The Earth's Axial Tilt

[chemist]

I just remembered a couple of riddles that were popular when I went to high school about two decades ago. Here's one of them:

Can you, with reasonable accuracy, decide how many degrees the Earth's rotational axis is tilting by looking at a normally detailed map of the world?

(Now, before anyone asks "tilting relative to what?" I will say that I am of course referring to the angle between the Earth's rotational axis and an imagined axis, going through the center of the Earth, that is perpendicular to the Earth's orbital plane (I am talking about the orbit around the sun here).)

Regards

[kelvinj]

If the normal detail includes the Tropic of Cancer and the Tropic of Capricorn, yes.

[chemist]

If the normal detail includes the Tropic of Cancer and the Tropic of Capricorn, yes.

I bet you thought that one was too easy... Well, I am just trying to entertain the TV readers.

Edited July 24, 2007 by chemist

[kelvinj]

Not too easy, it did make me think, I started with geographical details but soon came to a dead end.

[chemist]

Ok, so how about these related questions:

1) Assuming that you know the latitude of the Tropic of Cancer or the Tropic of Capricorn (these latitudes, in degrees, correspond to the Earth's axial tilt, as kelvinj correctly has pointed out already), can you determine the latitude of the Polar Circle for example, without looking at a map?

2) Bangkok is located on a latitude that lies approximately 13.75 degrees (decimal degrees) north of the Equator. The highest point in the sky that the sun will reach in Bangkok during the year is of course the zenith position (straight up, or, if you like, at an angle of 90 degrees relative to the local "plane" of the Earth's surface). But between which extremes (in degrees) will the position of the sun in the sky vary during one year (in Bangkok)? (We are talking about the highest possible position in the sky, and that position is of course reached around noon each day.)

Regards

Edited July 24, 2007 by chemist

[Pink Mist]

stolen from wikepeda

The axial tilt may equivalently be expressed in terms of the planet's orbital plane and a plane perpendicular to its axis. In our solar system, the Earth's orbital plane is known as the ecliptic, and so the Earth's axial tilt is officially called the obliquity of the ecliptic. In formulas it is abbreviated with the Greek letter ε (Epsilon).

The Earth has an axial tilt of about 23° 26’. The axis is tilted in the same direction throughout a year; however, as the Earth orbits the Sun, the hemisphere (half part of earth) tilted away from the Sun will gradually become tilted towards the Sun, and vice versa. This effect is the main cause of the seasons (see effect of sun angle on climate). Whichever hemisphere is currently tilted toward the Sun experiences more hours of sunlight each day, and the sunlight at midday also strikes the ground at an angle nearer the vertical and thus delivers more heat.

Conditions are more favorable to glaciation when obliquity is low, making it one of the Milankovitch cycles.

The obliquity of the ecliptic is not a fixed quantity but changing over time. It is a very slow effect, and at the level of accuracy at which astronomers work, does need to be taken into account on a daily basis. Note that the obliquity and the precession of the equinoxes are calculated from the same theory and are thus related to each other. A smaller ε means a larger p (precession in longitude) and vice versa. Yet the two movements act independent from each other, going in mutually perpendicular directions.

[kelvinj]

So, to get the lattitude of the Polar Circle, do we simply subtract 23 degrees 26 minutes from 90 degrees giving 66 degrees 34 minutes North, or does some more complicated geometry come into play?

[chemist]

So, to get the lattitude of the Polar Circle, do we simply subtract 23 degrees 26 minutes from 90 degrees giving 66 degrees 34 minutes North, or does some more complicated geometry come into play?

No, as far as I know no complicated geometry comes into play here. Your reasoning is correct, kelvinj (meaning that the latitude of the Polar Circle = 90 - the (value of the) latitude of the Tropic of Cancer/Capricorn = ca 66 degrees 34 minutes north.) The answer in decimal degrees is 66 + 34/60 = ca 66.57 degrees north.

More important than providing some correct numbers as answers is of course to understand why these numbers are correct. Your posts give me a strong feeling that you have indeed understood why, kelvinj.

bronco, I have read through your quote from Wikipedia, and although the text provides the value of the Earth's axial tilt, I can't find any clear mentioning of the relationship between this axial tilt and the latitude(s) of the Tropic of Cancer/Capricorn. Maybe I missed something here?

Now, as for the second question in my previous post, that one is a little harder to answer. A little hint: Instead of Bangkok, pick a point on the Equator and calculate the corresponding extremes of the sun's angle in the sky for that point.

Regards

[Humphrey Bear]

Surely on the Equator it will be between 90 degrees and 66.57 degrees to the horizontal (assuming your figure is correct).

When i was working in Indonesia - Sumatra - I stood on a line on the road that marked the equator. One foot in Northern Hemisphere, one in Southern. Now if it was mid-winter in the NH, it would be mid-summer in SH. So longest day in SH / shortest day in NH. So how come it seemed much the same to me?

[chemist]

Well, I realize that maybe some definitions would be in order when it comes to this puzzle. These definitions will be the ones that I learnt a long time ago, so please correct me if I'm wrong (or if for example Wikipedia has different, conflicting, definitions ).

Latitude degrees: 1 degree consists of 60 minutes, and a minute consists of 60 seconds. That is the traditional way of writing down latitudes (or longitudes). Another alternative is to use decimal degrees. An example: 10 degrees 30 minutes is equal to 10 + 30/60 = 10.50 decimal degrees.

The tropic of Cancer: This is the northernmost latitude (ca 23 degrees 26 minutes north, or ca 23.43 decimal degrees north) over which the sun will stand exactly "straight up" (at an angle of 90 degrees; in the zenith position) one time during one year. At any point on this latitude this happens on the day of the summer solstice of the northern hemisphere, i e during the longest day on the northern hemisphere (usually around June 22-23). On this day, the northern part of the Earth's rotational axis will point the most toward the sun during the year. Now, at any point north of the Tropic of Cancer the sun will never reach the zenith position. At any point south of the Tropic of Cancer (but north of the Tropic of Capricorn) the sun will reach the zenith position twice every year, as the zenith position is seemingly "oscillating" between the Tropic of Cancer and the Tropic of Capricorn.

I will throw in a hint here to the solution of problem number 2 in an earlier post: On the day of the summer solstice of the northern hemisphere, person 1 is standing exactly on the Tropic of Cancer, and around noon at this position he will see that the sun is straight above his head. Let's say that at the same time person 2 is standing on a point situated on the Equator and exactly south of person 1. Person 1, who is standing 23.43 degrees north of the Equator (i e on the Tropic of Cancer), looks at the sun at a 90 degrees angle. At what angle does person 2 look at the sun?

The Tropic of Capricorn: The same as for the Tropic of Cancer, but "the other way around". For example: The zenith phenomenon will reach this latitude (ca 23.43 decimal degrees south) on the day of the summer solstice of the southern hemisphere (around December 25).

The Tropics: The area between the Tropic of Cancer and the Tropic of Capricorn. Thailand, for example, is completely located in the Tropics.

A final clarification: Why is the Earth's axial tilt related to the Tropic of Cancer/Capricorn? Well, how about the following experiment?: Let's say we have a football through which we have forced a metal stick (but the ball still keeps its shape ). This of course represents the Earth with its axis of rotation. A person holds that ball with the stick/axis pointing straight up to the ceiling of the room where the experiment is done, and another person puts a laser pen ("the sun") on a nearby table so that the laser dot is appearing at the "equator" of the ball. We now have a case where the axial tilt is zero. Ok, then the person holding the ball tilts that ball with its axis so that the upper part of the ball/axis comes closer to the laser. Let's say he tilts the ball 23.43 degrees, which is equal to the latitude of the Tropic of Cancer. The laser dot will during the tilting move away from the "equator" of the ball and end up at a point that is located 23.43 degrees "north" of the ball's "equator"! Now this point on the ball experiences the zenith phenomenon, and this means that this experiment represents the summer solstice of the northern hemisphere of the Earth (i e this represents the situation when the northern part of the Earth's rotational axis is pointing the most toward the sun during one year).

I hope this was of some value .

Regards

Edited July 24, 2007 by chemist

[chemist]

Surely on the Equator it will be between 90 degrees and 66.57 degrees to the horizontal (assuming your figure is correct).

When i was working in Indonesia - Sumatra - I stood on a line on the road that marked the equator. One foot in Northern Hemisphere, one in Southern. Now if it was mid-winter in the NH, it would be mid-summer in SH. So longest day in SH / shortest day in NH. So how come it seemed much the same to me?

Your answer is almost correct when it comes to the equator.

During "midsummer" on the northern hemisphere, the sun is (at noon) shining from an angle of 90 degrees over the Tropic of Cancer (23.43 decimal degrees north). This means that the sun angle for the equator on this day is 90 - 23.43 = 66.57 degrees to the north. Similarly (following the same reasoning), when it is "midsummer" on the southern hemisphere the sun angle for the equator is 90 - 23.43 = 66.57 degrees to the south. So, the conclusion is: At the Equator, the sun "travels" between 66.57 degrees to the north and 66.57 degrees to the south during a one year period.

As for your very interesting question about standing over the equator, you can look at it this way: Compare northern latitudes with southern latitudes pairwise. For example, during midsummer on the northern hemisphere (NH) there is a large difference between 60 degr north and 60 degr south when it comes to the sun angle and the length of day. 30 degr north vs 30 degr south: The difference is getting smaller. 10 degr north vs 10 degr south: An even smaller difference. Now, as we come closer to the equator, the difference in these pairwise comparisons will approach zero.

A lot can be said about this, but at the moment I am exhausted. I hope my comments were of some help.

Regards

[thatguy]

"I stood on a line on the road that marked the equator. One foot in Northern Hemisphere, one in Southern. Now if it was mid-winter in the NH, it would be mid-summer in SH. So longest day in SH / shortest day in NH. So how come it seemed much the same to me?"

it's a joke son

[Tywais]

"I stood on a line on the road that marked the equator. One foot in Northern Hemisphere, one in Southern. Now if it was mid-winter in the NH, it would be mid-summer in SH. So longest day in SH / shortest day in NH. So how come it seemed much the same to me?"

it's a joke son

So, if you have a toilet on that line will the water circle right, circle left or just go straight down when you flush?

[pete_r]

One question I can't find an answer to is, why do we have 90 degrees in a right angle in the first place?

Why not a rounder number like 100, or 1000, or whatever else?

[Tywais]

One question I can't find an answer to is, why do we have 90 degrees in a right angle in the first place?

Why not a rounder number like 100, or 1000, or whatever else?

Originally it was determined to take 360 days for the sun to make one complete tract or circle.

http://www.wonderquest.com/circle.htm

Though that is one of a couple of theories.

[Kalavo]

One question I can't find an answer to is, why do we have 90 degrees in a right angle in the first place?

Why not a rounder number like 100, or 1000, or whatever else?

But we do! Instead of being called a degree, it's called a Gradian - there are 400 gradians in a circle. It is generally used in survey work where one gradian on a great circle on the earth is assumed to equal 100km.

Navigators however tend to stick with degrees, and one minute of a degree of arc a great circle is assumed to be 1 nautical mile (1852 metres).

Mathematicians on the othe hand prefer to use Radians - where 2 x PI radians is a full circle.

Edited July 29, 2007 by Kalavo