Everyday Astronomy

Reading

The Spinning Earth

We observe the universe from the surface of a spinning sphere -- the planet Earth. Because of Earth's rotation, the entire sky -- Sun, Moon, planets, and stars -- appear to turn once around us every day.

A time exposure of the night sky. As the Earth rotates, stars appear to move across the sky, creating the semicircular trails seen here. The star with the very short trail is Polaris, the `pole star'.

Evidence for a Spherical Earth

A variety of simple tests show the Earth is a sphere. This has been known for thousands of years.

Physics for the Enquiring Mind, Ch. 14, Fig. 9

Evidence for a Spinning Earth

In contrast, direct evidence that the Earth spins is rather subtle, and the conclusive tests are modern.

Physics for the Enquiring Mind, Ch. 14, Fig. 10

Solar and Siderial Days

The average time between one sunrise and the next, or one noon and the next, is 24 hours. This is known as the solar day. It's a convenient unit because, even in modern times, we still want to begin the day sometime around sunrise.

However, the Earth's period of rotation is actually 23 hours, 56 minutes, and 4 seconds -- a siderial day. If you notice a star rising at 9:00 pm one night, the next night it will rise at 8:56:04 pm.

Why are the solar and siderial days different? The answer is that the Sun appears to move slowly across the sky with respect to the distant stars, taking exactly one year to make a complete journey along the ecliptic.

Seasons of the Sun and Stars

If we use the distant stars as points of reference, we see the Sun appears to circle the Earth once per year. As already mentioned, the path of the Sun's yearly motion is called the ecliptic.

Just as the sky's apparent daily rotation is actually due to the rotation of the Earth, the Sun's apparent yearly motion is actually due to the Earth's revolution about the Sun.

Changing Constellations

At night, the part of the sky which we can see lies in the direction opposite to the Sun. The constellations visible in the night-time sky change over the course of a year as we orbit the Sun.

Changing Seasons. I

The Earth's axis of rotation is tilted by a constant 23.5° with respect to the axis of its orbit. As a result, the northern hemisphere gets more sunlight around the summer solstice (Jun. 21), while the southern hemisphere gets more sunlight around the winter solstice (Dec. 21). This change in the amount and direction of sunlight produces seasons.

Changing Seasons. II

Because the Earth's axis is tilted, the Sun's daily path across the sky changes from season to season. Only on the equinoxes (Mar. 20 & Sept. 23) does the Sun rise due east and set due west. In Hawaii and elsewhere in the tropics, the Sun actually passes directly overhead a couple of times per year!

Question 2.1

Many people think the summer is hotter than the winter because the Earth's distance to the Sun changes over the course of a year. If such a change in distance actually was the cause of the seasons, what would you expect when the Earth was closest to the Sun?

1. Summer in the north, and winter in the south
2. Summer in the south, and winter in the north
3. Summer in both the north and south
4. Winter in both the north and south

The Size of the Earth

Simultaneous observations at two places -- Alexandria and Syene -- enabled Eratosthenes to calculate the size of the Earth: R⊕ =  1 2 π  DAS  360° θ He got a radius of 3800 miles, a remarkably accurate result! (The modern value is R&oplus = 3963 miles.)

Physics for the Enquiring Mind, Ch. 14, Fig. 14

Phases and Motion of the Moon

If you watch the Moon for a few months, you can soon convince yourself that:

Phases

Any sphere illuminated by a distant source of light will show phases just like the Moon's. This can be demonstrated with a ball and a source of light, and the second homework assignment gives you a chance to try this for yourself. If you understand how phases work, you can `read' the Moon and figure out the direction toward the Sun.

Since this is true for any sphere, bodies other than the Moon show phases. For example, the Earth shows phases when seen from the Moon.

A common error is to suppose that the Moon's phase is due to a shadow cast by the Earth. This is false. The object casting a shadow on the dark side of the Moon is the Moon itself!

Phase Terminology

Waxing Crescent	First Quarter	Waxing Gibbous	Full

Waning Gibbous	Third Quarter	Waning Crescent

Some of these names are obvious, but others only make sense when we view the relationship between the Moon's phase and its orbit.

Cycles of the Moon. I

Cycles of the Moon. II

From this animation, which is fairly accurate, we can deduce a few more things about the Moon:

• The distance from the Earth to the Moon is not constant; it varies by about 13% from closest to furthest. Thus the orbit of the Moon is not a circle centered on the Earth. The variation in the Moon's distance was actually known to the ancient Greeks.

• The Moon generally keeps one side facing the Earth as it moves in its orbit, but it wobbles in a complex way. (Part of this wobble is connected with the variation in the Moon's distance, but we will need a theory of orbits to make this connection.)

Phases and Motion Revisited

The Moon revolves around the Earth, completing an orbit (with respect to the stars) in 27.3 days. The Moon is a ball illuminated by the Sun. It goes through a complete cycle of phases every 29.5 days. These times are different because the Earth (and Moon) are moving together in an orbit about the Sun, so it takes longer for the Moon to return to the same relationship with respect to the Sun than it does to return with respect to the stars.

Eclipses of the Sun and Moon

Physics for the Enquiring Mind, Ch. 14, Fig. 15

A solar eclipse occurs when the Moon's shadow falls on the Earth. A lunar eclipse occurs with the Earth's shadow falls on the Moon.

Value of Eclipses

Strictly speaking, eclipses are not everyday events. The plane of the Moon's orbit is tilted with respect to the plane of the Earth's orbit, so only once in a while do the Sun, Earth and Moon actually line up. But eclipses provided a powerful spur to early astronomy:

• Eclipses were impressive and a bit scary, so any ability to anticipate or predict eclipses was highly valued.

• Eclipses showed that simple ideas about light and shadows worked just as well in the heavens as they did on Earth.

• Eclipses provided early astronomers with an opportunity to estimate the Moon's size and distance from the Earth.

The Size of the Moon. I

Physics for the Enquiring Mind, Ch. 14, Fig. 15

The Moon's shadow narrows by almost exactly one lunar diameter in traveling from the Moon to the Earth. Astronomers deduced that the Earth's shadow must also shrink by about one lunar diameter by the time it reaches the Moon.

The Size of the Moon. II

During a total lunar eclipse, astronomers saw that the Earth's shadow appeared to be about 3 times bigger than the Moon. Since the shadow on the Moon is roughly one Moon diameter smaller than the Earth itself, the Earth must have about four times the diameter of the Moon. Since the Earth's radius was known, Aristarchus deduced that the Moon must be about 25% the radius of the Earth, or 950 miles.

A First Distance Scale

Combining their knowledge, ancient astronomers constructed the first astronomical distance scale:

• The Earth's radius was shown to be 3800 miles.

• The Moon's radius was shown to be about 25% of the Earth's radius, or 950 miles.

• Once the Moon's actual size was known, it's apparent size of about 0.5°, together with the small-angle formula, established that the Moon's distance is about 60 times the Earth's radius, or roughly 216000 miles.

• The Sun was known to be farther away than the Moon since the Moon can hide it during a solar eclipse. The exact distance was not known, but was clearly much greater than the Moon's distance.