The Little Dipper and the Earth’s Tilt and Rotation

In this Night Sky post I will discuss the Big Dipper’s companion constellation, The Little Dipper, and the most important (for history) star in the night sky, Polaris. We’ll also check out the earth’s tilt and why that even matters. If I can’t convince you how important the earth’s tilt is to YOU, then I’ve failed at my job here!

Meet the Little Dipper

The Little Dipper is more difficult to find in the night sky because the stars have a lower apparent magnitude (brightness) than the stars of the Big Dipper.  Polaris is the easiest to spot at apparent magnitude 2.02. This can be done by using the Big Dipper to help point us in the right direction. Once you have spotted the Big Dipper, use the stars at the far end of the cup, Merak and Dubhe, to point you in the direction of Polaris as shown in the drawing below.

How to locate Polaris and the Little Dipper using the easier to see Big Dipper

Polaris is about five times farther than the distance between Merak and Dubhe.  The reason this “only fairly” bright star is so important is because the axis of the earth’s rotation points almost directly at Polaris, and so it is an indicator of true north. Wherever you are in the northern hemisphere, if you can find Polaris you have a natural compass and a sense of direction. The stars Kochab, apparent magnitude 2.07, lies on the cup end of the Little Dipper and is almost as bright as Polaris. Pherkad, apparent magnitude 3 is a bit dim, but most people can still see it if they are far enough away from the city lights and if it is positioned high enough in the sky. Yilden (4.85), Ahfa al Farkadain (4.32) and Anwar al Farkadain (4.95) are dim enough that you may have to “imagine” you see them. Interestingly, Ahfa al Farkadain and Anwar al Farkadain, have retained their Arab names (see Night Sky One) because they were deemed too unimportant for the Europeans to give them names later.

Polaris is a yellow white “supergiant”, in the rare class of Cehpeid variable stars, which briefly means it varies in magnitude, unlike our sun which burns rather consistently. Kolchab, meanwhile, is a orange giant star. It is about 126 light years from the sun and it shines 130 times brighter because of it’s size. It’s surface temperature is of  4000K is cooler than our sun’s 5770K, however, which gives it a more orange color instead of white.

Orienting Our Self in the Solar System.

So as I mentioned above, the earth rotates around an imaginary axis that passes through the north and south poles once/day. The earth, in turn, revolves around the sun once/year and this describes a plane that does not change. This plane is called the “ecliptic” and the earth’s axis of rotation is tilted 23.5 degrees towards it. Interestingly, the other planets revolve around the sun in nearly the same plane as the earth and as shown in the picture to the left.

If the planed the orbital of the earth makes around the sun is taken to be zero, we can see here that the other planets vary by only a few degrees. Pluto is a bit of an exception; it is also not considered a planet by some, being far smaller than even our moon.

One might guess that all the planets going around the sun on the same plane is an indication that they were formed in a similar way at the same time. While this may be true, it is also true that planets are drawn to the same orbital plane over a long period. Imagine a rogue planet suddenly entering our solar system. The gravity of this new planet will be felt by the old planets and vice versa. Now if this doesn’t throw all the orbits completely out of whack (to the extent that they could collide or be thrown out of the solar system entirely). over time their mutual attraction to each other will eventually draw them all into nearly the same plane. Notice how different Pluto is. Whether Pluto can even be considered a planet is a matter of debate nowadays, but in any event, it is too small (low gravity) and too far away from planets like Jupiter to be pulled down. Because all the planets lie in about the same plane, they also follow roughly the same path as the sun across the sky as the earth turns. Yet one winter night close to Christmas, I was looking up at the sky, and saw that both Jupiter and Mars were quite high in the sky at the same time that the sun was so low in the sky during the day. This was curious to me until I thought it out more thoroughly. At night I was staring at the part of the sky where the sun would be a the beginning of summer! So, of course the ecliptic would be higher. The picture of the evolution of the four seasons below may help you visualize this.

The Four Seasons: Why you plant your garden, swim in the lake, rake the leaves, and shovel the snow off your driveway, at different times of the year.

Have you ever had the experience of being surprised by what other people don’t know? This happened to me with regard to why the seasons change. I have met many highly intelligent and educated people, some even in other sciences, that had wrong ideas – the most common one being that we must be closer to the Sun in the summer. I hope this doesn’t sound like I’m being an intellectual snob. I do, however, think it is terribly important for people to know what is perhaps the most important astronomical concept of all. After all, we change our entire wardrobe in winter versus summer, our heating and cooling bills change, it’s time to put the snow tires on and off, the world around us totally transforms – surely, this is a curious thing!! So I had to include a discussion of it somewhere in this blog!

Basically, the reason the seasons change has to do with the 23.5 ° tilt of the earth toward it’s ecliptic, or orbital plane, so that when the northern hemisphere is tilted toward the ecliptic, the southern hemisphere is tilted away, and vice versa. When one hemisphere is tilted toward the sun it receives more heat energy, which I will refer to as “insolation,” than when that hemisphere is tilted away. The reason why it receiveds more, or less, insolation is due to two factors seen in the figure below – which draws out the passage of the earth around the sun during one year.

The Change of Seasons over the Course of the Year. During summer, when a hemisphere is tilted toward the sun, the days are both longer and the sun is more direct. I have drawn the Earth at the correct 23.5° angle, but the relative sun/earth size and distance are way off!

First, and most obviously, the days are longer in the summer when the earth is tilted toward the sun. Look where I live, which happens to be exactly halfway between the equator and the north pole (really!). On the first day of summer, June 21st, my trip as the earth turns once (one day of course) passes through 15 hours, 34 minutes of light, the longest day of the year. On the first day of winter, December 21st, one turn of the earth takes me through only 8 hours, 49 minutes of light and that’s my shortest day. See the dotted lines. Obviously, the amount of insolation I get due to just how long the sun is shining is greatest on June 21st and least on December 21st. Secondly, and more subtly, yet very importantly, notice that on June 21st the sun is shining most directly down on my head (my zenith in the picture). Again it is the opposite on December 21st when I am tilted away from the sun and the sun is closest to the horizon. Imagine a flashlight shining directly down onto a tabletop and the nearly perfect circle of light it creates. Now, shine the light at an angle to the table. The light will be spread out over an extended oval and shine less brightly in any one place.

In this diagram, a one mile wide band of light shining directly from above makes a one mile diameter circle on the ground. If this one mile band is tilted 30° up from the ground, the diameter of light it makes is 2 miles.

So, to summarize simply, the sun shines longer in the summer, and when it does, it shines more intensely also. Finally, over the courseof a year, this change in insolation occurs slowly as the earth procedes in it’s orbit; on the first day of spring and fall, the days and nights are exactly the same length and the earth is tilted neither toward nor away from the sun.

Now I hope it is clear why my weather warms up as summer approaches and cools off as winter approaches, but why aren’t the average warmest and coldest days on June 21st and December 21st respectively? This is because, although the insolation is greatest/least on those days, the temperature depends on the heat energy escaping back out into space too, not just that coming in. The warmest day and coldest day, when the incoming heat equals the outgoing heat  is usually just about a month after the longest and shortest days. It takes some time to warm up and cool off.

Circumpolar Stars

Circumpolar stars are those stars that are always in the sky above your head, day or night, no matter what time of the year. If one is standing at the north pole (A in the diagram below), with Polaris directly above your head (zenith), or the south pole, which doesn’t have a star at the zenith, all the stars are circumpolar. This also means that Santa Claus, who I heard lives at the north pole (for just a wee bit longer), and the scientists working at the Amundsen-Scott South Pole Station, never see the same stars as the other. For people living on the equator (C on the diagram below), a generally more hospitable place, there are no circumpolar stars. This can best be seen in figure below describing the change of seasons where the night side of the earth in summer faces in the exact opposite direction than the night side in winter.  If you live on the equator, there are summer stars and winter stars and on June 21st and December 21st they don’t match at all. You’d be lucky to see Polaris, because it is sitting right on the horizon.

Ah, but what if you live in between the poles and equator like I do? This gets tricky. The picture I have drawn here looks complicated, but I’ll try and simplify it with the most salient points.  I live at B on the picture below with arrows pointing to Polaris and my zenith (overhead).

I live at “B”. Stars on the green side I see in the summer. Stars on the red side I see in the winter. Stars at the top are always above my head (even in the day). They never set. Some winter stars I could see in the summer, but they are above me when the sun is shining, and vice versa.

If you take a straight line that just touches the earth once where I’m standing (the tangent), on June 21st, you will get the green line and stars in the picture to the right of that line are visible in summer [Technically, since the earth is turning during the night, you see a half sphere of stars.] The stars to the left of the red line in the picture, and the half sphere it describes during it’s nighttime turn, are visible in the winter.  The blue cone at the top indicates where the two half spheres overlap. Stars beyond this cone are my (45 degrees latitude) circumpolar stars; stars I can see at night all year long. Here is a little movie of what my circumpolar stars look like at night. By now you should recognize The Big and Little Dipper and how they all revolve around Polaris. You will meet Casseiopia, (the “W”) opposite the Big Dipper, as our next constellation.

The circumpolar stars moving around Polaris at approximately 45°N latitude.

The Precession of the Equinoxes  



Ahem! Now this may sound technical, but it’s probably easier to visualize than the circumpolar stars.  I spoke above how the north pole of the earth’s axis is always pointed in the direction of Polaris. Well….not quite always.  The earth can be thought of like a large top that wobbles as it is about to fall; in this case making one complete wobble every 26,000 years. During your lifetime the Earth will always be pointing toward Polaris, and in fact, it will point most closely toward Polaris about one hundred years from now. We can see this in the picture to the lower right.

The circle shows where the earth’s north pole will point during the years numbered around it. In 14,000 years it will point toward Vega on the bottom of the circle.

The circle represents where Earth’s axis points over one 26,000 year period. At the year 2000 we were up near the top of the circle approaching Polaris at the end of the Little Dipper. The very bright star on the bottom of the picture is Vega (the star we used as a benchmark for Apparent Magnitude before) and our axis will point toward Vega in the year 14,000. Then, we, or whoever is here, will probably call Vega the “North Star”. The cause of this mechanical wobble is different from the top, in which case gravity is pulling it down. The cause of the earth’s slow wobble is also gravity, but this time it is the gravity of the sun pulling on the earth from the side.  The exact physics is more tricky than I care to explain very carefully here. I will  say, however, that the earth is not a perfect sphere, but bulges at it’s center from the centrifugal force of it’s spin, and that it is the sun pulling differentially on this bulge from one side compared to the other that causes this wobble. If the earth were a perfect sphere the earth would not wobble at all.

Whether or not this wobble of the earth’s axis seems important to you at this point I doubt. But indeed, it has a reasonably large impact on the earth. This is because the earth’s revolution around the sun is not a perfect circle, but an ellipse (like an oval).

The earth is current at perihelion (2) in the beginning of January, and at aphelion (1) in July. This will be the reverse in 13,000 years. Note that this picture exaggerates the difference between perihelion/aphelion for illustration purposes.

The sun’s center is just slightly toward one side of this ellipse, so there is, in fact, one time of the year when the earth actually is closer to the sun than at any other time (the perihelion). But this does not vindicate the “earth is closer to the sun in the summer” theory of the seasons. In fact, the earth is actually closest to the sun on January 2nd at the moment and by a couple million miles compared to it’s average of 93 million miles. Furthermore, Earth as a whole, due only to its distance to the sun, does indeed get more insolation during our northern hemisphere winter, which makes our winter slightly warmer than it would be otherwise, and summer a bit hotter in Australia. Because of the earth’s wobble, however, the date in the year when the earth is at perihelion travels all the way around the calendar until it finds it way back again after 26,000 years. Thirteen thousand years from now the earth will be closest to the sun in July, or our northern hemisphere summer. “Precession” is simply a strange and fancy word for this trip around the calendar. One might imagine that this precession could be the cause of natural climate change. After all, won’t the nothern hemisphere winter be even colder in 13,000 years when it is actually farther from the sun, in addition to the shorter days and the sun’s lower angle in the sky? Yes, indeed! But that will have to wait until a later post on “Climate Change”.

Good night! I hope I didn’t put you to sleep already.

Posted on November 17, 2012, in Uncategorized and tagged , , , , , , , . Bookmark the permalink. 10 Comments.

  1. Nice job. You are a great teacher.

  2. Great post, well done Craig!

  3. You drew those pictures yourself, didn’t you? I’m impressed! Thanks for another informational post. It bugs me too when people think that the slight decrease in distance to the sun when the earth tilts towards it would be the cause of summer. Come on people, think it through!

  4. Yes, I did Gustav, thanks. I told you I was overachieving.
    I’m not sure how many of my usual friends read my geekier posts, but I do get the impression that I’m occasionally helping an anonymous Malaysian girl or Trinidadian boy with their homework. 😉 Karma points maybe.

  5. This is all fine Craig, but what I really want to know is why does the ice melt faster at the north pole than it does at the south pole?

  6. Hey Dad! Well, that’s for three reasons really.
    1. The jetstreams are different. The jetstream is caused by the difference in temperature between two regions. It blows at the boundary. At the south pole there is a continent surrounded by water. The open water doesn’t go much below 30°F while the continent gets much colder. The water acts like a great heat source (see my “Water” essay!). For this reason, an almost perfectly circular jetstream blows around the pole and this jetstream actually acts as a barrier to incursions of warm air that could potentially melt the ice. At the north pole the warmer open water is nearer the pole with the cold land is to the south. Here, the jetstream is much more irregular, and warm air can occasionally blow very far north.
    2. The ice at the south pole is built up very high, In fact, it averages over a mile thick! It takes a while to melt that much ice. Actually, 70 percent of all the fresh water on the whole planet is there. At the north pole the ice was never much more than ten feet thick since it forms on top of the salt water and heavy ice loads on top would break through. Again, I refer you to my “Water” essay and why lakes don’t freeze all the way to the bottom. Ten feet is much easier to melt obviously! So the open water at the north pole is disappearing to us much quicker than on the land over the south pole.
    3. At the south pole, with an ice thickness of over a mile, the altitude of the top of the ice is pretty high. This is especially true when you consider than much of the south pole is mountainous (add a mile to the top of the mountains). For saturated air, the change in temperatureas you rise is about 3°F/1000 ft. and for dry air it is about 5.5°F/1000 ft. So even with saturated air the top of the ice is at least 18°F colder than it’s lowly sea level brother at the north pole.
    This is of course different over Greenland. Greenland contains about 29% of the world’s fresh water (only 1% left for all the lakes/rivers/ground water). The ice there is also at a high altitude, like at the south pole. But still it is subjected to the irregular jetstream and warm air finds it’s way there more easily. One day last July 97% of all the surface ice on Antarctica melted, even at the top!

  7. Hi,

    I have read your article. Good explanation. I am search for answers to a simple question.

    I understand that north pole of the earth’s axis is always pointed in the direction of Polaris and there is a precession of the equinoxes.

    My question is

    When it is a different location/season, how is it possible for earth’s north pole to fixed its axis to Polaris and at the same time titling at around 23.5 degree (to the top left as shown in your image above?

    Let’s say if the earth is at Summer location/season titling at 23.5 degree and pointing to Polaris, how is it possible during Autumn, when the earth is already at different location still able to point to a fixed Polaris star while still titling at 23.5 degree?

    I am a beginner. For me it appears when the earth is at Autumn, the titling of 23.5 degree at different location will be pointing to a different location with the seasonal change.

    I have seen a lot of images explanation that our

    1) earth appears rotating daily on the fixed Polaris star
    2) earth appears rotating yearly on the fixed Polaris star

    but how does the earth synchronize with the seasons and show that it still points to Polaris from different seasons?

    Yes, this is the question that puzzle me. Sorry, I am a beginner & I am learning.

    Do reply. I can’t find any video on Youtube that describe how it possible for the earth maintain’s its 2.5 degree title is able to fixed its North Pole to the direction of Polaris at AT DIFFERENT SEASONS since the earth is at different locations during those times.

    Have a nice day

    Terry

  8. Hi Terry,
    Thanks for your question. You’ve tried hard to describe your confusion. Let’s see if I can help you out. If it takes a few back and forth messages, that’s OK.
    Here are some thoughts which may help you out.
    1. Polaris is REALLY FAR AWAY. So far away in fact that even though the earth moves to the other side of the sun the earth’s axis doesn’t have to change the direction of the tilt to still be pointing at Polaris. In the short run (like a human lifetime) the earth is pointing in the same direction which always happens to be straight at Polaris. You might want to wiki “parallax”. The parallax in this case is very very small.
    2. Because the earth’s axis is always pointing in the same direction, at one point in the year the the northern hemisphere is tilted toward the sun and this is our northern hemisphere summer. When It gets to the other side of the sun in six months, the northern hemisphere is still pointing toward Polaris, but now is tilted away from the sun and this is our NH winter.
    Please let me know if this helped!!
    Craig

  9. Hi , If I am on the Equator, in December, what angle do I look to see the Big Dipper ? and at what time ? Sunset or just before sunrise ? I am guessing it will be low on horizon
    Thanks

  10. It will be super low on the horizon and pretty difficult to spot from the equator I think. Especially if you are in a humid place that dims the stars. After sunset it will briefly be above the horizon, then sink, and then reappear just before sunrise. I suggest waiting until spring when you should have a decent view.

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