Modern Astronomy

Lecture 4

September 4, 2002

Watch the skies! Watch the skies! .Tonight at 8PM, gather at the north entrance to the Union (next to the east end of the bridge across the river). We will make the short walk over to City Park where the sky is (relatively) dark, and identify some constellations.

The Tilt of the Earth’s Axis and the Seasons

The Earth’s axis is tilted 23.5 degrees with respect to the plane of its orbit around the Sun. This plane is called the ecliptic. The technical term for this tilt is obliquity of the ecliptic.

● The rotating Earth is like a huge gyroscope. It always points in the same direction. This direction is towards the semi-bright star Polaris (the North Star).

● To understand why the seasons occur, we need a connection between what we see in the horizon system and the big picture of the Earth in space. This connection is provided by the geometric concept of a tangent plane.

We are on the surface of a sphere (the Earth) but it doesn’t look like the surface of a sphere. It looks like a flat surface. What gives?

Think of our position (longitude and latitude) on the Earth. We see a few miles to the north, a few miles to the east, a few to the south, etc. If we draw this on a sphere, it looks like a very small, flat patch. We can represent this small patch by a plane which touches the surface of the Earth at the point we are standing. The Latin word for the infinitive to touch is tangere, so the geometric term for this plane is the tangent plane.

► Illustration of tangent plane with blackboard sphere.

As you move the position of the observer around on the Earth, the orientation of the tangent plane changes, and the location of the stars changes as well. At the north pole, the pole star would appear at the zenith (straight overhead). On the equator, the pole star is right on the northern horizon. At latitudes in between, it is at some intermediate altitude angle. This fact is the basis of all forms of navigation. Every people who have navigated across the open ocean (Greeks, Phoenicians, Maoris) have known this fact very well.

● Look at Figure 2.6 of your book for an illustration.

Now let’s see look at a diagram showing the annual motion of Earth around the Sun in space, and also showing the tilt of its axis.

At the summer solstice, the northern hemisphere is tilting directly towards the Sun. Six months later (the winter solstice), the northern hemisphere is tilting away.

The consequences of this for the appearance of the Sun in the sky can be illustrated with the next diagram.

At noon on the day of the summer solstice, the Sun is off to the right in this diagram. The observer sees it in the direction of the green arrow pointing to the right. The angle between the Sun and the zenith is small, and the angle between the southern horizon and the Sun is large. So the Sun is high in the sky.

On the day of the winter solstice, at noon, the Sun is in the direction of the green arrow pointing left. The angle between the zenith and the Sun is a large angle, and the angle between the southern horizon and the Sun is a small angle. The Sun is low in the sky.

The changing location of the Sun in the sky with the season, being high in the sky at noon in the summer, and low in the sky at noon in the winter, is a consequence of this 23.5 degree tilt. It is also due to the fact that the Earth. Like a gyroscope, continues to point in the same direction.

If you look at this diagram, you can also see how the seasons change as you go to different latitudes.