Prime Meridian, Dubhe and Merak

What is the Prime Meridian? And while we're at it, what's so special about the combination of Dubhe and Merak?

To really understand the answers, we go back to this table.

POINTER STAR LOCATIONS
Star Name	J2000 Right Ascension	J2000 Declination
Dubhe	11^h 03^m 43.67152^s	61° 45′ 03.7249″
Merak	11^h 01^m 50.47654^s	56° 22′ 56.7339″
Polaris	2^h 31^m 49.09456^s	89° 15′ 50.7923″

We encountered this Pointer Star Locations table when we were trying to figure out which way is up. We know that Right Ascension has something to do with what time a star starts rising in the sky, and that Declination tells us how far down from straight up we will find the star. However, we also know that both of those are just sort-of explanations.

Let's clear up the sort-of problem. The answer involves the Prime Meridian.

The Prime Meridian

To make sense of the table and to really understand pointer stars, we should start with the Prime Meridian.

Let us suppose we are standing at the Royal Observatory, Greenwich. Greenwich is NOT pronounced like a green sandwich. It is pronounced GREN-itch as if there were no w and with the Gren part pronounced like when or then. The Royal Observatory was ordered to be set up by King Charles II in 1675 a bit to the east of London (downstream on the Thames River) and was placed under the direction of the first astronomer royal John Flamsteed. You will come across John Flamsteed's name a lot in astronomy.

The astronomers working at the Royal Observatory decided that the Prime Meridian would be located there and this is now accepted by all astronomers. In other words, if you are standing at the Royal Observatory, your longitude is officially exactly zero. Everybody else's longitude tells how far to the east they are from the Royal Observatory. When we talk about how far we mean how far in degrees, not kilometers, because degrees are much more useful in astronomy and navigation

By the way, the longitude of 12366 Ridge Circle is −118° 29′ 3.8394″. That is, it is about minus 118 degrees to the east... or, easier, 118 degrees to the west. We use minus to go west and plus to go east from Greenwich, England. Dad was born in a town called Greenwich, Connecticut.

Why is there a minus sign in −118° 29′ 3.8394″? To go all around the world headed east from Greenwich, England you go 360 degrees total. In other words, the circle is divided into 360 degrees. Actually, that’s what “degree” means when we measure angles. One degree is 1/360 of the way around a circle. A circle is divided into 360 degrees, than each degree is divided into 60 minutes and each minute is divided into 60 seconds. Degrees, minutes and seconds are used to tell time (as in clocks) as well as to describe angles in mathematics, no matter what time it is. “Minute” (pronounced my-NYOOT) means small, so the term “minute” (prounced MIH-niht but spelled the same) is a small part of a degree, or, nowadays, 1/60 of a degree or 1/60 of an hour. A second is the next division of a degree or an hour (in other words, not the first, but the second small division), and is nowadays used to mean 1/60 of a minute.

So 12366 Ridge Circle is 118 degrees, 29 minutes 3.8394 seconds west of the Prime Meridian that runs through the Royal Observatory at Greenwich, England. Please notice that instead of writing out “degrees”, “minutes” and “seconds” we use punctuation marks, thus, −118° 29′ 3.8394″.

Latitude

Longitude tells you how many degrees east or west a place is from the Prime Meridian, but it does not tell you how far north or south the place is. For this we use latitude. The idea of latitude came about because of astronomy.

But let’s get back to the actual Prime Meridian at Greenwich.

Suppose you are standing there, looking at the sky, and let’s pretend that it is always dark so that you can see the stars all day and all night. Astronomers have mapped the sky in a way that is similar to mapping Earth. However, instead of degrees of longitude, and degrees of latitude we use “hours” of right ascension and degrees of declination.

Declination

Let’s handle declination first. If you keep looking, you will notice that all the stars are slowly circling one star: Polaris. They make it all the way around in 24 hours. They all seem to be going counter-clockwise. That is, when you see them under Polaris in the sky they are moving to the right, then up, then left to pass over Polaris and then down to where they were before. Stars that are at a greater angle away from Polaris seem to set as they get toward the West and later to rise from the East. In fact, that is what the Sun does: rises in the East, circles around Polaris and then sets in the West. Of course, you can’t actually see this because the Sun is so bright that it lights up the air enough to make Polaris invisible... but we are pretending that it is staying dark enough so that you can see the stars even during the day. This is happening because the Earth is turning to the right, if you are facing north. Stars on your right (that is, stars to the East) therefore seem to be moving up and then left.

In any case, each star always stays a constant angular distance away from Polaris, thus making its path a circle. That angle is the star’s “declination”.

You might ask why use a word that is related to “decline”, which seems to mean something like the star being lower. The answer is that if you were standing at the Earth’s North Pole, then Polaris would be the highest star in the sky, and all of the other stars would be lower. How much lower? Aha, that amount gives us their declination. Polaris is straight up, which is an angle of 90° away from being straight across (that is, on the horizon, which would be about at ground level). Therefore, other stars are at a lower angle, so their declination would be, for example, 72° or 10°.

A star that is right on the horizon would have a declination of 0°. But there are stars that are even lower, that would be visible if Earth were transparent, or that you would see if you moved south, away from the North Pole. The declination of those stars is a negative number, less than zero. If you could see through the Earth all the way down, a star that is straight down would have a declination of -90°. That declination would be straight up for someone standing on the Earth’s South Pole.

Right Ascension

This brings us to right ascension.

The fact that Earth spins on its axis gives us a convenient way to measure north and south. We measure down from the North Pole, which the axis passes through. The spin also defines the “Equator”, which is the circle around Earth that is equally far from the North and South Poles... halfway south from the North Pole, with a latitude of 0°. For latitude there is no natural place to start. That is why English astronomers chose the Royal Observatory as the place for 0° 0′ 0″, that is, for the Prime Meridian. Actually, there was an older Prime Meridian defined in the city of Prague when it was the capital of the Holy Roman Empire. When that empire pretty much collapsed, the English went their own way, and the rest of the world has followed.

The same kind of problem exists for right ascension. If you continue the Earth’s axis into the sky, in both directions you have two points that all the stars seem to travel around, so we call those the North and South Celestial Poles. We measure declination from the North Celestial Pole, as you know. But there is no particular place to start measuring how far around the Pole a star is.

Astronomers have decided to pick a place in the sky from which to measure. It is the place where the Sun is exactly over the Earth’s Equator at the instant that Spring begins. This point is in the constellation Pisces (the two fish). Everything between this point and the North Celestial Pole has a right ascension of 0^h 0^m 0^s. The same is true for everything between this point and the South Celestial Pole.

Suppose we are at the Equator, facing north with the Sun directly overhead. In one hour the Sun will have moved west, as will all of the other stars (pretend we can see them even during the day). If we now draw lines from straight up all the way to the Celestial Poles, we are crossing stars with a right ascension of 1 hour. Later, at 2:00 pm where we are standing, similar lines would go through stars with a right ascension of 2^h 0^m 0^s. These lines that we are drawing from straight overhead to the Celestial Poles are our “meridian”. Wherever you are you can draw a local meridian except, of course, if you are standing exactly on the Earth’s North or South Pole.

Because Earth rotates toward the east, the Sun and other stars rise (that is, ascend) in the East, which is on the right if you are facing the North Pole). If you were on the Equator directly under the Sun at noon on the first day of Spring, your meridian would be at right ascension 0^h 0^m 0^s and the stars on your meridian 20 seconds after 8:30 pm would have a right ascension of 8^h 30^m 20^s. They will have ascended to there, the highest they will ever get in the sky, from the right, if you are facing the North Pole. This is the idea behind “right ascension”.

Hours vs. Degrees

We have seen how the north-south direction is measured as degrees that are the same as degrees we use for measuring angles in mathematics. However, measuring around the circular path of stars is usually done with hours. Stars complete their circle in 24 hours. Since a circle has 360 degrees, then one hour’s worth of travel would be 1/24 of that, or 15°. When we are looking at the sky, sometimes it is easier to measure how far one star is from another in terms of degrees. If we then want to look something up on a star map, we should keep in mind that for the east-west direction we are looking for right ascension and should convert from degrees to hours by dividing by 15. In other words, if we are moving 45° east, which is half of a right angle (the angle between adjacent legs of a rectangle), we are moving 3 hours of right ascension.

A Repetition

If you watch the night sky for a few hours, you should notice that the stars are all circling around a point in the sky very near the star named Polaris. We call that point the sky’s North Pole. If you take the axis of Earth (the line that Earth turns around) and continue it into the sky from the earth’s South Pole through the North Pole, you go through that point. If you extend the line the other way, from the earth’s North Pole through Earth, through the South pole and into the sky, you go through the sky’s South Pole. The stars seem to circle around that point also.

A sky map is the inside of the surface of a sphere. The right ascension lines run down the map like the sections of an orange or the grooves in a pumpkin. All the right ascension lines meet at the sky’s North Pole and at the sky’s South Pole.

Everything halfway between the North Pole and the South Pole lies on the Equator... those points are all equally far from the North and South Poles. To measure the position of an object to the north or south of the Equator, we use declination. For everything on the Equator, the declination is zero: zero degrees, zero minutes, zero seconds. The North Pole is at 90 degrees and the South Pole is at −90°. Measuring declination in terms of hours doesn’t make sense, since the displacement in degrees from the equator doesn’t change with Earth’s rotation.

Our Question

So now we can explain our table and proceed to answer the first question: what is so special about the combination of Dubhe and Merak? Here is the table again.

POINTER STAR LOCATIONS
Star Name	J2000 Right Ascension	J2000 Declination
Dubhe α Ursae Majoris	11^h 03^m 43.67152^s	61° 45′ 03.7249″
Merak β Ursae Majoris	11^h 01^m 50.47654^s	56° 22′ 56.7339″
Polaris α Ursae Minoris	2^h 31^m 49.09456^s	89° 15′ 50.7923″

At this point, compare the locations of Dubhe and Merak. The declinations of the stars are different from each other (by about 5°). However, you can see that the right ascension of Dubhe is almost the same as the right ascension of Merak. By the way, those numbers in the table were correct at “J2000”, that is, at about noon on January 1, 2000. Things have changed since then, but very little.

Because the right ascensions of Merak and Dubhe are almost the same, if we draw a line between Merak and Dubhe the line will pretty closely run along their right ascension lines, or to take a right ascension line between the two stars, the line will be close to running along 11^h 2^m. In other words, the line between the stars is almost a right ascension line. But all right ascension lines end at the sky’s North Pole, so a line between Dubhe and Merak will aim almost straight at the North Pole. Now if you look at the declination of Polaris, you see that Polaris is very close to 90° declination, which is the declination of the North Celestial Pole. That means that the line we have drawn almost runs through Polaris. To put this another way, the line from Merak through Dubhe points toward Polaris.

Diagram of pointer stars aiming toward Polaris

Now the difference in declination between Merak and Dubhe is a little more than 5°. Do the subtraction. It is about 5° 22′ 7.0″. The difference between Polaris and Dubhe is 27° 30′, about 5 times as much. Therefore, if you draw a line from Merak (beta UMa) to Dubhe (alpha Uma), and then continue it for 5 times that distance, you get very close to Polaris (alpha UMi). If you hold your arm out straight, the width of your three middle fingers held together covers about 5° of sky. That can help you measure the angular distance between Dubhe and Polaris.

You are using Merak and Dubhe as “pointer stars” to help find something in the sky. What you find is Polaris, and also the North Celestial Pole (the North Pole of the sky) which is almost the same spot.

There is no meaning for the right ascension of the North Celestial Pole: it does not “ascend”... it just stays in the same place and everything else in the sky goes around it. (Actually, not everything else: the South Celestial Pole also stays in the same place.) The closer you get to a pole the less right ascension matters, since all the right ascension lines crowd together as they approach a pole. When it comes to star finding, we can ignore the right ascension of Polaris because its declination is so close to 90°.