00:07:38:04
If you do manage to get a cosmetologist to do that on your pinky, better give that person a really big tip. So the angular size of some object actually depends upon its physical size and how far it is away. Because if something's really near and it's very small, then it'll look big. But something really big and really far it'll look small.

00:07:38:09 - 00:08:09:00
My when I say look small, I mean its angular size is small. Next we can then pretend that all of the stars we can pretend. And this is a really big pretend that all the stars are on this dome that we're going to call the celestial sphere. And that is a very interesting thing to say, because now we're making up anything, a celestial sphere that is around to which the stars appear to be fixed.

00:08:09:02 - 00:08:32:07
And we want to be I want to be really clear, there is no such thing as the celestial sphere. It's a made up thing that's been with us since really ancient times and has formed philosophical thought for millennia, which is to go all agree that the altitude and azimuth system with its grids that we saw in the previous video, as well as the ecliptic and equatorial systems are being portrayed on a sphere.

00:08:32:13 - 00:08:54:25
This is just a really helpful map for getting us around the sky. So the two stars, as we can see from this angle, as viewed from Earth, have some angular separation on this sphere. And what does that kind of look like? The celestial sphere, again, is an imaginary sphere around the earth on which all heavenly objects appear to be located.

00:08:54:28 - 00:09:22:10
It appears to rotate around us. We know the earth is rotating, but we can think of the celestial sphere as rotating around us. The celestial sphere has in the celestial equator, the North Star Polaris is near what's called the North Celestial Pole, where nothing appears to rotate around it. And this equator is 90 degrees away from the North Celestial Pole, as well as the South Celestial Pole.

00:09:22:12 - 00:09:57:03
Equatorial coordinates are a different way of finding our way around the sky. We can establish that the North Celestial pole where Polaris is is that 90 degrees north declination or positive declination? -90 degrees declination is the South Celestial pole, And this is measured with respect to the celestial equator. The celestial equator is then matched as a kind of it's like an extension of latitude out into space.

00:09:57:06 - 00:10:22:19
And so that's our good way of thinking about it. And then we can also look at the right ascension, which is the hour, the number of hours of angle from the vernal equinox, which and the vernal equinox is where the ecliptic meets the celestial equator. The celestial equator is fixed with respect to the stars, and that's the extension of the Earth's equator out into space.

00:10:22:21 - 00:10:49:28
The ecliptic is the path that the sun takes, and the vernal equinox is one of two nodes where these two circles intersect. And what we do is we say that we're calling right ascension in hours, not degrees. And so there are 24 hours around the North Celestial Pole, and each of these hours is 15 degrees. That's our way of defining these two coordinates.

00:10:50:04 - 00:11:20:16
And that's helpful because when you think about, you say, wait a second, something that's on the celestial equator. If we wait one hour, it will move 15 degrees from its present position. So that's where that really comes from, right? Ascension is measured eastward around the celestial sphere. Once again, declination is an angle north or south of the celestial equator towards the poles and all objects in the sky can be given on terms of these two coordinate.

00:11:20:18 - 00:11:45:21
And this is a map on the celestial sphere, which is fixed with respect to the stars. Again, angular measurements are not distance measurements. They are projections on the sky. And we can say on the sky because we are pretending that the sky is this celestial sphere and things could be greatly distant from each other. Stars can be tens of light years away or thousands of light years away.

00:11:45:23 - 00:12:10:20
We just remember that this is a fictitious concept. So what does this mean? It helps to actually look at star trails. Star trails. Help us understand what we mean by the celestial sphere. And all you have to do is take a camera and open the shutter for some period of time and let the stars move. If you have to be in an extremely dark location for this to occur, this is not taken in daylight.

00:12:10:24 - 00:12:37:17
This is taken at night. And the reflection off of these rocks is a is is from starlight or even moonlight. What we're looking at here is this particular image taken by Matthew Seville. The stars in this time, exposure in the northern sky move counterclockwise around one point. So they seem to be rising on the right in the east and setting on in the west on the left.

00:12:37:20 - 00:12:58:15
There's almost no motion in the center, and that indicates where the celestial pole is. The altitude off the horizon of the celestial pole indicate to your latitude. So if it was directly overhead, you'd be at the North Pole. If it's directly on the horizon, you'd be at the equator. And if just like this, it's like 30 or so degrees.

00:12:58:15 - 00:13:18:16
It's about 30 or so degrees north latitude. And you can actually tell how long this exposure was by how long the Star Trail is and the length of the star trails in this image look less than 1/12 the way around of a circle. So I'm going to guess that this is roughly about a 15 minute exposure. And North is, of course, at the center of this image.

00:13:18:19 - 00:13:39:09
East is to the right. Again, Polaris is right in the center. And you can see that's the brighter ish star that seems to not be moving. And the only reason there's much brighter there is simply because it hasn't moved and because it hasn't moved it over exposes on the image that you see on the sky. Notice how some stars never rise or set.

00:13:39:09 - 00:14:03:04
Those are called circumpolar and they go below the North Pole. North Celestial Pole below Polaris. And they never go below the horizon. There are a number of stars there. Circumpolar. Now let's look east. This is a different photograph taken by Juan Carlos Casado. And this was published on the The World at Night Board. And so you can go check that out.

00:14:03:07 - 00:14:32:04
But I'm really looking at this concept from we're looking at the celestial equator. To the left of this image is to the direction of the North Celestial Pole. And to the right of this image is towards the South Celestial Pole. And directly in the middle of this is the celestial equator. This looks like this because we've projected a dome onto a two dimensional surface and allowed star trails to have it.

00:14:32:06 - 00:14:53:11
These star trails, of course, this takes many this was a many hour image. And he also superimposed it from a he did a secondary exposure on top. And the thing that goes dot, dot, dot, dot, dot across the middle, that's the sun. And this was done at the roughly at the equinox so that the sun could rise due east.

00:14:53:13 - 00:15:19:24
But you can see that the star trails appear to curve around the north celestial pole appear to curve around the south celestial pole, but they seem straight towards the east. And that's what we mean by the celestial. We can think of that as a projection of the latitude out of this space. So the latitude of the equator projected out into space is that data, Is that kind of dashed line which is representative of the sun.

00:15:19:27 - 00:15:36:27
Next time we're going to look at the celestial sphere in greater detail and go over all of these using A's sky simulator Stellarium as well as Skysafari. We'll see you next time.