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Watchers of the Heavens
Elevation of the Sun
You live on a plain, and as far as you can see, the world around you is absolutely flat (only careful observations of the ocean's surface suggest otherwise. - See the chapter "The Round Earth and Columbus" in From Stargazers to Starships) (FlexBook resource at www.ck12.org) This is discussed further in the chapter "The Angle of the Sun's Rays" in the FlexBook® resource From Stargazers to Starships at www.ck12.org.
The Mounting of a Telescope
Planets and the Zodiac
Note on Earth’s Rotation
The axis around which the Earth rotates points in a certain direction in the sky, and this is also the direction of the pole star (or more accurately, the north celestial pole). To the eye, the rotation of the sky is very, very slow (this is most noticeable when the Sun or Moon rises or sets).
Cassiopeia
Further Exploration
Astronomers call it "Ursa Major", Latin for "the great female bear", and some other languages also refer to it as the Great Bear. Because of their role in locating Polaris, these two stars are often called "the guides." And by the way - the last-but-one star in the handle of the "dipper".
The Ecliptic
The Planets and the Moon
The path of the sun across the celestial sphere is very close to that of the planets and the moon. If it happens to occupy exactly the same place on the celestial sphere, we get a solar eclipse because the moon is then between us and the Sun.
Exploring Further
The incision begins near the top of the gnomon fold and ends on the secondary line. In cut (4), the fin of the gnomon was separated from two pieces with curved contours. Fold these pieces so that they are also flat with the table.
Summer and Winter
In addition (as the drawing makes clear), the sun's rays strike the summer hemisphere more vertically than the winter. It also helps heat the ground, as further explained in the chapter “The Angle of the Sun's Rays” in the From Stargazers to Starships FlexBook® resource at www.ck12.org.
The monthly cycle of the moon (we won't capitalize the word here) must have mystified early humans—"ablution." This is the time it takes the moon to return to (approximately) the same position between the stars. The visible face of the moon has light and dark spots, which people have interpreted in different ways depending on their culture.
This strange rotation of the moon is maintained because the moon is slightly elongated along the axis that points towards the earth.
The Craters
The Airless Moon
In the Space Age
Achievements of “Project Apollo"
Since Apollo
Exploring Further
Some of the names he used for the Crater of the Moon are of people discussed in "Stargazers" - Tycho (distinguished by bright streaks radiating from it), Ptolemeus ("Ptolemæus"), Copernicus, Kepler, Aristarchus, Hipparchus, Erathosthenes; Meton and Pythagoras on the rim, near the North Pole. Part of the evidence has come from the nicely rounded impact remains found on Earth, e.g. The rocks were found to be old, indicating no significant change since the Moon's surface formed about 4.5 billion years ago.
Extensive video images from the Moon were transmitted to Earth – even one (by a remote-controlled camera) of the Apollo 17 crew's launch from the Moon.
Longitude
About Time: Local and Universal
Local Time (LT) and Time Zones
The Date Line and Universal Time (UT)
Right Ascension and Declination
Exploring Further
Through the transparent Earth we can see its equatorial plane, and its middle point is O, the center of the Earth. Longitude is measured from zero to 180◦ east and 180◦ west (or -180◦), and both 180 degree longitudes share the same line, in the middle of the Pacific Ocean. In the sky, the equator is also divided into 360 degrees, but the count begins at one of the two points where the equator meets the ecliptic—the one the Sun reaches around March 21.
However, the Celestial Globe uses terms and notations that differ somewhat from those of the Earth Globe.
Finding latitude with the noontime Sun
Longitude
Tales of Navigation #1: Robert Wood
Tales of Navigation #2: Nansen
It then crosses the north-south direction–. in the northern hemisphere, usually south of the observer. To find your latitude, you measure the angle a between the direction of the noon sun and the zenith. The direction to the Sun is in the plane of the equator, and we get λ=a.
They also provide formulas for deriving the altitude of the midday sun from observations made at other times.
Polar Coordinates
Azimuth and Elevation
One system ("polar coordinates") uses the length of the line OP from the origin to P (ie the distance from P to the origin) and the angle the line makes with the x-axis. It is not a religious symbol — the proportions are not right, and the markings on the stick do not seem appropriate. The problem of being blinded by the Sun later led to the invention of the 'back staff', where the sunlight fell on a target, not in the eye.
The astronomer moved the crosshair up and down until view B obscured one of the stars and view B'.
The Year
The Moon
The Islamic Calendar
The Persian Calendar
The Maya Calendar
Exploring Further
Suppose we observe the position of an asterine in the sky - for example, Sirius, the brightest of them all. One full rotation of the Earth is the time it takes for the star to return to its original position (of course, we are the ones moving, not the star). 530589 days, because it depends on the position of the Sun in the sky, and this position changes noticeably during each orbit.
The duration of the lunar cycle ("synodic period") gave rise to the division of time known as the month.
The Precession of the Earth’s Axis
Ice Ages
The Milankovich Theory
Exploring Further
The cause of the precession is the equatorial bulge of the Earth, which is caused by the centrifugal force of the Earth's rotation (the centrifugal force is discussed in a later section). Note: In the section on the calendar we saw that the Earth's rotation is very gradually slowed down by the tides, increased by the gravity of the Moon. At present, the northern winter occurs in the part of the Earth's orbit where the northern end of the axis points away from the Sun.
Goes beyond variations due to precession of the equinoxes and also includes variations of orbital eccentricity, inclination between the spin axis and the ecliptic, and in the precession cycle itself.
Columbus Again
The Greek philosopher Aristotle (384-322 BC) argued in his writings that the Earth was spherical, due to the circular shadow it cast on the Moon during a lunar eclipse. Nevertheless, his final estimate of the distance to India was close to Strabo's. Their aim was to devise a new unit of distance, equal to one part of the distance from the pole to the equator (as Eratosthenes showed, it is enough to measure part of that distance).
Your angle to the horizon is the tangent to the Earth - the line that touches the Earth's sphere at just one point, labeled B on this drawing.
Estimating Distance Outdoors
How far to a Star?
We are not asking for great accuracy, but are satisfied with an approximate value of the distance – say within 1 percent. The triangle A'B'C has the same proportions as the much larger triangle ABC, and therefore, if the distance B'C to the thumb is 10 times the distance A'B' between the eyes, the distance AC to the far landmark is is also 10 times the distance AB. When estimating the distance to a very distant object, our 'baseline' between the two observation points can also be large.
When measuring stellar distances, astronomers often use the parsec, the distance to a star whose annual parallax is 1 inch – one arcsecond.
A Few Extra Details
Aristarchus deduced the distance to the moon from the duration of a lunar eclipse around 270 BC (Hipparchus later found an independent method). A lunar eclipse occurs when the moon passes through the Earth's shadow, on the far side of the sun (hence it must be a full moon). Let this be the time it takes for the center of the moon to pass through the center of the shadow, about 3 hours (at eclipses of the longest duration, when the moon passes through the center of the shadow).
Seen from Earth, a "new moon" (occurring between the time a thin crescent is last seen before sunrise and the time it is seen just after sunset) occurs when the Moon in its apparent motion around the sky surpasses the Sun.
The Distance to the Moon
A more accurate calculation
Final comments
Hipparchus concentrated on point E on the edge of the Moon (drawing), which during totality, when seen from the Hellespont (point B) just overlaps point D on the edge of the Sun. If the Moon's diameter is half that of the Earth, the Sun must be 19/2 or almost 10 times wider than the Earth. The actual distance to the Sun is about 400 times that of the Moon, not 19 times, and the Sun's diameter is likewise about 400 times that of the Moon and more than 100 times that of the Earth.
In fact, the opposite argument was made: if the Earth revolved around the sun, it would be on opposite sides of the sun every six months.
Mars and Jupiter
Components of the Solar System
Early History, False Leads
This is most evident with Mercury and Venus going back and forth in the position of the Sun. Earth is also a planet, and there are others (too faint to see without telescopes), all of which orbit the sun at or near the ecliptic plane. The retrograde of the planets now looked similar to the retrograde of Venus and Mercury.
As the positions of the planets were measured more and more accurately, additional corrections had to be introduced.
