Everyday Astronomy

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Aspects of astronomy influence life on this planet in many different ways. Some key ideas in astronomy have been understood for thousands of years: the shape, size, and rotation of the Earth, the motion and phases of the Moon, seasonal changes, and the causes of solar and lunar eclipses. Studying these things will anchor our ideas on astronomy in everyday (or everynight) life.

Topics

Reading



     4.5 Rising and Setting Stars      p. 77
     4.7 The Reason for the Seasons      p. 81
     Star Party 1.1: Using the Sky Maps      p. 7
     4.1 The Phases of the Moon and Planets      p. 65
     4.2 Celestial Spectacles: Eclipses      p. 68
     4.2a Eerie Lunar Eclipses      p. 71
     4.2b Glorious Solar Eclipses      p. 68

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'. Star trails

[display rotation of sky]

A flat world inside a rotating celestial sphere
Physics for the Enquiring Mind, Ch. 14, Fig. 1
A spherical world inside a celestial sphere, with the Sun's
      yearly path
Physics for the Enquiring Mind, Ch. 14, Fig. 3
Thales' model -- a flat world inside a rotating celestial sphere. Early Pythagorean model -- a spherical world inside a rotating celestial sphere, with the Sun's yearly motion along the ecliptic.

Evidence for a Spherical Earth


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


Animation of Foucault's pendulum (http://physics.nad.ru/Physics/English/top10.htm)
Evidence for a spinning earth
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. Orbit of the Earth and views of
           constellations

Changing Seasons. I


The Earth and Sun at the solstices

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! Daily paths of the Sun on the solstices and equinoxes

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

In fact, the change in distance is too small to have much effect on the Earth's temperature.

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.)
Evidence for a spherical earth
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:

  • 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.

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!

A cartoon showing a crescent moon correctly
Tony Auth 8/20/2006
Correct (above) and incorrect (right) ways to draw a crescent Moon at night. The incorrect drawing implies that the Sun is above the horizon -- not the time to send someone to `swim with the fishes'.
  A cartoon showing a crescent moon incorrectly
The New Yorker 7/24/2006

Phase Terminology


crescent Moon 1st quarter Moon gibbous Moon full Moon
Waxing Crescent First Quarter Waxing Gibbous Full
gibbous Moon 3rd quarter Moon crescent Moon
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.

Phase and Orbit

The Moon's orbit about the Earth (not to scale!). Sunlight comes from right to left, as indicated by the orange arrows. Each of the 8 positions of the Moon in its orbit is labeled with the phase we observe on Earth. Note that exactly half the Moon's surface is always illuminated, but only at Full Moon is the entire illuminated portion visible from Earth.



Orbit of the Moon and phases

Cycles of the Moon. I


BOO!

Cycles of the Moon. II


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

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.

  Motion of the Earth and Moon
         during one month

Eclipses of the Sun and Moon


Geometry of solar and lunar eclipses
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:

The Size of the Moon. I

Geometry of solar and lunar eclipses
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.



Shadow of the Earth on the Moon

A First Distance Scale

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

Last: 1. Scales of Space and Time Next: 3. Revolution of the Spheres

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: August 31, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/ea.html
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