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# Sistem Kordinat

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### Sistem Kordinat

1. 1. Sistem kordinat <ul><li>Untuk menetapkan kedudukkan benda langit </li></ul><ul><li>2 nilai di perlukan ~ berapa tinggi & berapa jauh lingkarannya? </li></ul>
2. 2. Sistem Di Gunakan <ul><li>Ufuk Tempatan( Horizon) </li></ul><ul><li>Ekliptik (Ecliptic) </li></ul><ul><li>Khatul Istiwa(Equatorial) </li></ul><ul><li>Galaktik (Galactic) </li></ul>
3. 3. Bagaimana kita tentukan tempat atas bumi? <ul><li>Maps, mapquest, Google Map, GPS </li></ul><ul><li>If we ignore how high it is above the sea </li></ul><ul><li>To describe a spot on the surface of the earth, we use a set of numbers (degrees), called Coordinates </li></ul><ul><ul><li>Longitude </li></ul></ul><ul><ul><li>Latitude </li></ul></ul>0º
4. 4. <ul><li>Position in Degrees </li></ul><ul><ul><li>Longitude – connecting the poles, 360 degree, or 180 degree east + 180 degree West </li></ul></ul><ul><ul><li>Latitude – parallel to the equator, 0 – 90 N and 0 – 90 S </li></ul></ul><ul><ul><li>A location is the intersect of a (virtue) longitude line and a latitude line </li></ul></ul>Amherst 42°22′49″N, 72°31′25″W 0º 0º 90º N 90º S
5. 5. <ul><li>Φ (Phi)Latitude </li></ul><ul><li>λ (Lamda) Longitude </li></ul>
6. 6. Sistem Ufuk Tempatan a Azimuth A Altitude ( Ketinggian) Zenith Angle
7. 7. The horizon coordinate system <ul><li>Altitude </li></ul><ul><ul><li>Angle above the horizon </li></ul></ul><ul><ul><li>0° - 90° </li></ul></ul><ul><ul><li>The altitude of the north celestial pole equals the observer’s latitude on the earth </li></ul></ul><ul><li>Azimuth </li></ul><ul><ul><li>Angle measured eastward along the horizon, starting from the north </li></ul></ul><ul><ul><li>0° - 360° </li></ul></ul><ul><li>Zenith </li></ul><ul><ul><li>The extended vertical line intersects with the celestial sphere </li></ul></ul><ul><li>Meridian </li></ul><ul><ul><li>The great circle passing through the celestial poles and the zenith </li></ul></ul><ul><li>Horizon </li></ul><ul><ul><li>The great circle whose pole is the zenith </li></ul></ul>Meridian
8. 9. Zenith
9. 10. Pros and Cons of the horizon system <ul><li>Pros </li></ul><ul><ul><li>Easy to tell and understand </li></ul></ul><ul><li>Cons </li></ul><ul><ul><li>At different position on the earth, the same object has different coordinates </li></ul></ul><ul><ul><li>At different time, the same object has different coordinates </li></ul></ul><ul><li>The Coordinates of an object Change in the horizon system! </li></ul>
10. 11. Sistem Khatul Istiwa( Equatorial) <ul><li>α jarak hamal ( sudut jam) </li></ul><ul><li>β sudut istiwa (mel) (declination) </li></ul>
11. 13. Equatorial Coordinate System <ul><li>A system in which the coordinates of an object does not change </li></ul><ul><li>Like the longitude and latitude on the earth, we have Right Ascension and Declination in the Equatorial system </li></ul><ul><li>The equatorial coordinate system rotates with stars and galaxies </li></ul>
12. 14. <ul><li>Declination (DEC) </li></ul><ul><ul><li>A set of imaginary lines parallel to the Celestial Equator </li></ul></ul><ul><ul><li>0 ° at the celestial equator, increases from south to north </li></ul></ul><ul><ul><li>negative in the southern hemisphere </li></ul></ul><ul><ul><li>Dec of the north celestial pole is 90 ° </li></ul></ul><ul><ul><li>Dec of the south celestial pole is -90 ° </li></ul></ul>Equatorial Coordinate System 0 ° 90 ° -90 °
13. 15. <ul><li>Right Ascension (RA) </li></ul><ul><ul><li>imaginary lines that connect the celestial poles </li></ul></ul><ul><ul><li>The origin of the longitude of the earth is the Greenwich Observatory </li></ul></ul><ul><ul><li>The origin of the RA is Vernal Equinox </li></ul></ul>Equatorial Coordinate System What is Vernal Equinox? 0 ° 90 ° -90 °
14. 16. The equatorial system <ul><li>Ecliptic </li></ul><ul><ul><li>The earth revolves annually around the Sun </li></ul></ul><ul><ul><li>The Sun appears to moves from west to east on the celestial sphere </li></ul></ul><ul><ul><li>The path of the sun is called ecliptic </li></ul></ul>
15. 17. The equatorial system <ul><li>The earth’s axis is titled – line through the celestial poles is NOT perpendicular to the plane of ecliptic </li></ul><ul><li>23.5 degree angle between the celestial equator and the ecliptic </li></ul><ul><li>The ecliptic and the celestial equator intersect at vernal equinox and autumnal equinox </li></ul>
16. 18. The equatorial system <ul><li>RA </li></ul><ul><ul><li>360 degrees </li></ul></ul><ul><ul><li>Historically, use HOURS:MINS:SECS as unit – 24 hours </li></ul></ul><ul><ul><li>Starts from Vernal equinox (0 h) </li></ul></ul><ul><ul><li>increases from west to east </li></ul></ul><ul><ul><li>Stars w/ larger RA rise later </li></ul></ul>Andromeda: RA: 00 h  42 m  44.3 s DEC: +41° 16′ 9″ 0 h 6 h
17. 19. Vernal Equinox: RA DEC Summer Solstice: RA DEC Autumnal Equinox: RA DEC Winter Solstice: RA DEC Vernal Equinox: RA: 0h DEC: 0º Summer Solstice: RA: 6h DEC: 23.5º Autumnal Equinox: RA: 12h DEC: 0º Winter Solstice: RA: 18h DEC: -23.5º 0 h 6 h
18. 20. Sistem Ekliptik
19. 21. Sistem Galaktik
20. 23. The Celestial Coordinate System <ul><li>The celestial coordinate system; Just as any position on the earth can be located by specifying its terrestrial coordinates, any heavenly body can be located by specifying its celestial coordinates. </li></ul><ul><ul><li>Celestial equator (also known as the equinoctial): The basis for the celestial coordinate system. It is formed by projecting the terrestrial equator outward onto the celestial sphere . </li></ul></ul><ul><ul><li>Celestial meridians: Terrestrial meridians can be projected outward to the celestial sphere to form celestial meridians. Because of the apparent rotation of the celestial sphere with respect to the earth, these projected celestial meridians appear to sweep continuously across the inner surface of the sphere, making them inconvenient to use as a basis for lateral measurements of position on the celestial sphere. Hence, a separate set of circles are “inscribed” on the surface of the celestial sphere perpendicular to the celestial equator for use in describing the position of one point on the sphere relative to another. These great circles are called hour circles . </li></ul></ul>
21. 24. <ul><ul><li>Hour circle : A great circle on the celestial sphere perpendicular to the celestial equator and passing through both celestial poles. Every point on the celestial sphere has an hour circle passing through it. </li></ul></ul><ul><ul><li>“ Hour Circle of Aries ”: The hour circle passing through the First Point of Aries ( ) which forms the reference for the lateral coordinate of a point on the celestial sphere . It is analogous to the meridian passing through the observatory at Greenwich, which serves as the reference for the lateral coordinate of a point on the terrestrial sphere. </li></ul></ul>The Celestial Coordinate System
22. 25. <ul><ul><li>Declination (Dec): The celestial equivalent of terrestrial latitude . It is the angular distance of a point on the celestial sphere north or south of the celestial equator measured through 90 degrees. Declination is labeled with the prefix N (north) or S (south) to indicate the direction of measurement; prefixes are used to differentiate declination from latitude. The figure below depicts the declination of a star located 30 degrees off the celestial equator. </li></ul></ul>The Celestial Coordinate System Dec. = N30 0 (Overhead 16-1)
23. 26. <ul><ul><li>Hour angle : The celestial equivalent of longitude . It is the angular distance measured laterally along the celestial equator in a westerly direction through 360 degrees . </li></ul></ul><ul><ul><ul><li>Sidereal hour angle (SHA) : Hour angles measured in a westerly direction from the hour circle of Aries to the hour circle of a particular body. </li></ul></ul></ul><ul><ul><ul><li>For the purposes of celestial navigation, it is not only desirable to locate a body on the celestial sphere relative to Aries but also to locate a body relative to a given position on earth at a given time. To do this, two terrestrial meridians are projected onto the surface of the celestial sphere for use as references for hour angle measurements - The Greenwich meridian and the observer’s meridian. The celestial meridians thus projected are termed the Greenwich celestial meridian and the local celestial meridian . </li></ul></ul></ul>The Celestial Coordinate System
24. 27. <ul><ul><ul><li>Greenwich hour angles (GHA): Hour angles measured relative to the Greenwich meridian. </li></ul></ul></ul><ul><ul><ul><li>Local hour angles (LHA): Hour angles measured with respect to the local celestial meridian. </li></ul></ul></ul><ul><ul><ul><li>Both Greenwich hour angles and local hour angles are measured westward from a projected terrestrial meridian to a celestial hour circle moving ever westerly with the rotating celestial sphere. Consequently, both GHA and LHA values are constantly growing larger with time, increasing from 0 to 360 degrees once each 24 hours. They relate the rotating celestial sphere to the meridians of the earth. </li></ul></ul></ul><ul><ul><ul><li>Sidereal hour angles are measured between two hour circles on the celestial sphere; although the value of the SHA of the star changes with time as the stars move through space relative to one another, the rate of change is extremely slow. Hence for purposes of celestial navigation, sidereal hour angles are considered to remain constant . </li></ul></ul></ul>The Celestial Coordinate System
25. 28. <ul><ul><ul><li>The hour circle of Aries and the projected Greenwich and observer’s meridians are shown in the following figure. The resulting sidereal, Greenwich, and local hour angles (SHA, GHA, AND LHA) of the star at a given time are indicated. </li></ul></ul></ul><ul><ul><ul><li>It can be seen from the figure below that the GHA of the star (GHA ) is equal to the sum of the GHA of Aries (GHA ) plus the SHA of the star (SHA ): </li></ul></ul></ul><ul><ul><ul><li>GHA = GHA + SHA </li></ul></ul></ul>The Celestial Coordinate System = Aries = star
26. 29. The Celestial Coordinate System (Overhead 16-2) G  GHA LHA GHA SHA Pn Ps Celestial Equator
27. 30. <ul><ul><ul><li>For some applications in celestial navigation, it is advantageous to use an alternative angle to LHA to express the angular distance from the observer’s meridian to the hour circle of a body. This is called the meridian angle (t). The meridian angle is defined as the angular distance between 0 degrees and 180 degrees , measured at the pole nearest the observer, from the observer’s meridian either easterly or westerly to the hour circle of the body. The meridian angle is always labeled with the suffix E (east) or W (west) to indicate the direction of measurement. The significance of the meridian angle will be discussed later when solving the celestial triangle. </li></ul></ul></ul>The Celestial Coordinate System
28. 31. More about Celestial Coordinates <ul><li>Right Ascension (RA or  ) </li></ul><ul><li>- Sometimes Referred to in Hours </li></ul><ul><li>- 1 Hour = 15º </li></ul><ul><li>- 0 - 360 º or 0 - 24 Hours (h) </li></ul><ul><li>- Why Hours? </li></ul><ul><li>Because the sky rotates 360 º in 24 hours of time. So in 1 hour of time, sky appears to rotate by 15 º. </li></ul>Declination (DEC or  ) - 0º is Celestial Equator - +90º is Celestial North Pole - -90º is Celestial South Pole
29. 32. Your Meridian and Hour Angle <ul><li>Meridian </li></ul><ul><li>- A great circle through the north celestial pole and your zenith </li></ul><ul><li>- Perpendicular to your horizon </li></ul><ul><li>Hour Angle (HA) </li></ul><ul><li>- Angle between RA of object and your meridian </li></ul><ul><li>- 0 is at local meridian </li></ul><ul><li>- Positive hour angle goes west </li></ul><ul><li>- Negative hour angle goes east </li></ul>*Image taken from http://members.aol.com/satrnpres1/astronomy/meridian.gif Best time to observe a celestial object is when it has an hour angle of 0 because light travels through least amount of air and lessens atmospheric turbulence, extinction, and reddening
30. 33. How it looks on the Sky Meridian Hour Angle of Arcturus