Astronomy

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Scale of Astronomy

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1.) Astronomy is the science of the entire study of the entire universe. Regular fish = on meter and there are 40 scales of magnitude in the unverise. Stars are the size of a billion fishes, galaxies are 100 billion times bigger than stars and galaxy clusters are 1000 times bigger than that. Humans are in the middle.

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Thales

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- Greek, Inventor of Elemental Geometry and Stereography: two dimensional representation of three dimenisional surface on celstial sphere

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Aristotle

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Greek, taught a geo-centric (earth-centered) Universe with all motion following the “perfect” shape of circles. For almost 2,000 years this was the thinking in western Europe

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Aristarchus

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Greek, Measured the sizes and distances of the Moon and the Sun fairly accurately. Also proposed a Sun-centered universe.

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Hipparchus

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Greek, Creator of the first Star Catalog and inventor of the magnitude scale of stellar brightness still in use today.

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Ptolemy

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Egyptian, Mathematician who tried to make his bulky epicycle system work to explain the motions of the planets in the sky.

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Copernicus

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Polish, Published, posthumously, a text professing a heliocentric (Sun-centered) “solar” system of planets that accurately predicted the motions of the planets. Still used Aristotle system

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Clavius

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German, Jesuit Vatican astronomer to Pope Gregory XIII, who calculated a more correct value for the length of the tropical year. He provided the leap year cycle pattern to keep the civil year (integer solar days) and the tropical (seasonal) year in synch, what we call today the Gregorian Calendar. Wednesday October 4 1582 was followed by Thursday October 15 1582 to account for the extra days that had been added in since Julius Caesar introduced the simple 4-year pattern of leap years 1600 years earlier. Also created decimal and vernier scale

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Brahe

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Danish, From his underground observatory, Uraniborg, he studied and measured the heavens for more than 20 years. He compiled detailed observation logs of the locations of the stars, planets and comets, all before the invention of the telescope. He never processed any of the data and hired Johannes Kepler to analyze the data and provea Brahe-based Ptolemaic hybrid model of the Universe correct a year before Brahe’s death

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Galileo

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Italian, Often erroneously credited with inventing the telescope (Hans Lippershey), he constructed his own after reading a paper by Lippershey. He constructed three telescopes, each of slightly larger apertures. He was the first person to use a telescope to examine the heavens and discovered the largest moons of Jupiter, craters on the Moon, Sunspots, the Milky Way as individual stars, and the phases of Venus and Mercury

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Kepler

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Austrian, Processor of Brahe’s data and after failing to prove Ptolemy’s Epicycles or Brahe's hybrid model correct, proved Copernicus’ helio-centric system to be correct. Identified three laws of orbital motion.

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Newton

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British, Brilliant mathematician who provided three laws of motion that explained the falling motion of an apple and the orbital motion of the Moon and planets as a result of the same force: gravity. Invented the Reflecting telescope and Calculus.

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Halley

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, The 2nd Astronomer Royal who discovered that comets are cyclical phenomenon and they follow the same orbital motion laws established by Kepler and Newton. The comet he used to prove his theory bears his name today and still returns every 76 years.

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Harrison

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, Carpenter, clockmaker and inventor of the Marine Chronometer and solver of the "Longitude Problem". He is responsible for modern accurate timekeeping and made it possible for ships to accurately calculate their positions on the open sea. He is credited with inventing jewel bearings, roller bearings, bi-metallic strips for temperature compensation, the grasshopper escapement and the gridiron pendulum.

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Rotation

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a circular motion around a body on an axis where the axis passes through the body in question. The earth “Spins every day

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Revolution

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the circular motion around a body on an axis where the axis does not pass through the body in question. A complete circuit is an orbit. Earth revolves around sun yearly.

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Zenith

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a topocentric term referring to the point on the celestial sphere that is directly over your head, or straight up relative to local gravity. Every point on the Earth has its own unique zenith.

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Nadir

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a topocentric term referring to the point on the celestial sphere that is directly under your feet. The anti-zenith or straight down relative to local gravity.

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Horizon

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a topocentric term referring to the collection of points, all 90 degrees away from the zenith. It surrounds the observer, 360 degrees, where the Earth would meet the sky, if there were no intervening obstructions. At sea, it is where the sea meets the sky, if viewed from sea-level.

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Meridian

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a topocentric term that refers to an imaginary line on the celestial sphere that runs from the North Celestial Pole through the zenith and continues to the South Celestial Pole. Both Celestial Poles are simultaneously visible only from the Geographic Equator, so the Meridian (in the northern hemisphere) will intersect the horizon at true South. It should be noted that the Meridian (in the Northern Hemisphere) does not continue to the Northern Horizon, but only runs from Celestial Pole to Celestial Pole. All points on the Celestial Sphere that share a Right Ascension value will cross the meridian (transit) at the same time.

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Azimuth

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One of the two topocentric angular parameters describing the location of an object or point in the sky. Specifically just the horizontal component as measured clockwise from North, along the horizon. North is usually considered to be 0 degrees with East as 90, South as 180, and West as 270 degrees.

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Altitutde

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One of the two topocentric angular parameters defining the location of an object or point in the sky, specifically just the vertical component as measured straight upwards from the true horizon toward the zenith. The horizon has an altitude of 0 degrees and the zenith, an altitude of 90 degrees. Also referred to as Elevation, but the term Altitude is preferred.

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transit

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the act of crossing the Meridian or the point in time when an object in the sky or a particular point on the Celestial Sphere is on the Meridian, crossing it moving from East to West. All objects on the Celestial Sphere will transit at some point each day. All points sharing a common

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New Moon

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No part of the moon is illuminated. . Since the Moon and the Sun are so close together in the sky when this occurs, the Moon rises with the Sun and sets with the Sun. Moonrise and Sunrise occur at generally the same time.

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Waxing Crescent

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The illuminated portion of the Moon still faces the Sun, as always, but the Moon is no longer directly in front of the Sun, so that we can see a small portion of the Moon illuminated on the right hand side
As it moves farther from the Sun in the sky, the Moon also rises later each day and sets later each night

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First Quarter Moon

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At this point, the crescent has grown to completely fill the right side of the Moon and the Moon has completed one fourth of its trip around the Earth. The Moon will rise about 6 hours after the Sun (noon) and be found high in the sky near the meridian at sunset. The Moon will then set about 6 hours after the Sun in the middle of the night.

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Waxing Gibbous

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when left half starts to become illuminated after full right is already illuminated. Moon rises after noon and sets after midnight closer to dawn each day

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Full moon

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At last the Moon completes one half of its orbit and is on the opposite side of the Earth from the Sun. We see its full disk completely illuminated as the Moon passes through the Full phase. The Moon is at its brightest at this point. Located opposite the Sun in the sky, the Moon rises as the Sun sets, spends the whole night crossing the sky, transiting at midnight, setting as the Sun rises..

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Waning Gibbous

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when moon de-illuminates from left to right. Duringthis phase, each day the Moon rises after sunset, later and later, transits after midnight, later and later, and sets after sunrise, later and later. It is during this phase that the Moon may be seen after sunrise, during the morning hours in the western sky.

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Third Quarter

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When the Moon completes three fourths of its orbit, the waning gibbous phase has shrunk to the point that one half of the Moon's disk is illuminated. With this quarter phase it is the left half of the Moon's disk that is illuminated. The Moon is to Earth's right as we face the Sun. The Third Quarter Moon rises at midnight, transits at sunrise and sets at noon.

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What causes the Earth's pole precession? How long is that cycle?

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The previous discussion about the Moon's perigee describes what is called the Progression of the Moon's Apsides. The discussion about the Moon's nodes describes what is called the Regression of the Moon's Nodes. The bulge of the Earth's equator together with the 23 1/2 degree tilt of the Earth's axis causes a similar effect on the Earth's axis of rotation. In attempting to "flatten" out the tilt of the Earth's spin, all the Sun can succeed in doing is twisting the axis rotation.

This produces the 26,000- year wobble of the Earth's axis that is referred to as the Precession of the Pole (also referred to as the Precession of the Equinox).

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What is the largest cyclical perturbation of the Moon called? When was it discovered?

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The largest cyclical perturbation of the Moon actually has a name, the Evection. It was discovered by Hipparchus, and Ptolemy mentions it prominently. These ancient astronomers did not know why it occurred, but they did detect its effect on the position of the moon.

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Why are the progression of the perigee and regression of the nodes considered secular?

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This perturbation of the Longitude of the Ascending Node (Ω) is secular in nature because the result of the perturbation is that the angle is constantly decreasing (moving west in R.A.). The observed effect is that the Moon's ascending and descending nodes move westward along the ecliptic about 1.5 degrees per lunation.

The perigee advances 1 second of Right Ascension (eastward) every 36 minutes of time. This moves the perigee around in the plane of the orbit, once completely in 6 years and a few days. Both of these secular perturbations are, as are most perturbations of the moon's orbit, caused by the sun. The sun is the most influential third body one can possibly inflict on the moon's unsuspecting osculating orbit.

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What is Kepler's equation good for?

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Kepler also developed an equation (“Kepler’s equation”: M = E - e sin(E) ) to follow the motion of a body in orbit around the Sun and then predict its position after a specified amount of time.

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What is the relationship of the osculating orbit and Newton's 2-body system? 3-body system?

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In one sense the osculating orbit is theoretical. No real body can attain such an orbit and maintain it for long. The real world does not contain simple 2-body systems. Multiple bodies are part of real systems and they exact their influence on the osculating orbit. In a 3-body (or n-body) system, outside influences will distort and otherwise modify an osculating orbit into a new osculating orbit. In reality, for most orbits, the osculating orbit parameters change only very slowly and the parameters can be used to predict the position of the body over a period of many orbits. As more time passes, the accuracy of the calculated position comes into question. Newton stated that Kepler's equation was perfectly good for 2-body systems, but an equation for a 3- body system would be very complicated, if it existed at all. He was unable to create a 3-body solution and stated that it was probably beyond the ability of humans to compute

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What is a perturbation? What kinds of perturbations are there? What does a perturbation affect?

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A periodic or linear modification of one (or more) of the 5 parameters of the osculating orbit of a body…

Perturbations occur in two varieties, Secular and Cyclical. Secular perturbations are those variations that are linear in their nature, varying in value in one direction or the other, increasing or decreasing, positive or negative, potentially forever (or until the perturbing force is removed or altered). Cyclical perturbations, on the other hand, cause an oscillation or rhythmic variation in an osculating element, back and forth, increasing and decreasing, synchronized or coordinated with some gravitational encounter with a third (or fourth, or fifth, …) body.

Sparkles thinks that perturbations effect the moons orbit but don’t trust him on that.

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What is the difference between a progression or regression and a precession?

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The previous discussion about the Moon's perigee describes what is called the Progression of the Moon's Apsides. The discussion about the Moon's nodes describes what is called the Regression of the Moon's Nodes. The bulge of the Earth's equator together with the 23 1/2 degree tilt of the Earth's axis causes a similar effect on the Earth's axis of rotation. In attempting to "flatten" out the tilt of the Earth's spin, all the Sun can succeed in doing is twisting the axis rotation. This produces the 26,000- year wobble of the Earth's axis that is referred to as the Precession of the Pole (also referred to as the Precession of the Equinox).

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Waning Crescent Phase

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The Crescent phase returns in a shrinking form with just the left side of the Moon illuminated less and less each day. Like the two kinds of Gibbous phases there are two kinds of Crescent phases and this is the shrinking crescent. This Crescent Moon rises before the Sun, transits before noon, and sets before the Sun, but closer and closer to sunset

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Conjunction and Opposition

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.) moon is in conjuction with sun at new moon phase. At opposition during full moon phase. A conjuction is a close passage of two celestial bodies.

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Solar Day

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the time from one transit of Sun until the next transit of the Sun. The time is not constant. Different then a mean solar day which is an average of solar days throughout an entire year. Definition of our civil 24 hour day.

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Sidereal day

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the time from one transit of any particular star (or point on the celestial sphere) until the next transit of that same star. A true 360-degree rotation of the Earth on its axis, which is covered in 23 hours 56 minutes 4.091 seconds (of mean solar time). is shorter than a Mean Solar Day by about 4 minutes. It is shorter because of earth’s wobbling axis.

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Spinning in the solar system

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The earth rotates towards the east so we see the sky move to the west. All planets in the solar system rotate to the east and revolve around the sun to the east and all moons revolve to the east so everything goes westwards or counter clock wise.

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Latitude

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– north-south component on the grid. Measured in degrees away from equatorial line. Posative values are towards the north pole and negatives toward the south.

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longitude

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the east-west component on the grid. Measured in degrees away from the Prime Meridian.

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Declination

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The north-south component of the grid system used to describe the location of an object or point on the celestial sphere.

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Right Acension

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the east-west component of the grid system used to describe the location of an object or point on the celestial sphere. It is similar to longitude in application, but is not measured in degrees, minutes, and seconds. It is instead measured in units of time as defined by the Earth’s rotation. The units of time applied are hours, minutes, and seconds, with 24 hours defined by one complete turn of the sky. The minutes and seconds of Right Ascension should not to be confused with arc-minutes and arc-seconds of longitude, latitude, or of declination. One hour of Right Ascension is equivalent to 15 degrees (360 degrees / 24 hours). One minute (of time) of Right Ascension is 15 times larger than one minute of declination. The same is true for a second of Right Ascension relative to a second of declination. The zero hour point of Right Ascension is defined by the beginning of spring, the spring equinox. Right Ascension increases in value in an eastward

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Cincinnati's latitude and longitude

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latitude – 39.8 degrees north and longitude is 84.3 degrees west.

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Two great circles on celestial sphere

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Eclipltic – is the geometric plane of the Earth’s orbit. Since the earth rotates around the sun on this plane, the sun is viewed moving along on the ecliptic from earth. Earth is tilted 23.45 degrees on ecliptic.
Celestial equator - is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space. As a result of the Earth's axial tilt, the celestial equator is inclined by 23.4° with respect to the ecliptic plane.

When those two intersect you have the equinox.

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Seasons

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-seasons are due to earhts 23.5 degree tilt
-Vernal Equinox – signals spring
- Summer Solstice – begins summer
- each of the seasons occupies a specific length of time but for each season it is a different length of time
- spring and summer are longer than winter and autumn. Winter is the shortest

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Tropical Year

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actual time it takes for earth to go around sun

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Sidereal year

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time it takes earth to rotate around sun according to the stars. 20 minutes shorter than tropical year. If seasons went by this, they would shift so they are tied to tropical year instead.

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First point of Aries

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same thing as the vernial equinox. Because of earth’s rotation on axis, its not in Aries constillation anymore, but actually in pisces. Proves the earth is slowly rotating on axis.

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Astronomical unit

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= invented by keplar and is 92,955,622 statute miles
- earth has a 25,000 mile gerth

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statute mile

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a unit of distance derived from the Latin “mille”, meaning one thousand. The applied distance was the equivalent to 1,000 left and right strides of a well-drilled Roman Legionnaire. Today it is recognized as 5,280 feet. Roman soldiers were often used (paid) to measure off distances between towns and villages because the lengths of their strides were so even and predictable.

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nautical mile

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a unit of distance derived from trigonometric analysis of the Earth. This is the linear distance across the Earth’s surface described by 1 arc-minute of angle as measured from the center of the Earth. It is about 15% longer than a statute mile, a little longer than 6,076 feet.

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degree

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one of the units defined by the Babylonians to define circular or angular measurement. 360 degrees define a complete circle.

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arc-minute

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a sub-division of a degree (1/360th of a circle) into 60 equal finer divisions. Equal to 1/60th of a degree, or 1/21,600th of a complete circle. It is symbolized by a single accent or quote following the value, as in 31’ (thirty-one minutes). It is an angular measurement and not related to any unit of time.

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arc-second

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: a sub-division of an arc-minute (1/21,600th of a circle) into 60 equal finer divisions. Equal to 1/60th of an arc-minute, 1/3,600th of a degree, or 1/1,296,000th of a complete circle. It is symbolized by a double accent or quote following the value, as in 8” (eight seconds). It is an angular measurement and not related to any unit of time.

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Three apparent motions of the moon

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1. . First, the Moon’s orbit is tilted or inclined about 5 degrees relative to the Ecliptic. This is why the Moon’s path in the sky does not follow the Ecliptic exactly, but does not wander too far from it, either, crossing the Ecliptic twice during a lunation (full trip around the Earth).

2. . Second, the Moon’s orbit is an ellipse, not a circle, so there are times during its orbit when it is closer to the Earth than other times

3. Third, the elliptical nature of the Moon’s orbit causes it to change its angular velocity throughout the orbit so that there is a “fast” part of the orbit and a “slow” part of the orbit.

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Retrograde motion

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The motion in question is called retrograde motion and it occurs when a particular planet, "wandering" eastward along the ecliptic for the most part, slows down, stops and then moves westward for a while. It soon (several weeks later) slows down, stops moving westward, and begins moving eastward again.
-This temporary, apparent, "backwards" motion against the Celestial Sphere is caused by the Earth orbiting the Sun faster than the planets that are farther from the Sun.
-all the planets farther away from the earth have retrograde motion. They are called superior planets.

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Ptolmeys solution to retrograde motion

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Ptolemy attempted to explain the backwards motion in the sky by placing the planets on a small circular path that was not quite centered on a larger circular path. Offset circles on circles: Epicycles

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Copernicus' solution to retrograde motion

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proposed a helio centric solar system.

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Keplers three laws

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1. The orbit of every planet is an ellipse with the Sun at one of the two foci

2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.[1]

3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
-third equation uses p as orbital period, a as the semi major axis in oribt, m as mass and g as gravitational constant.

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Newton's inverse square law

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.) called inverse square law because the force and accerlation is inversely proportional to the square of the mass of an object and vector.