Modul-2 : System of Coordinates

Lecture Slides of GD. 2213 Satellite GeodesyGeodesy & Geomatics Engineering

Institute of Technology Bandung (ITB)

Hasanuddin Z. AbidinGeodesy Research DivisionInstitute of Technology BandungJl. Ganesha 10, Bandung, IndonesiaE-mail : hzabidin@gd.itb.ac.id

Version : Agustus 2010

ZZE

Y

YEX

XE Earth

CoordinateReferenceSystem

CoordinateReference Frame

Positioning Method

Geodetic Datum

ReferenceEllipsoid

Earths Geometryand Kinematics

EarthsGravity Field

SPECTRUM OF POSITIONING

Hasanuddin Z. Abidin, 2007

PositioningApplications

Position of a point can be stated quantitatively and qualitatively.

Quantitatively, position of a point is defined by coordinates,either in 1D, 2D, 3D or 4D.

Coordinates can also be used to quantitatively describe thetrajectory of a moving point.

In order to standardize and assure the consistency of informationon coordinates, the coordinate system is required.

Coordinate system will ease the geometrical and dynamicaldescription, computation and analysis of coordinates, both inspatial and temporal domain.

Coordinate System

Hasanuddin Z. Abidin 1997-2007

Origin of the coordinate system. Orientation of the coordinate axes. Variables (distances and/or angles) used in defining

point position in the coordinate system.

Coordinate System Parameter

Hasanuddin Z. Abidin 1997-2007

Coordinate Origin

Axis Orientation

Coordinate Variables

Geocentrik (in the Earths center) Topocentrik (on the Earths surface)

Earth-Fixed Space-Fixed

Distances : Cartesian (X,Y,Z) Angles & Distance : Geodetic (j,l,h)

Hasanuddin Z. Abidin 1997-2007

CartesianCoordinates:(NA, EA, UA)

Examples ofCoordinate System

Parameters (1)

TopocentricCoordinate System UA

AZenith (U)

East (E)

North (N)

EANA

Earthssurface

GeocentricCoordinateSystem

Cartesian Coordinates:(XA, YA, ZA)

Geodetic Coordinates:(jA, lA, hA)

lAjA

hA

AZ

Y

XYA

XA

ZAGreenwich

Pole

Geocentre

Earthssurface

Hasanuddin Z. Abidin 1997-2007

Examples ofCoordinate System

Parameters (2)

P

x

y

Px

Py

P

0

P

0 P

Map ProjectionCoordinate System

2D-Geodetic (Geographic)Coordinate System

Map Coordinates :(xP,yP)

2D-Geodetic(Geographic)Coordinates :

(jP,lP)

Coordinates : (a,d)

Y

Z

XVernal Equinox

CEP J2000.0

Geocentre

Equatorg a

d

Star

Right AscensionCoordinate System

Sistem dan Kerangka Referensi Koordinat

Hasanuddin Z. Abidin, 2010

SISTEM REFERENSI adalah sistem (termasuk teori, konsep,deskripsi fisis dan geometris, serta standar dan parameter) yangdigunakan dalam pendefinisian koordinat.

KERANGKA REFERENSI dimaksudkan sebagai realisasi praktisdari sistem referensi, sehingga sistem tersebut dapat digunakanuntuk pendeskripsian secara kuantitatif posisi dan pergerakantitik-titik, baik di permukaan bumi (kerangka terestris) ataupundi luar bumi (kerangka selestia atau ekstra-terestris).

Kerangka referensi biasanya direalisasikan dengan melakukanpengamatan-pengamatan geodetik, dan umumnya direpresentasikan

dengan menggunakan suatu set koordinat dari sekumpulan titikmaupun obyek (seperti bintang dan quasar).

Kerangka Inersia (Inertial Frame)

Hasanuddin Z. Abidin, 1997

Hukum Newton-I (Hukum Inersia) : Tiap benda akan tetapberada dalam keadaan diam atau dalam gerak lurus teratur,kecuali bila dipaksa merubah keadaan itu dengan gaya-gayayang bekerja padanya.

Kerangka Inersia adalah kerangka referensi dimana hukumNewton-I berlaku (valid).

Kerangka inersia bergerak dalam ruang dengan kecepatantranslasi yang konstan, tapi tanpa pergerakan rotasional.

Seandainya pusat dari kerangka mengalami percepatandalam pergerakannya, maka kerangka tersebut dinamakanKerangka Kuasi-Inersia.

Sistem Koordinat Geodesi Satelit Sistem referensi koordinat yang umum digunakan dalam bidang

Geodesi Satelit adalah CIS (Conventional Inertial System) danCTS (Conventional Terrestrial System).

CIS, sistem koordinat referensi yang terikat langit, dalamgeodesi satelit digunakan untuk pendeskripsian posisidan pergerakan satelit.

CTS, sistem koordinat referensi yang terikat bumi, dalamgeodesi satelit digunakan untuk pendeskripsian posisidan pergerakan titik-titik di permukaan bumi.

Hasanuddin Z. Abidin, 2000

Pendefinisian CIS dan CTS serta perelisasiannya menuntutpemahaman yang baik tentang dinamika dari sistem Bumi kita

baik secara internal maupun eksternal dalam sistem luar angkasa

Sistem Bumi & Dinamika nya

Mean distance from the Sun: 1 AU (149,600,000 km/ 92,960,000 mi)

Length of year: 365.26 days

Rotation period: 23.93 hours

Mean orbital velocity: 29.79 km/sec (18.6 mi/sec)

Inclination of axis: 23.45

Average temperature: 59 F (15 C)

Diameter: (equatorial) 12,756 km (7,926 mi)

Number of observed satellites: 1

FAKTA BUMI

Hasanuddin Z. Abidin, 2006

Human Population of the Earth: 6,820,000,000 (May 2010)Highest Elevation on Earth - Mt. Everest, Asia: 8850 mLowest Elevation on Land - Dead Sea: 417.27 m below sea levelDeepest Point in the Ocean - Challenger Deep, Mariana Trench,Western Pacific Ocean: 10924 mHighest Temperature Recorded:

57.7C - Al Aziziyah, Libya, September 13, 1922Lowest Temperature Recorded:

-89.2C - Vostok, Antarctica, July 21, 1983Water vs. Land: 70.8% Water, 29.2% LandAge of the Earth: 4.5 to 4.6 billion yearsAtmosphere Content: 77% nitrogen, 21% oxygen,

and traces of argon, carbon dioxide and water

http://geography.about.com/od/learnabouttheearth/a/earthfacts.htm

FAKTA BUMI

Shape ofThe Earth

Actual

Mathematical

http://campus.everettcc.edu/Departments/sciences/klyste/Earth_Shape.htm

Bentuk Permukaan Bumi

Hasanuddin Z. Abidin, 2006

Perspective view of the Geoid(Geoid undulations 15000:1)

GEOID

It is an equipotential surfaceof the Earths gravity field.

It is often referred to as aclose representation or physicalmodel of the figure of the Earth.

This is the surface that mostclosely approximates sea levelin the absence of winds, oceancurrents, and other disturbingforces.

Hasanuddin Z. Abidin, 2006

The Earths Geoid

Departures from the ellipsoid (m)

http://www.csr.utexas.edu/grace/gravity/gravity_definition.html

The Earths Geoid

http://dgfi2.dgfi.badw-muenchen.de/geodis/WWW/welcome.html

The Earths Geoid

The Earth's shape resembles an ellipsoid(its equatorial radius is about 21 kilometersgreater than its polar radius) but it is not aperfect ellipsoid.

Because of this resemblance, an ellipsoid is used to approximatethe bulk of the Earth's shape, and departures from the ellipsoid arerepresented by the geoid elevation above or below the ellipsoid.

In geodesy, a reference ellipsoid is a mathematically-definedsurface that approximates the geoid, the truer figure of the Earth.

Because of their relative simplicity, reference ellipsoids are used asa preferred surface on which geodetic network computations areperformed and point coordinates such as latitude, longitude, andelevation are defined.

Reference Ellipsoid

ab a = Semi-Major Axis= Equatorial Radius

b = Semi-Minor Axis= Polar Radius

Flattening = f = (a-b)/a

Ellipsoidal Parameter

For mathematical purposes, theEarth is represented bya certain reference ellipsoid

ReferenceEllipsoid

Hasanuddin Z. Abidin, 2006

Sumber gambar : Internet

Ellipsoidof the Earth

SeveralReferenceEllipsoids

http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys.html

Pergerakan Bumi

Hasanuddin Z. Abidin, 2001

Bumi bergerak bersama galaksi kita relatif terhadapgalaksi-galaksi yang lain.

Bumi berputar bersama sistem matahari kita di dalam galaksi kita. Bumi mengorbit mengelilingi matahari bersama planet-planet lainnya. Bumi berputar terhadap sumbu rotasinya. Kerak-kerak bumi juga bergerak (relatif sangat lambat)

relatif satu terhadap lainnya.

Tiga jenis pergerakan bumi yang terakhir tersebut, berpengaruh dalampendefinisian sistem koordinat yang digunakan dalam geodesi satelit.Dalam hal ini ada 3 sistem koordinat yang banyak digunakan yaitu :

1. CIS = Conventional Inertial System.2. CTS = Conventional Terrestrial System.3. Sistem Koordinat Ellipsoid

The galaxy we live in is calledthe Milky Way Galaxy , aHubble type Sb spiral galaxy,containing about 100 billionstars. It is about 100,000 lightyears in diameter and has athickness of about 2,000 lightyears. It is rotating eastwards orcounterclockwise. The period ofrotation for our region of thegalaxy is 200,000,000 years.Like other galaxies, the Milkyway has a bulge, a disk, and ahalo. Pictures shows the MilkyWay Galaxy from the side andfrom the top

http://sankofa.loc.edu/savur/web/thegalaxies.html

Galaksi Bima Sakti (Milky Way)Dimana Bumi ?

Sumber Gambar : Internet Hasanuddin Z. Abidin, 2010

Sistem Matahari Kita dan Bumi

Hasanuddin Z. Abidin, 2010

Pergerakan Bumi

http://www.planetperformance.org/ Hasanuddin Z. Abidin, 2010

Eksentrisitas orbit 0.0167. Periode orbit 365.24 hari. Kecepatan Bumi dalam orbit 29.8 km/detik.