# III.4 The Earth's Three Motions

The Earth turns (rotation around the polar axis), goes along on its orbit (revolution around the Sun), swings smoothly as un unbalanced spinning top (equinoctial precession).

As long as you live on the Earth, these motions remain imperceptible. So during the ancient times, the Greek astronomers thought that the sky was moving around a motionless Earth (in the opposite direction of real Earth motions).

The next pages don't tell you which one of Earth and Sky is moving. They only show you how you can see the effect of these motions in the stars.

It's easy to detect the rotation (an activity for 12 years old, Astronomy On-Line basic level), it's more difficult to detect the revolution (Astronomy On-Line middle level) and much more to detect the precession (here, an activity for 16 years and more, Astronomy On-Line advanced level).

## The Earth swings smoothly as an unbalanced spinning top

Figure 1

### Equinoxes and g and g' spots:

Let's sum up results of previous exercises.

• The rotation of the Earth around its axis establishes on the sky the circle of the equator plane.
• The motion around the Sun establishes the ecliptic circle in the sky.
• The polar axis is not perpendicular to the ecliptic plane, so the equator and ecliptic planes make a dihedral angle about 23.5o; wide.
• The Earth belongs to both planes, so it lies on their intersection. We denote this line (gg').
• The Sun, wich is the centre of the Earth'sannualorbit, belongs to the ecliptic plane too. But it is rarely in the equator plane.

When the Sun is in the North side of the equator plane, in Spring and Summer, on the Earth at the North Pole, one day lasts for six months.

When the Sun is on the South side of the equator plane, in Autumn and Winter, on the Earth at the North Pole, one night lasts for six months.

So the Sun passes through the plane twice a year :

at spring equinox, as seen from the Earth, the Sun is locatesd just on the g spot and at autumn equinox, it is located on the g' spot.

The geometric consequences of equinoxes are well-known : when the Sun crosses the equator plane, the bound of "night" and "day" on the Earth is a meridian circle (the poles are on this circle) and its plane is perpendicular to (gg'). So on these dates, night and day each last about 12 hours.

### How to find the date of equinox with an ordinary equipment:

Figure 2

A simple vertical stick (named gnomon by the Ancient Greeks) is enough to find the day of equinox.

During this day, the end of the shadow follows a straight East-West line. This line and the top of the stick locate the equator plane because on this date, the sun-rays that reach the Earth are on the equator plane.

During the other days of the year, the end of the shadow is curved (generally an hyperbolic arc).

We can see such kinds of arcs on sundials, corresponding to the date.

### How to locate easily the (gg') line in the sky:

As this line crosses the Earth, we have to find only one spot on it : g or g'.

The previous observations (plane perpendicular to polar axis or lines of planets) give coarsely the directions of equator and ecliptic. It is not enough to get precisely their intersection but if you can observe a lunar eclipse near equinox, it's all right !

### Equipment required :

• one photo of the Moon among the stars during an eclipse (take this photo with a 28 or 50 mm focal length);
• an equipment to mesure angles (sextant, Orion's belt...) which gives the scale of the photo; and
• a calendar to have the date of this eclipse ; and a gnomon or any kind of sundial to get the date of equinox.

### How to do it:

We suppose that we know the direction of the ecliptic (with preceding eclipses) but not precisely the positions of g and g'spots that we want to locate.

• First you must identify the zodiacal constellation on the photo (in Autumn, it will probably be Pisces and in Spring Virgo).
• By the Moon, draw the line which represents eclipctic.
This very night, the Moon is not on g or g'but it is at the opposite point of the Sun.
• Establish the scale of the photo.
• Compute the days from equinox to eclipse. And as you know that the Sun goes on 360o; in 365 days, you can locate the opposite point of the Sun at the date of the equinox.
If this eclipse takes place in Spring, this opposite point of the Sun is the Automn equinoctial point (g').
• Measure the angle between this point and the brightest stars (especially note the position of alpha Virgo also called Spica and you will be able to compare it with Ancient measurements).

## The equinoctial precession:

In about 128 BC, Hipparcos, a great Greek astronomer, observed a lunar eclipse in Rhodos. He noticed that the brightest star in Virgo, Spica, rose 6o; before the g' spot.

He knew that 169 years before, Timocharis and Arystillus in Alexandria had performed the same measurement, but their result was 8o;.

Hipparcos concluded that the whole sky was gently moving around the ecliptic pole. This motion produces the Spring equinox whereas the Sun has still to move 43 " on before it reaches the place that it left for the previous Spring equinoxe.

So we understand the word "precession" : each year, the equinox is 43 " 'sooner' as g is moving in the opposite sense to what the Earth does.

After Copernicus's work, even if the Sky doesn't move any more, we can always see the Sun moving along the ecliptic and g point is still precessing. But we explain this as a different motion of the Earth : the precession is a slow rocking of the polar axis. Within 26.000 years, it draws a cone of 23o opening, around the ecliptic pole.

If you want to verify this value, you must do like Hipparcos, and compare your own results with Hipparcos' ones.

Try to do it during the next lunar eclipses....

### To complete:

Precession is caused by the gravity of the Moon which creates a return coupling with the equatorial roll of the Earth.

This drawing (Figure 3) represents different positions of the Earth on its orbit (seen from ecliptic northern pole at the begenning of each season in 1996).

Since Hipparcos, the Sun-g line had turned about 30o; to the great displeasure of astrologers because the zodiacal "signs" no longer correspond to the constellations.

The grey zones mean "night". Polar axis projections on the ecliped plane are the arrows.

The Earth moves in the direct sense (opposite to the clock's hands) and g in the other sense (like the clock's hands).

At the equinox, this arrow is perpendicular to (Sg).

Figure 3

 Author: D. Toussaint, CLEA 20, rue Renaudot F-10 160 Aix-en-Othe Contact: Josée SERT