Does anyone know why the Arctic and Antarctic circles are at 66.5 degress?

[Johnny5]

Does anyone know why the antarctic circle and the arctic circle are at 66.5S and 66.5 N respectively?

 

Thank you

[ed84c]

That is the point at which the temperature of the sea water on average is below 0*c, if i remember correctly.

[Johnny5]

That is the point at which the temperature of the sea water on average is below 0*c, if i remember correctly.

 

Thanks Ed

 

Regards

[darth tater]

Actually it is because the Earth's axis is on a 23.5 degree tilt relative to the plane of it's orbit around the Sun.

 

That is what causes our seasons.

[Johnny5]

Well which is it?

 

i know the earth is tilted at 23 degrees relative to the ecliptic plane, but is this why the arctic and antarctic circles are at 66.5?

[Callipygous]

Actually it is because the Earth's axis is on a 23.5 degree tilt relative to the plane of it's orbit around the Sun.

 

That is what causes our seasons.

 

ok... so your saying if it werent on any tilt at all we would have ice caps everywhere but the equator?

[darth tater]

Well which is it?

 

i know the earth is tilted at 23 degrees relative to the ecliptic plane' date=' but is this why the arctic and antarctic circles are at 66.5?[/quote']

 

 

Yes.

 

As I said, the tilt is 23.5 degrees, so on the 1st day of summer in the Northern hemisphere, the sun does not dip below the horizon above the Arctic circle and on the first day of Winter, it does not quite come up.

 

In the Southern Hemisphere, the opposite takes place.

[Jacques]

66.5= 90 - 23.5

[Johnny5]

66.5= 90 - 23.5

 

I realized that too Jacques, but I still don't get the significance.

 

Let me sort of start off something here, and maybe someone can help out.

 

I have a very important goal currently, and that is to find a reference frame in which to mathematically analyze the motion of the earth around the sun.

 

But it seems that has already been done by Kepler (yes i knew that ).

 

Ok so anyways...

 

I have to build the whole thing up one step at a time.

 

The first thing is to find the origin of the frame.

 

The best place would be the center of mass of the solar system, but I have no idea how to compute it yet.

 

However, to a good approximation, the center of mass of the sun is the center of mass of the solar system, since most of the mass in the solar system comes from the sun. I of course know how to compute it, but in order to do that I would need the exact location of all the planets right now, relative to the sun, and their distances away, and also their masses.

 

Now, with the knowledge that the earth orbits the sun in an ellipse, we can carry out the analysis with the XY axes in the plane of earth's orbit. It just so happens that most of the other planets also have their orbits in this plane.

 

This plane is called the ecliptic plane.

 

The Z axis of the frame is perpendicular to the ecliptic plane.

 

Now, the earth is spinning on an axis, but the axis isn't perpendicular to the ecliptic plane. If it were perpendicular to the ecliptic plane, then the equator of earth would always lie in the ecliptic plane. But in reality, the earth is spinning around an axis which points towards the north star.

 

Now, the earth has regular seasons, marked by the spring equinox, autumn equinox, and summer and winter solstices.

 

First let's start with the summer solstice. The date of the summer solstice is June 21st.

 

Use the following picture:

 

Notice that all points above arctic circle recieve sunlight 24 hours/day on June 21st

 

In the above picture, start with the summer solstice, which occurs on June 21st. Focus on the vector which starts at the center of inertia of the earth, and passes through the north pole, and which points at the north star.

 

Because of the 23 degree angle this vector makes with the ecliptic plane, the arctic circle is tilted towards the sun, and the antarctic circle is tilted away from the sun. Thus, for a whole 24 hours, all places on earth above the arctic circle recieve sunlight all day long, while all places on earth below the antarctic circle are in darkness all day long.

 

Then sixth months later, the opposite is true. The vector still points to the north star, but now the earth is on the opposite side of the frame. So on December 21st (The winter solstice), it is now all points below the antarctic circle which receive sunlight 24 hours a day, while all points above the arctic circle are in darkness 24 hours a day.

 

And so clearly, this tilt is what is responsible for the seasons.

 

Oh I think I get it now, I think I just answered my own question.

 

On June 21st, the earth is where it is in the picture. sunlight is approaching from right to left, and strikes half the globe at any moment, while the other half of the globe is in darkness (nightime on the other side of the world).

 

But the earth is tilted and spinning, so imagine a conic section, a plane which cuts the earth right through that Arctic circle.

 

 

Here is a definition of the arctic circle

 

Now focus on the curved arc, which runs from the highest point on earth receiving sun [math] \alpha [/math], to the north pole.

 

In one 24 hour period, the point alpha traces out the arctic circle.

 

That is a way to understand, and remember what the arctic circle is.

 

Of course the earth will have moved further along in its elliptical path, but the point is clear.

 

If you stopped time on june 21st, and spun the earth around its spin axis one time, the point alpha, would trace out the arctic circle in the rest frame of the sun.

 

And the antarctic circle can be similarly understood, and remembered.

 

So the location 66.5 isn't arbitrary at all.

 

It is 90 degrees minus the earth's exact tilt.

 

Thank you Jacques, I thought so, but I subtracted 23 from 90, and got 67, not 66.5, i should have just rounded.

 

Regards