Astronomy 10: Lecture 4
Reading Assignment: Arny Essay 2 pg. 177, pgs. 41-52, Cosmos Chpts 3 & 7
Determining Longitude is much more difficult. You need a precise and accurate watch or clock in order to do this correctly. There are two best ways to do this.
If you wanted to use stars for Longitude determination you would go about it in the same as with the Sun. But now you need to use a Sidereal Clock. Recall that the Sidereal Day is 23 hours 56 minutes.
- Compare the Local Solar Time to the time on a watch that reads the Mean Solar Time of a known longitude. For example: Say your watch is calibrated so that when it reads 12:00 noon the Sun is transiting as seen from a longitude of 0° (the prime meridian). If your watch is reading 24 hour as opposed to 12 hour time (i.e., 1:00 PM = 13:00) then your watch is reading what is called Universal Time. Now, your watch reads 12:00, you know that at 0° Longitude the Sun is at the meridian. But in your sky the Sun is still 2 hours away from transit (your local solar time is 10:00). The Sun is East of the meridian, so you are West of 0° Longitude. Earth rotates 360° in 24 hours and likewise the Sun completes a full circuit in 24 hours (definition). So the Sun moves at a rate of 15°/hour. If the Sun is 2 hours from transit then it is 30° from the meridian (in the plane of its path through the sky that day). You are at a Longitude of 30° West of Greenwich.
- Similarly you could wait for the Sun to transit in your sky (local noon) and read off the time on your watch set to Universal Time. If you read a time of 06:00 then that means that the Sun is 6 hours before noon in Greenwich which places you East of 0°. 6 hours of time corresponds to 90° of angle. So you are at 90° East Longitude.
Before the invention of the clock it was very difficult to navigate on long sea voyages. Nowadays we have network of satellites in orbit of Earth they are all in contact with one another via radio waves. All you need is a cheap, hand-held receiver to tap into their signal. They use triangulation to locate you to an accuracy to within a few meters!
The system of time keeping on Earth is based on the celestial rhythms that our ancestors were well tuned-in to.
The 24-hour day is defined at the time it takes the Sun to go from one transit to the next.
If you were telling time by a sundial, 12:00 noon would always be when the Sun is transiting the meridian. NOTE: A.M. means ante meridian (before meridian), and P.M. means post meridian (after meridian).
Mean Solar Day
Because the Earth's orbit is elliptical, the Sun does not always take exactly 24 hours to make a complete circuit in the sky. When we are closer to the Sun it takes longer than 24 hours to go around once, and when we are farther away than average it takes less time to go around the sky once. So 24 hours is the average (or mean) time between transits of the Sun. So when your clock is working on Mean Solar Time and reads 12:00 noon, the Sun may or may not be at the meridian.
Because your local time is dependent on your Longitude there are an infinite number of local times on Earth. This is trouble when you are trying to travel or communicate with someone in a different location. In the early days of the American Railroad different places along the rail would have different local times and it was impossible to make up a schedule for everyone. If the train was supposed to leave at 12:00 noon from New York city bound for Boston, the trouble would arise from the fact that it wasn't 12:00 noon in Boston when the train left New York. So when is the train supposed to arrive? To overcome this difficulty the Time Zones were created. There are around 24 time zones on Earth, each roughly 15 degrees of longitude in width. Their borders are drawn with political rather than geographic boundaries. The time that is kept within a time zone is the Mean Solar Time for the line of longitude at the center of the time zone. For example: In the Pacific Time Zone when it is 12:00 PM the Sun is transiting as seen from a longitude of 120° West of Greenwich. Everywhere else in that time zone will see the Sun either to the West or East of the meridian at 12:00 noon.
The Months are based on the 29 day cycle of the Moon's phases (its synodic period). Each quarter of the cycle (e.g., New Moon to 1st Quarter) takes about 7 days, and hence Months are about 4 weeks long. The current calendar months do not conform to the Moon's cycles perfectly and so the date of the New or Full Moon drifts through the month as the years pass. There are typically 12 to 13 cycles of the Moon every year.
The year is the time it takes for Earth to complete one full orbit. This can be measured in a number of different ways. It can be measured as the time between Vernal Equinoxes or Summer Solstices, for example. It can also be measure by the Sun's return to a given position in the stars. As such the year is a Sidereal period. Indeed the Vernal Equinox is the time when the Sun is at the crossing of the ecliptic with the celestial equator. This used to be the start of the year when the Romans first invented a calendar to keep track of the days of the year.
These days time is measured by the oscillation of cesium atoms and not the spinning of the Earth. Devices that measure these oscillations are called atomic clocks. They keep the most precise time possible to measure in nature (with perhaps the exception of pulsars). With such precision we are now becoming aware of the fact that Earth's spin is not constant, nor is it's orbital rate. The Moon is slowly drifting away from Earth and slowing down. But the calendar we keep is based on the rhythms of nature.
II. The History of Astronomy
- ~17,000 BC, Lascaux cave paintings depicting celestial events
- The Pyramids built with celestial alignments accurate to within a few minutes of arc.
- Used Diurnal Motions as a clock
- Developed sexagesimal (60) counting system: 360 degrees in circle, 60 minutes per hour, 60 seconds per minute, etc.
- Compiled tables of planetary motion
- Predicted eclipses
- No understanding of why events occurred, no pictures of orbits, no geometry!
- Well-preserved historical records dating back 3000 years
- Oldest records of comets, eclipses, sunspots, etc.
- Astronomy tied to political bureaucracy and functioning of government
- Decline in the importance of Astronomy after 1200 AD
- Developed a complicated and extremely accurate calendar
- precise tables of for motions of Moon and Venus
- predicted eclipses
All cultures on Earth have made some understanding of the motions of the heavens. But the contribution by the Greeks of the use of a scientific reasoning was special and led to great discovery.
The Greek Contribution
- Pythagoras of Samos (circa 580 - 500 BC)
- Mystical understanding of the Cosmos using mathematics
- Numbers as a bridge between humans and the divine mind
- Invented the roots of the western musical scales
- Believed in a spherical Earth, by reasoning alone and not with any evidence whatsoever.
- Postulated that Sun, Moon, and planets move in concentric circles
- Believed the distances were in ratio with musical harmony: Music of the Spheres
- Plato (circa 428 - 348 BC)
- Student of Socrates (c. 470 - 399 BC)
- Ascendency of the role of deductive reasoning.
- Believed sensory experience to be subjective, that pure thought was preferable to experiment.
- Urged astronomers to think about the heavens, but not to waste their time observing them.
- Philosophy was the work of the mind
- Manual Labor was for slaves
- The Physical World is merely a shadow of the perfect world of the forms
- The Pythagorean solids and their correspondence to the 5 Elements:
- Fire - tetrahedron (4 sides, triangles)
- Earth - cube (6 sides, squares)
- Air - Octahedron (8, triangles)
- Water - Icosahedron (20, triangle)
- Cosmos - Dodecahedron (12, pentagons) : knowledge of this shape suppressed by Pythagoreans
- Eudoxus (circa 408 - 356 BC)
- Devised a model of the Universe as an answer to a challenge put forth by Plato.
- Universe consisting of nested spheres with the planets attached
- Retrograde Motion a result of planets being attached to smaller spheres affixed to the larger spheres: epicycles
- Aristotle (384 - 322 BC)
- Student of Plato's Academy
- Worked in almost every field of known science and philosophy!
- Believed that every effect has a cause
- Important innovation: Universe can be described by natural laws inferred by rational thought
- Invented a system of Physics: mostly quite wrong, but had a strong common sense appeal - suffered from lack of experiment in some cases (Pythagorean bias)
- Founded science of mechanics (physics of motion)
- developed the idea of force, impetus theory of motion (wrong, but still widely held even today)
- Thought force was required to keep a body in motion
- Separate laws for Earth and the Heavens
- Gravity on Earth but not in Heavens
- Natural motion is straight lines on Earth, circles in Heaven
- Reasoned that Earth was spherical based on observations of Earth's shadow on the moon, the fact that different stars can be seen farther south than Greece, etc.
- Believed in a Earth-Centered Universe with the Heavens rotating above - Geocentric
- Heraclides (circa 388 - 310 BC)
- Proposed that Earth is rotating to explain the daily motions of the heavens.
- Proposed that Mercury and Venus orbit the Sun because they never get very far from the Sun
- His ideas were soundly rejected by the Aristotle school of thought
- Aristarchus of Samos (circa 310 - 230 BC)
- Measured the relative sizes and distances to the Moon and Sun
- Found the Sun to be Bigger than Earth!
- Reasoned that the Sun rather than Earth is the center of the Universe and the Earth is one of the planets
- His ideas again rejected by Aristotle, no parallax of stars
- Eratosthenes of Cyrene (276 - 194 BC)
- Director of the Library of Alexandria
- Read an account of the Sun's path on the Summer Solstice in the southern frontier city of Syene.
- He realized that Earth must be curved and correctly calculated its size
- Hipparchus of Rhodes (190 - 120 BC)
- Synthesized Babylonian and Greek data with new Greek geometrical models
- Constructed the largest star catalogs in existence at the time
- Discovered the precession of Earth's axis
- Refined Aristarchus' measurements
- Measured the length of the year to an accuracy of 6 minutes!
- Devised a system of brightness for the stars: magnitudes: still in use today (much to the chagrin of modern astronomers)
Ptolemy (circa 140 AD)
Claudius Ptolemaeus, a.k.a Ptolemy, was also a director of the Library of Alexandria in his time. He is sometimes considered the last great natural philosopher of classical times. (I would argue however that this identification falls to the last director of the Library of Alexandria, Hypatia, who was brutally murdered by a Christian lynch mob in 415 AD.) He put together a model of the Universe that did not change much for 1500 years. Ptolemy used the collected observations of Hipparchus to build his model and to measure the parallax of the Moon, and thereby make another measurement of its distance.
His model was marked by using the geocentric model first developed by Eudoxus. He considered a heliocentric model, like that proposed by Aristarchus, but immediately rejected it based on Aristotelean physics. He made alterations to the geocentric model, added some epicycles within epicycles in order to make the model explain all of Hipparchus' data. He also offset some of the spheres so that they were not necessarily concentric with Earth. The most important thing about this model was that it was able to predict the positions of the planets with great accuracy (at least to the level that people were able to measure in those times). The model contained no explanation for how or why these motions occurred (it had no physics).
In subsequent centuries the alterations made to the model would be to add more epicycles into the model. This was done primarily by Arabic astronomers in medieval times. In the end some planets would have as many as 80 epicycles in order to be able to properly predict where they would be.
Ptolemy also codified the pseudoscience of astrology into the form which is still in use today. That just goes to show that great genius is no guarantee against being dead wrong.
In the beginning Astrology and Astronomy were one and the same. The basic tenets of modern Astrology (Ptolemy's system) are that a person's character and destiny can be understood from the positions of the Sun, Moon, and Planets at the moment of his/her birth. Astrologers use a chart called a horoscope and claim to be able to predict and explain the course of life and to help people, companies, and governments with decisions of great importance.
Skeptical Questions for Astrology:
- What is the likelihood that 1/12th of the world's population is having the same kind of day?
- Why is the moment of birth and not conception critical?
- If the mother's womb can keep out astrological influences until birth, can we do the same with a cubicle of steak?
- If astrologers are as good as they claim, why aren't they richer?
- Are all the horoscopes done before the discovery of the three outermost planets incorrect?
- Shouldn't we condemn astrology as a form of bigotry?
- Why do different schools of astrology disagree so strongly with each other?
- If the astrological influence is carried by a known force, why do the planets dominate?
- If astrological influence is carried by an unknown force, why is it independent of distance?
- If astrological influences don't depend on distance, why is there no astrology of stars, galaxies, quasars, etc.?
- Why can twins have different fates?
Scientific investigations of horoscope predictions find them to be no better than random guessing. Furthermore horoscopes tend not to be predictions at all but rather just advice. The advice is clothed in such vague language as to make an interpretation in hindsight seem as if the horoscope had actually predicted something.
Sun sign descriptions of personality are so general that any person can identify some of themselves in the description. Read a couple and figure out the percentage of the description that is actually fitting. Typically no better than 50%. Random guessing again.
Ancient Sun sign dates are plain wrong due to the precession of Earth's axis.
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