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Amateur Astronomers Association of New York

AAA Astronomy Class Spring 2010

Astronomy
Astronomy is the study of objects and phenomena outside of Earth. It is broken into three areas:
ا Our Solar System - study of a single star and its retinue (studied since cave man). ا Stellar astronomy - stars in a single galaxy (studied since 19th century) ا Galactic astronomy and cosmology - study of galaxies and the universe (since 20th century)

How We Will Proceed
We will study these areas from a historical perspective, mimicking the development of human understanding of the universe.
We begin as cave men observing the sky. We will assume we are located here in New York and spring is just beginning. As we proceed we will develop our own terminology. To start: ا We walk on the Earth. ا Above us is the sky. ا The boundary between the two is the horizon.

The Daytime Sky

The Sun
ا Sometimes an extremely bright, round, yellowish object appears in the sky. When it does the sky and Earth are bathed in its light. ا This object moves across the sky and eventually disappears below the horizon. When it does sky and Earth darken. ا We will call this object the Sun. ا When the Sun is in the sky we have daytime; otherwise we have nighttime.

Daytime and Nighttime
ا Light (daytime) and darkness (nighttime) alternate. ا Daytime begins when the Sun appears in the sky (sunrise) and ends when it goes below the horizon (sunset). ا At nighttime, when the sky is dark, we can see a multitude of points of light. ا For now let us look at the daytime sky.

Daytime
ا Just before the Sun comes into view, the sky brightens. ا When the Sun appears on the horizon (called sunrise), Earth and sky are fully lit. ا In the course of the daytime, the Sun moves across the sky, getting higher. ا After reaching a highest point, it falls back toward the horizon. ا The Sun eventually falls below the horizon (sunset). The sky darkens and nighttime soon begins.

Daily Movement of Sun

Twilight
ا There is a smooth transition from nighttime to daytime (and vice versa). ا The sky begins to brighten in the period just before sunrise. ا The sky begins to darken in the period just after sunset.

Day
ا In common usage the word "day" unfortunately has two different meanings: (1) the period of time when the Sun is up (what we have been calling "daytime") (2) the period of time between consecutive sunrises (or sunsets), or one daytime + one nighttime. ا To avoid confusion, we will use daytime to mean (1) and day to mean (2).

The Sun's Changing Position!
ا If we look at the Sun regularly, over time its position at sunrise and sunset changes, along with the path it takes as it crosses the sky. ا Let's look at the change in the Sun's path every 90 days. ا We begin around this time of year.

Sun's Path on Day 1
ا (chart 4)

Sun's Path on Day 91

Sun's Path on Day 181

Sun's Path on Day 271

Sun's Path on Day 361

What We See
ا On Day 91, the Sun rises and sets at very different locations compared to Day 1. The Sun's path on Day 91 is longer and higher than that of Day 1. ا On Day 181, the Sun's path looks very much like that of Day 1. Between Days 91 and 181 the Sun has "reversed" its movement. ا On Day 271, the Sun's path is now very short and much lower. ا On Day 361, the Sun once again moves along a path very similar to that of Day 1 or Day 181.

Seasons
ا Day 1 was chosen to be roughly the first day of what we now call spring, Day 91 the start of summer, Day 181 that of autumn and Day 271 the beginning of winter and Day 361 the return of spring. ا On day 1 (also 181 and 361) the Sun takes an intermediate path across the sky. Daytime and nighttime are about the same length. ا On the first day of summer (day 91) the Sun takes its highest path across the sky. This is the longest daytime of the year. ا On the first day of winter (day 271) the Sun takes its lowest path across the sky. This is the shortest daytime of the year.

Seasons and Weather
ا These periods are called seasons. ا During spring (autumn) the weather is moderate. As we proceed the Sun moves higher (lower) in the sky and the days are warmer (colder). ا When the Sun is highest in the sky, summer begins. The weather is at times oppressively hot. Conversely, when the Sun is lowest, winter begins and the days are very cold. ا The cycle of seasons and weather repeats: spring->summer->autumn->winter-> spring->summer->autumn->winter->...

Importance of Tracking the Seasons
ا In the temperate regions of Earth, extremes of temperature occur. Summer is hot and winter is cold. In between, spring and autumn are moderate. ا To survive, early man developed two strategies: 1. Gather naturally-growing crops and hunt animals 2. Domesticate animals for their milk and meat. ا Either strategy must take the seasons into account. Many animals (whether domesticated or wild) need to migrate. Crops only grow certain times of the year. ا Early man needed to know when the weather would change. How?

Keeping Track of the Seasons
ا A convenient way to keep track of the seasons was to mark the points on the horizon where the Sun rose or set. Prehistoric sites such as Stonehenge contain stones positioned to form sight-lines indicating the position of the Sun at the beginning of each season. Alternatively, an object could be positioned to cast a shadow around noon. The length of the shadow (longest in winter, shortest in summer) could be used.

ا

Directions in the Sky
ا Although the location of sunrise and sunset change each day, the direction where the Sun is highest doesn't change. We call this direction south. The time when this occurs is called noon or midday. ا The direction opposite south is north. ا The direction midway between north and south in the area where sunrise occurs is east. ا The direction opposite east, the area where sunset occurs, is west. ا Why can't we just say east is the direction where sunrise occurs? Because this direction changes!

Directions in the Sky

Something Strange
ا You may have noticed something strange about the directions in the sky. ا In a map of Earth, if north is "top" and south is "bottom", then west is "left" and east is "right". ا But here west and east are reversed. This is because we are looking up, not down.

The Year
ا Because the cycle of seasons repeats it is possible to figure out when a particular season will begin. ا Keeping track of how many days it takes for the Sun to go through the cycle of seasons, we find the cycle is 365 or 366 days long. This period of time is called the year.

The Night Sky
ا At night the Sun disappears below the horizon. The sky darkens. ا We see many points of light in the sky we call stars. ا Just as the Sun moves from east to west during the daytime, the stars move the same way during the night. ا One object stands out. It is about the size of the Sun. It is bright but nowhere near as bright as the Sun. It is the Moon.

Nighttime Sky
ا (image of static nighttime sky)

The Moon
ا After the Sun, the next brightest object in the sky is the Moon. ا The Moon can appear either in the daytime or at night. It changes its position with respect to the Sun or stars each day. ا The Moon is round like the Sun but fainter. ا Most of the time only part of the Moon is visible! We say the Moon goes through phases. ا When the Moon is near the Sun only a small part of it is lit. As it gets farther from the Sun more and more of it is lit. ا The period of time when the Moon circles the sky and goes through a complete set of phases is called a month.

Phases of the Moon
ا ا ا ا ا As the Moon goes around the Sun, its phases can be related to the position of the Moon relative to the Sun. At New Moon, the Moon is in line with the Sun and cannot be seen. At First Quarter, the Moon is ج of the way around the sky. It rises at noon and sets at midnight. Half of the Moon is lit, the part facing the Sun. (In the northern hemisphere it is the right half that is lit.) A Full Moon occurs when the Moon is opposite the Sun. That is, the Moon rises at sunset and is up all night, setting at sunrise. Now the entire Moon is lit. At Last Quarter the Moon rises at midnight and sets at noon. Like First Quarter, half the Moon is lit, but it is the opposite half. Between New Moon and First Quarter, and again between Last Quarter and New Moon, only a small portion of the Moon is lit - a crescent. The crescent is thinner when close to New Moon, Between First Quarter and Full Moon, and again between Full Moon and Last Quarter, most of the Moon is lit. We say the Moon is gibbous.

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Moon's Phases

http://www.moonconnection.com/moon_phases.phtml

Moon from New to Full

Moon From Full to New

Close-Up of the Moon's Phases

Movement of the Moon
ا As the Moon goes through its set of phases every 29.5 days, it makes a complete circle in the sky, but its path is curious. ا During part of the trip, the Moon moves in a high arc in the sky, similar to the path of the Sun in summer. ا But part of the trip, it moves in a low arc, like the Sun in winter. ا At other times the Moon moves in intermediate positions. ا This movement is like the year-long path of the Sun.

Learning About the Sun From the Moon
ا The Moon takes about 29.5 days to go through its cycle of phases (for example, from Full Moon to the next Full Moon). ا If we check the Moon's position against the stars, we see it only takes about 27.3 days to circle the sky. ا Because the Sun is opposite the Full Moon, it must be moving with respect to the stars to account for the difference!

Lunar Eclipse
ا Every so often, at Full Moon, a shadow creeps across the Moon's surface. ا Most of the time, the entire Moon can be seen, but the region in shadow is darkened or reddish. ا The shadow may cover the entire Moon, or only a portion of it. ا In the former case it is called a total lunar eclipse; in the latter a partial lunar eclipse.

Solar Eclipse
ا Similarly, every so often at New Moon, part of the Sun seems to be disappear, as if something is taking a growing black bite out of the Sun. ا In most cases, called partial solar eclipses, only a portion of the Sun disappears. ا Rarely, in a total solar eclipse, the entire Sun disappears. The sky turns dramatically dark and bright stars and planets can be seen. A bright region surrounds the now-invisible Sun. ا After a short period of time, the sky brightens as part of the Sun reappears. Eventually, the entire Sun is restored to view.

When Do Eclipses Occur?
ا Eclipses are rare. Most of the time New Moon and Full Moon pass without incident. ا Why aren't there eclipses of the Sun and Moon every New Moon and Full Moon? The answer wasn't known to prehistoric man.

Stars
ا At night, the sky is filled with thousands of stars. ا These are points of light that move together across the sky. ا Some stars are brighter than others, and some like redder than others; otherwise there is little to tell them apart.

A Strange Rotation
ا With careful observation we notice they the stars, indeed everything in the sky, is rotating around a fixed point in the sky. ا Some stars, close to this fixed point, don't set! ا The Sun, Moon and planets follow this rotation, but also have a second motion of their own.

Rotation Around Pole Star

Planets
ا Besides stars and the Moon, other objects can be seen in the night sky. ا The stars move across the sky in unison, never changing position with respect to each other. ا But these other objects DO change their position. They are now called planets, from the Greek word for wanderer. ا The planets move roughly along the same path as the Sun and Moon.

Mercury and Venus
ا Mercury never appears far from the Sun. Most of the time it is too close to the Sun to be seen. ا It can be seen either in the morning sky before the Sun rises, or in the evening sky after the Sun sets. ا At most, Mercury is only visible for about 7-14 days at a time. ا Venus is similar to Mercury, except it gets farther from the Sun, both in the morning and evening sky, and can be seen for months until it is too close to the Sun.

Mercury's Movement (Morning) 3/23 - 4/20 2010

Venus's Movement (Morning) 3/8 - 9/25 2010

Mars, Jupiter, Saturn
ا The movements of these three planets are quite different from those of Mercury and Venus. ا Initially, they come into view just before sunrise and rise earlier each night, moving eastward among the stars and slowly brightening. ا Eventually they slow, then reverse their movement, going west among the stars. This change of direction is called retrograde motion. During this period the planet is brightest. ا After a period of time, the planet again slows down and reverses direction, once again moving eastward. From this point on it slowly approaches the Sun, eventually disappearing into the bright dusk.

Mars's Movement 12/3/2008 - 2/8/2011

The Changing Night Sky
ا Look at the stars one evening shortly after sunset, and look again a few weeks later. ا Some of the stars you had seen in the west have disappeared. They have been replaced by some new stars in the east. ا For example, look at the following charts a month (30 days) apart.

First Day of Spring "8 PM"

First Day of Spring Two Hours Later ("10 PM")

One Month Later "8 PM"

The Sun and the Stars
ا This can be explained if the Sun moves eastward among the fixed stars. ا If we look at the sky shortly after sunset once every few weeks, we will see a slowly-moving change in the sky. ا The stars previously low in the west have now disappeared, replaced by new stars in the east. ا The same is true every time we look. After awhile we notice that the stars that disappeared have now risen in the east! ا After a year, we note that the stars have returned to the same position they were a year ago. (Note: This does not apply to the Moon or planets.)

Comets and Meteor Showers
ا Once in a while a strange object appears. It is fuzzy and sometimes has a long tail. ا Considered by many a harbinger of bad tidings, these comets were feared. ا On some nights flashes of light moving quickly across the sky are seen. These meteors sometimes appear regularly from year to year; the event is then called a meteor shower.

Mesopotamians
ا Around 3000 BC civilization arose. By civilization I mean a group of people who had figured out how to live at a permanent location growing enough food to provide a surplus. ا Such civilizations appeared in China, India, Egypt and Mesopotamia (roughly modern-day Iraq). ا Among these peoples, the ones who made the most advances in astronomy were the Mesopotamians.

Babylonians
ا Different groups of people living in this region became prominent over time. ا Such groups as the Sumerians, Akkadians, Assyrians, Hittites ruled. ا In 700 BC the Babylonians took over. A new sophistication developed in their study of the sky.

Babylonian Contributions
ا They discovered the daytime and nighttime sky were continuous. Stars and planets, invisible in daytime, could be seen at night. ا For example, at an eclipse of the Sun, some stars and planets can be seen during the day. Specific stars can be recognized from their familiar pattern. These were stars currently missing from the night sky.

Coordinate Systems
ا The Babylonians also developed a coordinate system to specify the location of an object in the sky. ا A coordinate system assigns a series of numbers (coordinates) which uniquely identify a point on an object. ا The dimensionality of the object is the number of coordinates required. ا The Babylonians pictured the sky as the surface of a sphere, requiring two coordinates.

The Celestial Sphere
ا The earlier Mesopotamians had come up with a coordinate system based on the fixed point around which the stars rotated. ا The fixed point, called the celestial north pole, had a diametrically opposite point (the celestial south pole). ا The points equally distant from the two poles formed the celestial equator. ا The sphere rotates around its poles once every day, carrying all objects with it.

Celestial Sphere

The Ecliptic
ا The Babylonians found that the Sun followed a path in the sky that repeated each year. This path we call the ecliptic. ا The Moon and planets move close to the ecliptic, but not exactly on it. At times they are north of the ecliptic, then cross it to move south of the ecliptic. Later they begin moving north, crossing the ecliptic a second time. ا The points where the ecliptic is crossed are called nodes. If the Moon or planet is moving south the point is a descending node, otherwise an ascending node.

Ecliptic Coordinate System
ا As their interest shifted to the motions of the Sun, Moon and planets, a coordinate system based on the ecliptic was created. ا The ecliptic was broken up into 12 equally-sized pieces. These pieces were given the name of the constellation. ا Since there are 360ہ in a circle, each constellation took up 30ہ. So the longitude of an object might be "Leo 18ہ". ا The latitude of an object would be the number of degrees north of south of the ecliptic.

Ecliptic -- Spring Evening

Ecliptic - Autumn Evening

The Sun's Path Along the Ecliptic (Showing Underlying Stars, Constellations)

The Sun's Location Affects the Evening Sky
ا As the Sun moves eastward along the ecliptic it makes a complete cycle in 1 year (this is essentially the definition of a year). ا Each day the Sun moves about 1ہ to the east (actually 360/365ج degrees). ا As the Sun moves each day, at night new stars come into view in the east, while stars that were in the west disappear. ا So we have the notion of "winter stars", "spring stars", etc.

Eclipses Revisited
ا Although the Sun moves exactly on the ecliptic, the Moon does not. ا Most of the time the Moon is north or south of the ecliptic, ranging up to 5ہ above or below. Because it is not in the same plane as the Earth and Sun at these times, no eclipse can occur. ا Only when the Moon crosses the ecliptic (that is, at or near a node) can an eclipse occur.

The Moon's Path and the Ecliptic 4/14/2010 - 4/26/2010 New to Full

The Moon's Path and the Ecliptic 4/28/2010 - 5/10/2010 Full to New

How Often Do Eclipses Occur?
ا If the Moon always crossed the ecliptic at the same points we would always have eclipses at the same time of year. ا In fact, the Moon's path changes significantly from year to year. ا Notice the significant movement of the descending node of the Moon's orbit in a year's time. The node has moved from Gemini into Taurus.

Precession of Moon's Node 4/15/2010 - 4/27/2010

Precession of Moon's Node 4/5/2011 - 4/17/2011

Precession of the Moon's Nodes
ا The nodes of the Moon's path move about 19 days earlier each year, a phenomenon called precession. ا This leads to a cycle of nodes every 27.21 days ا After 18.61 years the nodes have made a complete cycle along the ecliptic. ا Amazingly at Stonehenge the positions of some stones seem to indicate ancient man was aware of this.

When Do Eclipses Occur?
ا We know eclipses occur at Full Moon (lunar) or New Moon (solar). ا Each phase of the Moon repeats about 29.53 days (synodic month = S). ا The Moon must also be near the ecliptic. This occurs roughly every 27.21 days (draconic month = N). ا So if an eclipse occurs on day D, another will appear after a period which is a multiple of S and N. ا To a good approximation, 223 * S = 242 * N = 6,585.3 days = 18 years 10.3 days (or 11.3 days depending on the number of leap years during the period). ا This period is called the Saros.

Planets and the Ecliptic
ا The paths of the planets also are close to the ecliptic (though not exactly on it). ا They cross the ecliptic at ascending and descending nodes. ا Like the Moon, their orbits precess, but much more slowly than the Moon.

The Babylonian Universe
ا As the Babylonian era ended, their view of the universe was: ا Everything in the sky rotated around the north celestial pole daily. ا Superimposed on this motion, the Sun, Moon and planets had their own motion along the ecliptic. The Moon took a month to circle the sky, the Sun a year, each planet its own period of time.

The Greeks
ا The Greeks built on the work of the Babylonians. ا Their contributions were the result of their ability to think abstractly to a greater degree than their predecessors. ا As early as ca. 500 BC Pythagoras founded a school of philosophy/religion. Among his students some believed Earth was round. Some even believed the universe was centered around the Sun, not Earth. ا Euclid (fl. 300 BC) developed geometry. Although there is no evidence he directly applied his knowledge to astronomy, others did.

Arguments That Earth Is Round
ا The only two objects whose shape we can see (Sun, Moon) are round. ا Earth's shadow, cast on the Moon during a lunar eclipse, is curved. ا As ships sail away, we can still see the top of their masts while their hulls have moved below the horizon. ا As we move north or south, towards or away from the pole star, its position changes consistent with Earth being round, not flat.

Latitude = Height of North Star
ا The Greeks knew that if Earth was round, the height of the North Star could be used to determine your latitude, with good accuracy. ا Here is the proof:

Latitude = Height of North Star

http://homepage.mac.com/astronomyteacher/documents/latalt.pdf

Latitude = Height of North Star

Distance of Sun and Moon Aristarchus of Samos (ca. 250 BC) ا Aristarchus had a clever idea to calculate the relative distances of the Sun and Moon from Earth. ا He knew at First Quarter (when the Moon would appear exactly 50% lit), the angle Earth-Moon-Sun would be exactly 90ہ. Then by measuring the angle Moon-EarthSun he could find the relative distances of Sun and Moon.

Distance of Sun and Moon (continued)

Distance of Sun and Moon (concluded)
ا Unfortunately, Aristarchus' attempt failed. He computed the distance of the Sun as 20 times that of the Moon. He was wrong by a factor of about 20. ا The main reason was that angle MES was nearly 90ہ itself (and MSE extremely small). A small error in measuring it produced a large error in distance. ا Another factor was the difficulty of determining exactly when the Moon was half lit.

Circumference of Earth Eratosthenes (ca. 225 BC)
ا Eratosthenes heard reports that on the first day of summer in the town of Syene the Sun at noon was directly overhead and its reflection was seen in a deep well. ا In Alexandria, which was directly north of Syene, Eratosthenes measured the height of the Sun at noon on that day. From the shadow cast by a vertical stick he learned the Sun was 7ہ from overhead.

Circumference of Earth (continued)

Circumference of Earth (concluded)
ا Since the angle from Alexandria to the center of the Earth to Syene was 7ہ, he reasoned D / C = 7 / 360
where D = distance from Alexandria to Syene and C = circumference of Earth. ا He measured the distance D and found the circumference C to be around 40,000 km, close to the true value.

Hipparchus (ca. 125 BC)
ا Hipparchus created the outstanding star catalogue of his time. It contained at least 850 stars, and their position and magnitude (brightness) was given. ا While doing so, he compared the positions of stars he observed with those of an old Babylonian catalogue. ا He noticed these had changed systematically. In particular, the point around which the stars revolved had moved!

Precession
ا This movement was called precession. Because of it, the position of the north celestial pole and the celestial equator changes. ا The intersection of the celestial equator with the ecliptic causes the seasons to change as well. So this precession is called the precession of the equinoxes (the solstices are affected as well). ا The precession causes the Earth to act like a spinning top that wobbles. A complete wobble takes about 26,000 years.

Stars (12 Noon Jan 1, 700 BC)

Stars (12 Midnight Jan 1, 700 BC)

Stars (12 Noon Jan 1, 2000 AD)

Stars (12 Midnight Jan 1, 2000 AD)

Stars (12 Noon Jan 1, 15000 AD)

Stars (12 Midnight Jan. 1, 15000 AD)

Ptolemy (ca. 150 AD)
ا Claudius Ptolemy created the best star catalogue of his time. ا He is best known for his attempt to explain retrograde motion, which was still a major problem for everyone trying to explain the movements of the planets. ا Since a circle was the "perfect" shape for an orbit, Ptolemy added epicycles (circles whose centers revolve around larger circles). However, his system did not accurately reproduce retrograde motion.

Ptolemy's Epicycles

The Dark Ages
ا And then ... basically nothing for 1000 years. ا Greek science was represented by Aristotle, who believed in a geocentric system. ا Plato was not friendly to astronomy. ا The Romans, who succeeded the Greeks in Europe, were engineers, not abstract thinkers.

Renaissance
ا Almost all the great astronomical works of antiquity were lost. ا Most notable of the survivors was Ptolemy's Syntaxis, which became the Almagest when translated into Arabic. ا Eventually these works were translated into Latin and became available in Europe. ا Slowly the study of the solar system was reawakened.

Copernicus (1473-1543)
ا Nicolaus Copernicus, on his deathbed, agreed to publish his work "On the Revolutions of the Heavenly Spheres". ا In it he states the Sun is the center of the solar system. Some Greeks had proposed similar theories, but Copernicus worked his system in full mathematical detail (the work was about 40 years in the making). ا Copernicus explained the motion of the heavens as we see it by postulating the rotation of the Earth, its revolution about the Sun, and the tilt of Earth's rotational axis. ا Because Copernicus retained circular orbits, he added epicycles in order to duplicate Earth's motion.

How Things Move
ا Copernicus explained the daily movement of the stars with a rotating Earth. ا The Sun did not move; Earth's revolution around it created the illusion. ا Earth takes exactly one year to orbit the Sun. ا The other planets move around the Sun as well, and what we see is a combination of our motion and theirs. ا The Moon does revolve around Earth.

How Things Move (continued)
ا The ecliptic is really the plane of Earth's orbit around the Sun. ا The Moon and other planets also orbit around the Sun, but in slightly tilted orbits from ours. ا The celestial equator and the ecliptic are both great circles. They meet each other twice a year, at the spring (ascending node) and autumn (descending node) equinoxes. ا The celestial equator and the ecliptic are farthest apart at the summer and winter solstices. At these times the two circles are 23حہ apart.

Ecliptic and Celestial Equator 4/14/2010 9 PM EDT

Terminology
ا Copernicus placed Mercury and Venus closer to the Sun than Earth. These were called inferior planets. ا Mars, Jupiter and Saturn are farther from the Sun than Earth, and are called superior planets.

Inferior Planets
ا Inferior planets stay close to the Sun as viewed from Earth. They are best seen when farthest from the Sun at maximum or greatest elongation, either east of the Sun (when they appear in the evening sky) or west of the Sun (in the morning sky). ا When they move from the morning into the evening they are farther from Earth than the Sun. This event is called superior conjunction. ا When they move from the evening to the morning sky they are closer to Earth than the Sun. This is inferior conjunction. ا At conjunctions the planet is lost in the Sun's brilliance.

Superior Planets
ا Superior planets can be when they are opposite and setting at sunrise. ا The planets are closest time. ا They are in conjunction are in line with the Sun, The planet is not visible the bright Sun. best seen at opposition, the Sun, rising at sunset to Earth around this
with the Sun when they as seen from Earth. at this time because of

Retrograde Motion
ا For all the trouble retrograde motion caused the ancients, the solution was simple once a Sun-centered solar system was accepted. ا When an inner planet passes an outer planet, it is moving faster along a shorter path. The outer planet seems to move backwards with respect to the background stars.

Explanation of Retrograde Motion

Synodic vs. Sidereal Periods
ا The synodic period of a planet (or other solar system object) is the time between two consecutive configurations (e.g., oppositions or conjunctions) as seen from Earth. ا The sidereal period of a planet is its true orbital period with respect to the stars. ا The synodic period can be found by observation. The sidereal period must be calculated from the synodic period.

Planetary Configurations

Time
ا We live our lives by the Sun. Our day can be thought of as the time between consecutive noons (when the Sun is due south). ا Nowadays we break up the day into 24 hours, each of which is made up of 60 minutes, which in turn is made up of 60 seconds.

The Sidereal Day
ا In one day, the Earth actually rotates a little over 360ہ because of its revolution about the Sun! ا If the Earth rotated exactly 360ہ each day, the same stars would appear at a given time. ا It takes about 23 hours 56 minutes for Earth to rotate exactly 360ہ. This is called the sidereal day. ا The extra four minutes each day changes the appearance of the sky.

Sidereal vs. Synodic Day

Finding Sidereal Period from Synodic Period (Inferior Planet)

Finding Sidereal Period from Synodic Period (Superior Planet) ا For a superior planet, the formula changes because Earth laps the outer planet. ا We get
1/P = 1/E - 1/S where E = Earth's sidereal period, S = the planet's synodic period and P = the planet's sidereal period.

Synodic and Sidereal Periods of the Planets
Planet
Mercury Venus

Synodic period
116 days 584 days

Sidereal period
88 days 225 days

Earth Mars
Jupiter Saturn

--780 days
399 days 378 days

1.0 year 1.9 years
11.9 years 29.5 years

Finding the Size of Planet Orbits Inferior Planets

Finding the Size of Planet Orbits Superior Planets

Distances of Planets from the Sun (in AU)
Planet
Mercury Venus Earth Mars Jupiter Saturn

Copernicus
0.38 0.72 1.00 1.52 5.22 9.07

Modern
0.39 0.72 1.00 1.52 5.20 9.54

Finally Explaining the Seasons
ا Once a moving Earth that revolved around the Sun was accepted, it became easier to accept that the daily rotation of the heavens was caused by Earth's own rotation. ا Because the axis of rotation of Earth is tilted to the plane in which it orbits the Sun, at different times of the year Earth's poles point towards or away from the Sun. ا The first day of summer occurs in the northern hemisphere when the north pole is most tilted toward the Sun. Half a year later winter begins when the north pole is tilted away from the Sun. On the first day of spring and autumn neither hemisphere is favored. ا The opposite occurs for the southern hemisphere - summer begins when the south pole is titled toward the Sun, and winter begins when the south pole is tilted away from the Sun.

Tycho Brahe (1546-1601)
ا Tycho Brahe was a Danish nobleman obsessed with the sky. ا He built a magnificent observatory on the island of Hven. This was before telescopes were invented; instead Brahe produced unprecedented accuracy of planet positions with huge quadrants and other equipment. ا After the king died, Tycho lost favor in the court and moved to Prague in 1599, where he was sponsored by King Rudolf II, Holy Roman Emperor. ا Theory was not Tycho's strength. He developed a solar system in which all the planets orbited the Sun, but the Sun orbited Earth.

The Telescope (1609)
ا The telescope was developed in the late 16thearly 17th century. ا Using them, planets appear as small balls of light, while stars remain points. ا Jupiter has four moons revolving around it. ا Saturn has what is eventually found to be a ring. It has one moon. ا Venus and Mercury have phases, like the Moon. ا Dark spots were found on the Sun.

Galileo (1564-1642)
ا In 1609 Galileo was among the first to look at objects in the sky with a telescope. ا The magnification of Galileo's scopes ranged from 3x to 20x. ا With the largest it was possible to see craters and mountains on the Moon, four moons going around Jupiter, another Moon around Saturn and phases of Venus and Mercury. ا These observations helped to deal a death blow to the geocentric view of the solar system.

Galileo's Telescope

Johannes Kepler (1571-1630)
ا Kepler worked as Tycho Brahe's assistant for several years. When Tycho died Kepler inherited his measurements of planetary positions. ا After years of studying he came up with his three laws of planetary motion:

Kepler's First Law
ا The orbit of a planet around the Sun is an ellipse with the Sun at one focus. ا Circular orbits had been the obsession of almost everyone. ا An ellipse is defined as the set of points whose distances from two given points is a given positive number. ا The given points are called foci (plural of focus). ا The result is an "elongated circle".

Ellipse

Kepler's Second Law
ا A line from the planet to the Sun sweeps out equal areas in equal intervals of time. ا As a consequence of this, a planet moves faster when it is closer to the Sun.

Kepler's Third Law
ا The square of the orbital period of a planet is proportional to the cube of the semimajor axis of its orbit. ا Since we can find the orbital period of a planet by observation, we in effect have a scale model of the universe. But what is the scale? ا http://www.physics.sjsu.edu/tomley/Kepler 12.html

A Problem with Time
ا The fact that the orbit of Earth around the Sun is an ellipse, not a circle, has an effect on our timekeeping. ا By Kepler's Second Law, Earth will move faster around the Sun when it is closer to it; slower when it is farther away. ا This means the length of the day, defined as the time interval between two consecutive noons, will vary.

Fixing the Problem
ا We solve this problem by inventing a mean solar day. The length of this day is an average of the lengths of days throughout the year. It is this day that we use. ا Because this day is used, when our watch reads noon, the Sun may be slow or fast by up to 16ح minutes.

Isaac Newton (1643-1727)

Newton's Laws of Motion
ا 1. A body remains at rest, or moves in a straight line at constant speed, unless acted upon by an outside force. ا 2. The acceleration of an object (change in velocity) is proportional to the force acting upon the object. F = ma ا 3. When a body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.

Newton's Law of Gravitation
Two bodes attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Using calculus (which he invented) Newton proved Kepler's Laws.

Scale of the Solar System
ا Kepler's third law solves the problem of the relative distances of the planets in the solar system, but what are the actual distances? ا In 1672, Gian Cassini estimated the distance from Earth to Mars by the method of parallax. With a confederate in French Guiana a few thousand miles away, they measured the position of Mars with respect to nearby stars. The change in position yielded a crude estimate of the Earth-Mars distance (it turned out be about 7% off).

Accurate Distance Measurements
ا The transits of Venus across the Sun in 1761 and 1769, and in 1874 and 1882 provided more accurate distances. ا A close pass by the asteroid Eros in 1900-01 enabled better estimates. ا In the 1960's, radar was used to get much more accurate distances. ا Since then space probes have produced more accurate values. ا Average Distance from Earth to Sun (1 AU) = 92,955,807 miles.

Halley Predicts His Comet
ا Sir Edmund Halley applied Newton's laws to 24 comets seen from 1337 to 1698 whose positions had been measured. ا He discovered the comets of 1531, 1607 and 1682 moved in almost identical orbits separated by about 75 years. He believed they were the same comet and predicted it would return in 1758. ا Halley died in 1742, but on Christmas Day 1758, the comet was seen. Since then it has been known as Halley's Comet.

Herschel Discovers Uranus (1781)
ا William Herschel (1738-1822) was the greatest observer of the sky in his era. Unlike most of his contemporaries, he did not study planets but rather the other odd objects of the sky - star clusters and nebulae. ا Nevertheless, in 1781 he discovered a bluish non-stellar object he had not noticed before. Subsequent observations indicated the object did change its position. Herschel had stumbled upon a planet! ا Eventually named Uranus after the Roman god of the sky, Uranus was a sensation, despite being much fainter than the other planets, barely visible with the naked eye from a dark sky.

Asteroids: Bode's Law and Ceres
ا In 1772 Johann Bode noticed (he was not the first) that the relative distances of the known planets in order were 0.39, 0.72, 1.00, 1.52, 5.20 and 9.54. (Distances given in astronomical units) ا This sequence can be approximated by the formula (n + 4)/10, where n = 0, 3, 6, 12, (24), 48, 96, except that there is no planet corresponding to 24 (which would have distance 2.8). ا Belief in "Bode's Law" grew when Uranus was discovered. Its distance of 19.2 AU agreed well with the predicted value 19.6 ا A group of astronomers known as the Celestial Police determined to find the missing planet. ا In 1801, Giuseppe Piazzi discovered Ceres, which turned out to have distance 2.77, a good fit for "Bode's Law".

Asteroids: More Found
ا Ceres was very small, but was treated as a fullfledged planet. ا In the next few years, three more similar objects were found: Pallas, Juno and Vesta. All four objects were in the same general area of the solar system, lying between the orbits of Mars and Jupiter. ا Speculation that the four might be survivors of a planet that was destroyed. In any case all four were treated as planets.

Asteroids: 19th Century
ا After the first four, no asteroids were found until 1845! A handful more were found, all by visual observation through a telescope. ا In the second half of the 19th century, it become possible to take long photographic exposures of the sky. As a result much fainter objects could be found. ا The result was dozens, then hundreds, of asteroids were found.

Asteroids: Planets No More
ا As the number of asteroids exploded, many barely visible even in a telescope, the sentiment grew that asteroids, even the first four, should not be considered planets. ا Nowadays, more asteroids are discovered than ever. Worry about a rogue asteroid colliding with Earth has led to funding and many telescopes world-wide are used mainly to find asteroids. ا The result is thousands of asteroids are discovered each month. ا A rough estimate gives the total number of asteroids as between 1.1 and 1.9 million.

"Bode's Law"
ا What happened to Bode's Law? ا When Neptune was discovered, its distance to the Sun was 30.06 AU. This is not in good agreement with the prediction of 38.8. ا Bode's Law is now considered a fluke.

Neptune: Discovery (1846)
ا Uranus's orbit was studied by astronomers, who found the planet was not moving exactly in the ellipse it was supposed to be traveling in. ا Urbain Le Verrier and John Couch Adams separately speculated that a planet farther than Uranus could account for the deviation. ا Both Le Verrier and Adams reached an estimate for the position of this unknown planet. ا Le Varrier notified the Berlin Observatory of his calculations, and that night Johann Galle observed the planet that would be called Neptune.

Neptune: Controversy
ا For many years the British tried to claim themselves as "co-discoverers" of Neptune. ا In fact, Adams had several different predictions, which were not as good as Le Verrier's. Evidence for this was recently found in Chile, where a British scientist had been hoarding Adams' calculations.

Pluto Discovered by Tombaugh
ا Believing an outer planet was modifying Neptune's orbit, wealthy amateur Percival Lowell began hunting for it. ا Many photographic images were taken of the sky at different times. ا A young assistant, Clyde Tombaugh, looked at the images with the help of a "blink comparator". ا This was a device that enabled him to compare two photographs of the same region of the sky taken at different times. The stars would all have the same position, but a planet would have moved and the change of position could be recognized.

Pluto (continued)
ا On February 8, 1930, Tombaugh saw an object had moved. It was subsequently found in the sky. ا Named after Pluto, the Roman god of the underworld, it was too small to be the cause of any perturbations in Neptune's orbit. (It turned out the "perturbations" were errors in measuring Neptune's position.) ا At magnitude 14 Pluto is extremely faint, and requires a large telescope to be seen. Nevertheless it was recognized as a bona fine planet. (more later)

Comets
ا Objects originally from the far solar system, some comets approach the inner solar system, either by being perturbed by a distant object or being flung into a nearparabolic orbit. ا Occasionally, a comet may be perturbed by Jupiter or another large planet. As a result it might leave the solar system entirely, or instead may move into an orbit closer to the Sun. ا Some of these perturbed comets are in the asteroid belt. ا Comets are made or ice and rock. When approaching the Sun, they warm up and some of the ice sublimates, creating the tail.

Kuiper Belt
ا Astronomer Gerard Kuiper (among others) suggested there may be a region in the solar system beyond Neptune where a large number of small bodies would be found. These would be the source of short-period comets (period less than 150 years). ا In 1992, after five years of searching, David Jewett and Jane Luu discovered the first KBO (Kuiper Belt object).

Kuiper Belt (continued)
ا The belt is roughly from 30 to 55 AU from the Sun. ا Like the asteroid belt, it consists of smaller objects. ا Over 1,000 objects have been found; it is estimated some 70,000 objects over 100 km are present in the belt.

Pluto - Planet No More
ا Since its discovery, it was found that Pluto was smaller than originally thought. ا The discovery of several large KBOs convinced most astronomers that bodies larger than Pluto would eventually be found. ا In 2005, Eris (originally images in 2003) was discovered. Since it had a satellite, its mass could be computed and turned out to be 27% larger than Pluto. ا At the 2006 meeting of the International Astronomical Union, Pluto was demoted to "minor planet" status. In the same group were placed the asteroid Ceres and KBOs Eris, Haumea and Makemake.

Largest KBOs
Name Diameter (km) Discovery

Eris
Pluto Makemake

2397
2320 1500

2005
1930 2005

Sedna
Chiron

1400
1205

2003
1978

Haumea
Orcus Quaoar

1150
946 844

2005
2004 2002

Ixion

650

2001

Trans-Neptunian Objects

The Oort Cloud
ا The Oort cloud is a spherical cloud of comets surrounding the solar system at a huge distance from the Sun - a light year or more. ا It is believed the comets formed near the Sun are were scattered far away by interactions with a giant planet, especially Jupiter.

Formation of the Solar System
ا We believe the solar system formed 4.55 to 4.56 billion years ago from material in a molecular cloud containing hydrogen, helium and some "heavy" elements and molecules. ا Under its own gravity, part of this material began to collapse. Most of the mass collected in the center, eventually forming the Sun, while the rest flattened into a "protoplanetary disk".

Formation of Planets and Moons
ا The protoplanetary disk eventually collapsed to form planets. In some cases portions of the disk split off and formed satellites of the planet. ا The planets and almost all of their large satellites move around the Sun in a counterclockwise direction (as seen from the north). ا Satellites (or moons) may have formed in other ways. Some small moons may have been gravitationally captured by a planet. Earth's own Moon may be a special case (see below).

Was Earth's Moon Formed by a Collision?
ا Earth has a large iron core, but the Moon does not. ا This seems to imply that unlike most large moons of the solar system, the Moon was not created at the same time and place as Earth. ا Some astronomers have advanced a dramatic scenario for the formation of the Moon: ا Some time after Earth formed, but early in the history of the solar system, a large object struck Earth with a glancing blow. A large part of Earth's relatively lightweight mantle was sheared off. ا Subsequently Earth recovered some of its material, but the rest became the Moon. This would explain the lack of a iron core.

The Sun's (and Earth's) Future
ا In about 5 billion years the Sun will become a red giant and expand outwards, possibly incinerating the inner planets. ا Eventually the Sun will lose most of its matter and surround itself with a planetary nebula. ا The Sun itself will become a white dwarf, then over trillions of years slowly radiate its energy until it goes dark.

References
ا "Astronomy Before the Telescope", edited by Christopher Walker, St. Martin's Press ا "Universe", by William J. Kaufmann, Freeman. ا "The Nine Planets" website, www.nineplanets.org. ا "Wikipedia" website (supply keyword) ا "Astronomy Picture of the Day" website, apod.nasa.gov/