Open Course : Astronomy : Introduction : Lecture 3 : Motion of the Earth

3.1 The Solar System Viewpoint

(Discovering the Universe, 5th ed., §1-4, §1-6)

We now know that the diurnal motion of the stars and the Sun is due to the Earth's rotation.

In addition, the movement of the Sun along the ecliptic is actually because of the Earth's revolution around the Sun.
Let's now consider the point of view where we are fixed with respect to the stars, located above (north of) the Earth, looking down on it and observing these motions.
First we notice that, looking down on the Earth's north pole, it is rotating counterclockwise.

Such a rotation is essentially a definition of a "north pole".
The side of the Earth facing the Sun is in daylight, and the side away from the Sun is at night.

Twelve noon would be halfway through the daylight portion, and twelve midnight would be on the opposite side of the Earth, halfway through the night portion.
The Sun sets around 6 P.M. as we are carried into the dark side, and rises around 6 A.M. as we are carried back into daylight.
Since the Sun rises in the east and sets in the west, these directions must be defined in terms of the rotation: east is in the direction of rotation and west is opposite to that direction, no matter where we stand on the surface of the Earth.
Continuing further "north", we are able to see the Earth's orbit around the Sun.

The Earth's orbit is very nearly circular, and it defines a plane in space called the plane of the ecliptic.

As the Earth moves around the orbit, we say that the Earth revolves around the Sun (to distinguish this motion from rotation).

The Earth's revolution is in the same counterclockwise direction as its rotation.
Because of the revolution of the Earth, stars shift their position relative to the Sun.

For example, in the picture at the right (representing the passage of about two months' time), a star which was overhead at midnight (i.e. directly opposite the Sun) is now overhead at a different time.

Question: about what time is it in the second position?

As a result of the Earth's revolution, from day to day a particular star will transit (or rise, or set) at earlier and earlier times.

This is the same 4 min/day differentiating the sidereal day from the synodic day.

3.2 The Tilt of the Earth's Axis

(Discovering the Universe, 5th ed., §1-6)

Moving from directly above the Earth's orbit down outside one edge of the orbit, we can get a perspective view.

We then observe that, with respect to the perpendicular to the ecliptic plane (which points to orbital north), the Earth's axis is tilted at an angle of 23.5°:

Equivalently, we can say that the Earth's equator is at an angle of 23.5° to the ecliptic plane.

The tilt angle is fixed, so the Earth's axis maintains the same orientation with respect to the stars as the Earth revolves around the Sun.

When the Earth's north pole is tilted directly towards the Sun, the latter is highest in the sky (in the northern hemisphere), which is what we called the summer solstice.

Here in Atlanta, the Sun is 33.4° - 23.5° = 10.2° away from the zenith at the summer solstice.
When the north pole is tilted directly away from the Sun, the latter is lowest in the sky (in the northern hemisphere), which is the winter solstice.

Here in Atlanta, the Sun is 33.4° + 23.5° = 57.2° away from the zenith at the winter solstice.
As before, the intermediate positions are the vernal and autumnal equinoxes.

Here in Atlanta, the Sun is 33.7° away from the zenith at the equinoxes.
Note that (in the northern hemisphere) daytime (the light part of the circle the person is standing on) is longest at the summer solstice, and it is shortest at the winter solstice.

Question: what effect will this have on daily temperature?

Daytime and nighttime have roughly equal length at the equinoxes, hence the name,which means "equal night".

3.3 Precession

(Discovering the Universe, 5th ed., §1-7)

The Earth is not a perfect sphere; instead, it is slightly oblate, i.e. it bulges in the middle along the equator.

This bulge is due to its rotation and the fact that it is not completely rigid.

As a result, the equatorial diameter is 43 Km greater than the polar diameter, a difference of 0.34%.
Because the force of gravity weakens with distance, the Sun and Moon have non-uniform gravitational forces on the Earth, pulling harder on the near side of the bulge than on the far side.

This differential gravitational force is called a tidal force.

Basically, the Sun and Moon try to "straighten" the rotation axis to bring it in line with the orbital axis.
However, instead of straightening, the Earth's rotation axis precesses, i.e. it exhibits a slow, conical motion around the orbital axis.

Precession is the same effect you see with a top.

As long as it is spinning, the top does not fall over, and likewise the Earth's axis won't straighten.
The Earth's precession is a very small effect; it takes 26,000 years for the axis to make one full circle!

Currently the Earth's axis points within a degree of the star Polaris, and it will slowly get closer until around the year 2100, when it reaches a minimum separation of 27 minutes of arc.

Almost 5000 years ago the Earth's axis pointed towards the star Thuban in the constellation of Draco, and this star was used by the ancient Egyptians as their pole star.

In 6,000 years the Earth's axis will point towards the star Alderamin in Cepheus, and in 12,000 years it will be near Vega in Lyra.

The Earth's precession can be easily observed by standing at the Earth's north pole, where the north celestial pole is at the zenith, and watching how that point changes over time (note the year in the lower-left corner):

The circle traced out by the north celestial pole can also be observed on the celestial sphere.

Two different positions, now and 13,000 years in the future, are noted in the picture at the right.
As the precession of the axis occurs, the orientation of the celestial equator will also change, since it is necessarily perpendicular to the axis.
However, the ecliptic is fixed on the sphere.

As a result, the intersections between the celestial equator and the ecliptic, the equinoxes, move along the ecliptic 50 arc sec (3.3 sec R.A.) per year.

The vernal equinox moves in the direction shown.

Currently, the vernal equinox is in Pisces; 2000 years ago it was in Aries; in another 1000 years, it will move into Aquarius.
This movement of the celestial equator relative to the ecliptic is called precession of the equinoxes.

Obviously, this effect is so slow that it is only observable over many years.

Precession was discovered by the Greek astronomer Hipparchus, who had access to several centuries of Greek and Babylonian records.

3.4 The Calendar

(Discovering the Universe, 5th ed., §1-5)

The sidereal year is defined to be the time for the Sun to return to the same position against the stars.

The sidereal year is equal to 365.25 d + 9 min 10s.
The tropical year is the time for the Sun to return to the same position relative to the Earth's axis, e.g. summer solstice to summer solstice.

Because of precession, the tropical year is 20 min 24 s shorter than the sidereal year, equal to 365.25 d - 11 min 14 s.
Neither of these is an integer number of days.

The early Roman calendar (~300 B.C.) had 365 days per year, so it was short by roughly one day every four years.

As a result, the date of the equinoxes and solstices moved forward on the calendar.
In the original Roman calendar the vernal equinox was on March 24.

By 45 B.C. it had moved into late May, so the first Roman Emperor Julius Caesar subtracted 63 days from the calendar to bring the equinoxes back to their traditional dates (more than two months were therefore "redone").
To keep the equinoxes fixed, Caesar decreed that every four years an extra leap day would be added to the calendar, at the end of the year (February).

A year with a leap day added is called a leap year, and this calendar is known as the Julian Calendar.
Then, the calendar was too long by 11 min 14 s /year.

Even this small amount can build up with time, and the vernal equinox began to move backward on the calendar, about 1 day every 128 years.
By 325 A.D. the vernal equinox had moved three days to its current location on March 21.

At this time the Roman Emperor Constantine I convened the Council of Nicaea, to establish dates for the Christian holidays.

Easter, in particular, was based on the date of the vernal equinox.
The vernal equinox continued to move backward on the calendar.

By 1582 the vernal equinox had moved another ten days.

On the advice of astronomers, Pope Gregory established a new calendar system which accounted for the extra 11 min 14 s.

In the Julian calendar, century years had always been leap years; in the new calendar, that would no longer be true, except in years divisible by 400:

1600 leap year
1700 not a leap year
1800 not a leap year
1900 not a leap year
2000 leap year
2100 not a leap year
....

This arrangement is known as the Gregorian Calendar.

Since there is still not a perfect match with the tropical year, even further corrections will eventually be necessary.
Gregory also added ten days to the calendar to bring the vernal equinox back in alignment with the dates established by the Council of Nicaea.

Ten days were therefore "lost" when October 5, 1582 was decreed to be October 15, 1582.

Now the vernal equinox always occurs on or near March 21.
Despite its scientific merit, the Gregorian Calendar was widely distrusted in northern Europe, which had only recently broken away from the Catholic church in the Reformation, and in the Eastern Orthodox countries of eastern Europe.

So, it wasn't until 1752 that the Gregorian Calendar was finally adopted by England and its colonies.

Most eastern European countries didn't adopt the Gregorian Calendar until the early 20th century!
Extra: you can learn more details about calendars, including non-western calendars, at the Calendars and their History web site.

Thanks to Martin Weinelt and his Online Map Creation web page, which generated most of the images of the Earth used in this document.

©1996-2001 Scott R. Anderson
Last update: 2002 February 13
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Open Course Info

Introduction to Astronomy

Lecture 3: The Motion of the Earth

Look in the calendar, and bring me word.

-- Shakespeare, Julius Caesar