Sistem kordinatSistem kordinat

Untuk menetapkan kedudukkan benda Untuk menetapkan kedudukkan benda langitlangit2 nilai di perlukan ~ berapa tinggi & 2 nilai di perlukan ~ berapa tinggi & berapa jauh lingkarannya?berapa jauh lingkarannya?

Sistem Di GunakanSistem Di Gunakan

Ufuk Tempatan( Horizon)Ufuk Tempatan( Horizon)Ekliptik (Ecliptic)Ekliptik (Ecliptic)Khatul Istiwa(Equatorial)Khatul Istiwa(Equatorial)Galaktik (Galactic)Galaktik (Galactic)

Bagaimana kita tentukan tempat Bagaimana kita tentukan tempat atas bumi?atas bumi?

Maps, mapquest, Maps, mapquest, Google Map, GPSGoogle Map, GPS

If we ignore how high If we ignore how high it is above the seait is above the sea

To describe a spot on To describe a spot on the the surfacesurface of the of the earth, we use a set of earth, we use a set of numbers (degrees), numbers (degrees), called called CoordinatesCoordinates• LongitudeLongitude• LatitudeLatitude

0º

0º

Position in Degrees–Longitude – connecting the poles, 360 degree, or 180 degree east + 180 degree West–Latitude – parallel to the equator, 0 – 90 N and 0 – 90 S–A location is the intersect of a (virtue) longitude line and a latitude line

0º

90º N

90º S

Amherst42°22′49″N, 72°31′25″W

ΦΦ (Phi)Latitude (Phi)Latitude

λλ (Lamda) Longitude (Lamda) Longitude

Sistem Ufuk TempatanSistem Ufuk Tempatan

a Azimuth

A Altitude ( Ketinggian)

Zenith Angle

The horizon coordinate The horizon coordinate systemsystem AltitudeAltitude

• Angle above the horizonAngle above the horizon• 0° - 90°0° - 90°• The altitude of the north The altitude of the north

celestial pole equals the celestial pole equals the observer’s latitude on the earthobserver’s latitude on the earth

AzimuthAzimuth• Angle measured eastward Angle measured eastward

along the horizon, starting from along the horizon, starting from the norththe north

• 0° - 360°0° - 360° ZenithZenith

• The extended vertical line The extended vertical line intersects with the celestial intersects with the celestial spheresphere

MeridianMeridian• The great circle passing The great circle passing

through the celestial poles and through the celestial poles and the zeniththe zenith

• Horizon– The great circle whose pole is

the zenith

Meridian

Zenith

Pros and Cons of the horizon systemPros and Cons of the horizon system ProsPros

• Easy to tell and understandEasy to tell and understand ConsCons

• At different position on the At different position on the earth, the same object has earth, the same object has different coordinatesdifferent coordinates

• At different time, the same At different time, the same object has different object has different coordinatescoordinates

The Coordinates of an The Coordinates of an object Change in the object Change in the horizon system!horizon system!

Sistem Khatul Istiwa( Equatorial)Sistem Khatul Istiwa( Equatorial) αα jarak hamal ( sudut jam) jarak hamal ( sudut jam) ββ sudut istiwa (mel) sudut istiwa (mel)

(declination)(declination)

Equatorial Coordinate SystemEquatorial Coordinate System A system in which the A system in which the

coordinates of an object coordinates of an object does notdoes not change change

Like the longitude and Like the longitude and latitude on the earth, we latitude on the earth, we have have Right AscensionRight Ascension and and DeclinationDeclination in the in the Equatorial systemEquatorial system

The equatorial The equatorial coordinate system coordinate system rotates with stars and rotates with stars and galaxiesgalaxies

DeclinationDeclination (DEC) (DEC)• A set of imaginary A set of imaginary

lines parallel to the lines parallel to the Celestial EquatorCelestial Equator

• 0 0 °° at the celestial at the celestial equator, increases equator, increases from south to northfrom south to north

• negative in the negative in the southern hemispheresouthern hemisphere

• Dec of the north Dec of the north celestial pole is 90 celestial pole is 90 °°

• Dec of the south Dec of the south celestial pole is -90 celestial pole is -90 °°

Equatorial Coordinate SystemEquatorial Coordinate System

0 °

90 °

-90 °

Right AscensionRight Ascension (RA) (RA) • imaginary lines imaginary lines

that connect the that connect the celestial polescelestial poles

• The origin of the The origin of the longitude of the longitude of the earth is the earth is the Greenwich Greenwich ObservatoryObservatory

• The origin of the The origin of the RA is RA is Vernal Vernal EquinoxEquinox

Equatorial Coordinate SystemEquatorial Coordinate System

0 °

90 °

-90 °

What is Vernal Equinox?

The equatorial systemThe equatorial system EclipticEcliptic

• The earth revolves The earth revolves annually around annually around the Sun the Sun

• The Sun appears to The Sun appears to moves from west moves from west to east on the to east on the celestial spherecelestial sphere

• The path of the sun The path of the sun is called is called eclipticecliptic

The equatorial systemThe equatorial system The earth’s axis is titled – The earth’s axis is titled –

line through the celestial line through the celestial poles is poles is NOT NOT perpendicular to the perpendicular to the plane of eclipticplane of ecliptic

23.5 degree angle 23.5 degree angle between the celestial between the celestial equator and the eclipticequator and the ecliptic

The ecliptic and the The ecliptic and the celestial equator celestial equator intersect at vernal intersect at vernal equinox and autumnal equinox and autumnal equinoxequinox

The equatorial systemThe equatorial system RARA

• 360 degrees360 degrees• Historically, use Historically, use

HOURS:MINS:SECSHOURS:MINS:SECS as unit – 24 hoursas unit – 24 hours

• Starts from Vernal Starts from Vernal equinox (0 h)equinox (0 h)

• increases from increases from west to eastwest to east

• Stars w/ larger RA Stars w/ larger RA rise laterrise later

0 h

6 h

Andromeda:RA: 00h 42m 44.3s DEC: +41° 16′ 9″

0 h

6 h

Vernal Equinox: RA DECSummer Solstice: RA DECAutumnal Equinox: RA DECWinter Solstice: RA DEC

Vernal Equinox: RA: 0h DEC: 0ºSummer Solstice: RA: 6h DEC: 23.5ºAutumnal Equinox: RA: 12h DEC: 0ºWinter Solstice: RA: 18h DEC: -23.5º

Sistem EkliptikSistem Ekliptik

Sistem GalaktikSistem Galaktik

The CelestialThe Celestial Coordinate System Coordinate System

The celestial coordinate system;The celestial coordinate system; Just as any position on the earth can be Just as any position on the earth can be located by specifying its terrestrial coordinates, any heavenly body can be located by specifying its terrestrial coordinates, any heavenly body can be located by specifying its located by specifying its celestial coordinates.celestial coordinates.• Celestial equatorCelestial equator (also known as the equinoctial): (also known as the equinoctial): The basis for the celestial The basis for the celestial

coordinate system. It is formed by projecting the terrestrial equator coordinate system. It is formed by projecting the terrestrial equator outward onto the celestial sphere .outward onto the celestial sphere .

• Celestial meridians:Celestial meridians: Terrestrial meridians can be projected outward to the Terrestrial meridians can be projected outward to the celestial sphere to form celestial meridians. Because of the apparent celestial sphere to form celestial meridians. Because of the apparent rotation of the celestial sphere with respect to the earth, these projected rotation of the celestial sphere with respect to the earth, these projected celestial meridians appear to sweep continuously across the inner surface celestial meridians appear to sweep continuously across the inner surface of the sphere, making them inconvenient to use as a basis for lateral of the sphere, making them inconvenient to use as a basis for lateral measurements of position on the celestial sphere. measurements of position on the celestial sphere. Hence, a separate set of Hence, a separate set of circles are “inscribed” on the surface of the celestial spherecircles are “inscribed” on the surface of the celestial sphere perpendicular perpendicular to the celestial equator for use in describing the position of one point on the to the celestial equator for use in describing the position of one point on the sphere relative to another. sphere relative to another. These great circles are called These great circles are called hour circleshour circles..

• Hour circleHour circle:: A great circle on the celestial sphere A great circle on the celestial sphere perpendicular to the celestial equator and passing perpendicular to the celestial equator and passing through both celestial poles. Every point on the through both celestial poles. Every point on the celestial sphere has an hour circle passing through celestial sphere has an hour circle passing through it. it.

• ““Hour Circle of AriesHour Circle of Aries”:”: The hour circle passing The hour circle passing through the First Point of Aries ( ) which through the First Point of Aries ( ) which forms the forms the reference for the lateral coordinate of a point on the reference for the lateral coordinate of a point on the celestial spherecelestial sphere. It is analogous to the meridian . It is analogous to the meridian passing through the observatory at Greenwich, passing through the observatory at Greenwich, which serves as the reference for the lateral which serves as the reference for the lateral coordinate of a point on the terrestrial sphere. coordinate of a point on the terrestrial sphere.

The CelestialThe Celestial Coordinate System Coordinate System

• DeclinationDeclination (Dec): (Dec): The celestial The celestial equivalent of terrestrial latitudeequivalent of terrestrial latitude. It is the . It is the angular distance of a point on the celestial sphere north or south of 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 celestial equator measured through 90 degrees. Declination is labeled with the prefix N (north) or S (south) to indicate the direction of measurement; the prefix N (north) or S (south) to indicate the direction of measurement; prefixesprefixes are used to differentiate declination from latitude. The figure are used to differentiate declination from latitude. The figure below depicts the declination of a star located 30 degrees off the celestial below depicts the declination of a star located 30 degrees off the celestial equator.equator.

The Celestial Coordinate System

Dec. =N300

(Overhead 16-1)

• HourHour angle angle:: The celestial equivalent of longitudeThe celestial equivalent of longitude. It is the . It is the angular distance measured laterally along the celestial angular distance measured laterally along the celestial equator in a westerly direction equator in a westerly direction through 360 degreesthrough 360 degrees..

Sidereal hour angle (SHA)Sidereal hour angle (SHA):: Hour angles measured in a westerly Hour angles measured in a westerly direction from the hour circle of Aries to the hour circle of a direction from the hour circle of Aries to the hour circle of a particular body. particular body.

For the purposes of celestial navigation, it is not only desirable to 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 on the celestial sphere relative to Aries but also to locate a body relative to a given position on earth at a given time. 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 To do this, two terrestrial meridians are projected onto the surface of the celestial sphere for use as references for hour angle of the celestial sphere for use as references for hour angle measurements - The Greenwich meridian and the observer’s measurements - The Greenwich meridian and the observer’s meridian. The celestial meridians thus projected are termed the meridian. The celestial meridians thus projected are termed the Greenwich celestial meridianGreenwich celestial meridian and the and the local celestial meridianlocal celestial meridian..

The Celestial Coordinate System

Greenwich hour angles Greenwich hour angles (GHA):(GHA): Hour angles measured relative to the Hour angles measured relative to the Greenwich meridian.Greenwich meridian.

Local hour angles Local hour angles (LHA):(LHA): Hour angles measured with respect to the Hour angles measured with respect to the local celestial meridian.local celestial meridian.

Both Greenwich hour angles and local hour angles are measured Both Greenwich hour angles and local hour angles are measured westward from a projected terrestrial meridian to a celestial hour westward from a projected terrestrial meridian to a celestial hour circle moving ever westerly with the rotating celestial sphere. circle moving ever westerly with the rotating celestial sphere. Consequently, both GHA and LHA values are constantly growing Consequently, both GHA and LHA values are constantly growing larger with time, increasing from 0 to 360 degrees once each 24 larger with time, increasing from 0 to 360 degrees once each 24 hours. They relate the rotating celestial sphere to the meridians of hours. They relate the rotating celestial sphere to the meridians of the earth.the earth.

Sidereal hour angles are measured between two hour circles on the Sidereal hour angles are measured between two hour circles on the celestial sphere; although the value of the SHA of the star changes celestial sphere; although the value of the SHA of the star changes with time as the stars move through space relative to one another, with time as the stars move through space relative to one another, the rate of change is extremely slow. Hence for purposes of celestial the rate of change is extremely slow. Hence for purposes of celestial navigation, navigation, sidereal hour angles are considered to remain constantsidereal hour angles are considered to remain constant..

The CelestialThe Celestial Coordinate System Coordinate System

The hour circle of Aries and the projected Greenwich and observer’s The hour circle of Aries and the projected Greenwich and observer’s meridians are shown in the following figure. The resulting sidereal, meridians are shown in the following figure. The resulting sidereal, Greenwich, and local hour angles (SHA, GHA, AND LHA) of the star Greenwich, and local hour angles (SHA, GHA, AND LHA) of the star at a given time are indicated. at a given time are indicated.

It can be seen from the figure below that the GHA of the star (GHA 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 ) is equal to the sum of the GHA of Aries (GHA ) plus the SHA of the star (SHA ):the star (SHA ):

GHA = GHA + SHA GHA = GHA + SHA

The Celestial Coordinate System

= Aries= star

The Celestial Coordinate System

(Overhead 16-2)

G

GHA

LHA

GHA SHA

Pn

Ps

Celestial Equator

For some applications in celestial navigation, it is For some applications in celestial navigation, it is advantageous to use an alternative angle to LHA to advantageous to use an alternative angle to LHA to express the angular distance from the observer’s express the angular distance from the observer’s meridian to the hour circle of a body. This is called meridian to the hour circle of a body. This is called the the meridian angle (t).meridian angle (t). The meridian angle is defined as The meridian angle is defined as the angular distance between the angular distance between 0 degrees and 180 0 degrees and 180 degreesdegrees, measured at the pole nearest the observer, , measured at the pole nearest the observer, from the observer’s meridian from the observer’s meridian either easterly or either easterly or westerlywesterly to the hour circle of the body. The meridian to the hour circle of the body. The meridian angle is always labeled with the suffix E (east) or W angle is always labeled with the suffix E (east) or W (west) to indicate the direction of measurement. The (west) to indicate the direction of measurement. The significance of the meridian angle will be discussed significance of the meridian angle will be discussed later when solving the celestial triangle. later when solving the celestial triangle.

The CelestialThe Celestial Coordinate System Coordinate System

More about Celestial More about Celestial CoordinatesCoordinatesRight Ascension (RA or Right Ascension (RA or ))

- Sometimes Referred to in - Sometimes Referred to in HoursHours - 1 Hour = 15º- 1 Hour = 15º - - 0 - 3600 - 360º or 0 - 24 Hours (h)º or 0 - 24 Hours (h) - - Why Hours?Why Hours? Because the sky rotates 360Because the sky rotates 360º º in 24 in 24

hours of time. So in 1 hour of time, sky hours of time. So in 1 hour of time, sky appears to rotate by 15appears to rotate by 15º.º.

Declination (DEC or ) - 0º is Celestial Equator - +90º is Celestial North Pole - -90º is Celestial South Pole

Your Meridian and Hour AngleYour Meridian and Hour AngleMeridianMeridian - A great circle through the north - A great circle through the north

celestial pole and your zenithcelestial pole and your zenith - Perpendicular to your horizon- Perpendicular to your horizonHour Angle (HA)Hour Angle (HA) - Angle between RA of object and - Angle between RA of object and

your meridianyour meridian - 0 is at local meridian- 0 is at local meridian - Positive hour angle goes west- Positive hour angle goes west - Negative hour angle goes east- Negative hour angle goes east

*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

How it looks on the SkyHow it looks on the Sky

Meridian

Hour Angle of Arcturus