Coordinates. Definition of terms

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1 Crdinates Definitin f terms C Lcal crdinates C Gegraphical C Latitude - angular measurement f a lcatin n Earth frm the equatr C Lngitude - angular measurement f a lcatin n Earth frm the Prime Meridian C Sky C Altitude - angle f a celestial pint abve the hrizn C Azimuth - angle f a celestial pint frm true nrth C Zenith - pint n the celestial sphere which is directly abve yur head C Nadir - pint n the celestial sphere which is directly belw yur feet C Celestial crdinates C Declinatin - angular measurement f a celestial lcatin frm the celestial equatr C C Right Ascensin - angular measurement f a celestial lcatin frm the first pint in Aries (celestial prime meridian) C C Terrestrial Crdinates Nrth Ple 1 T a very gd apprximatin the Earth is a smth sphere. Any pint n the surface can then be described in terms f tw angles, named the latitude and the lngitude. Lngitude Latitude Latitude Latitude f a pint n the Earth s surface measures hw far that pint lies nrth r suth f the equatr. It is defined as the angle between tw imaginary lines, ne cnnecting the pint t the center f the Earth, and the ther cnnecting the nearest pint n equatr t the center f the Earth. Designatins are made t define whether the pint is nrth f the equatr r suth f it. There are sme general statements that can be made. Suth Ple Prime Meridian Definitin f Latitude and Lngitude fr a pint n the Earth s surface 1 The equatrial diameter f the Earth is nly abut ne quarter f a percent lnger than the plar diameter, which means that the Earth if very nearly spherical. Als, the tp f Mt. Everest is nly abut ne tenth f a percent further frm the center f the Earth than is a pint at sea level, and the Earth is very nearly smth.

2 C Any pint n the equatr has a latitude f 0. C The Nrth Ple has a latitude f 90 N. C Any pint in the nrthern hemisphere has a latitude which lies between 0 and 90 N. Fr example the latitude f Lndn, England is abut 51 N. C The Suth Ple has a latitude f 90 S. C Any pint in the suthern hemisphere has a latitude which lies between 0 and 90 S. Fr example the latitude f Cape Twn, Suth Africa is abut 33 S. Lngitude Lngitude f a pint n the Earth s surface measures hw far that pint lies east r west f the Prime Meridian. The Prime Meridian is an imaginary line running alng the Earth s surface frm the Nrth Ple t the Suth Ple, passing thrugh Greenwich, England. (Greenwich is just east f Lndn.) Designatins are made t define whether the pint is east f the Prime Meridian r west f it. There are sme general statements that can be made. C Any pint n the Prime Meridian has a lngitude f 0. Since the Prime Meridian runs thrugh Greenwich, it (and Lndn itself) has a lngitude f 0. Other cities with a lngitude f 0 include Accra, Ghana and Brdeaux, France. C Any pint n the Earth s surface directly ppsite the Prime Meridian has a lngitude f either 180 E r 180 W C Since yu have t fly west frm Lndn t reach any city in the Americas, all lcatins in the United States have a west lngitude. Examples include New Yrk (73 W), Chicag (87 W), and San Francisc (122 W). Sky Crdinates There are tw schemes fr defining the lcatin f a pint in the sky, ne based lcal n lcal crdinates, and the ther n a universal set f lcal crdinates. Lcal Crdinates At any ne time any bserver can see half f the sky, the prtin which lies abve the hrizn. The ther half is hidden frm view since it lies belw the hrizn. Nte thugh, that bservers at different places n the Earth have different hrizns, and therefre see different prtins f the sky (althugh bth still see half.) This is nt a significant difference fr tw peple standing a few feet frm each ther, but is a large difference fr bservers in different cities, sat New Yrk and Chicag. Als, because the Earth rtates n its axis even a fixed bserver will see different prtins f the sky (althugh again always half) at different times. This is why sme stars appear t rise abve the hrizn and thers t set belw it. It is nt that the stars that have mved, it is the hrizn which has mved as the Earth rtates. Altitude

3 The altitude measures the psitin f a pint in the sky abve the hrizn. It is defined as the angle between tw imaginary lines, ne frm the bserver t the pint and the ther frm the bserver t the hrizn directly belw the pint. Pints belw the hrizn are smetimes given a negative altitude. There are sme general statements that can be made. Altitude and Azimuth C Any pint directly n the hrizn has an altitude f 0. That means that the altitude f any bject (such as a star) as it rise, r as it sets, is als 0. C The maximum pssible altitude is 90. This crrespnds t the pint in the sky which is directly abve the bservers head, referred t as the zenith. Different bservers in different lcatins have different zeniths, althugh each ne will describe it as the pint directly verhead, and each ne will give it an altitude f 90. C All ther pints in the sky which are visible have an altitude between 0 and 90. C Since the Earth rtates n its axis, the altitude f any bject in the sky (such as a star) will cntinuusly change. The exceptin t this is the star Plaris, since it is lcated at the psitin f the Nrth Celestial Ple (see belw). Azimuth The azimuth measures the psitin f a pint in the sky relative t the nrth. It is defined as the angle between t tw imaginary lines, ne frm the bserver t the hrizn directly nrth f the bserver, and the ther ne frm the bserver t the hrizn directly belw the pint. It is always measured frm the nrth twards the east, frm 0 t 360. There are sme general statements that can be made. Hrizn W 270 N 0 Azimuth 90 E C Any pint due nrth f the bserver has an azimuth f 0. C Any pint due east f the bserver has an azimuth f 90. C Any pint due suth f the bserver has an azimuth f 180. C Any pint due west f the bserver has an azimuth f 270. C Since the Earth rtates n its axis, the azimuth f any bject in the sky (such as a star) will cntinuusly change. The exceptin t this is the star Plaris, since it is lcated at the psitin f the Nrth Celestial Ple (see belw) it always has an azimuth f S Definitin f Azimuth, lking dwn frm zenith Celestial Crdinates As we saw abve, the lcal crdinates are specific t a particular bserver, at a particular time. Whereas they are easy t use, cmmunicating infrmatin abut a particular lcatin t a different bserver, r ne which is lking at the sky at sme ther time, is fraught with difficulties. The different bservers have

4 different lcal crdinates. T vercme this difficulty astrnmers have develped a set f celestial crdinates which everyne can agree n, regardless f their individual lcatins n the Earth s surface, r n when they are lking at the sky. The disadvantage is that celestial crdinates are relatively difficult t use, unless yur telescpe has previusly been aligned with stars whse celestial crdinates are knwn. The starting pint f the Celestial Crdinates is t imagine that all f the stars in the sky (including thse which are belw the hrizn) are the same very large distance frm us. In this mdel all f the stars are psitined n the Celestial Sphere, with the Earth at the center f the sphere. If we take the axis f rtatin f the Earth, which runs thrugh its nrth and suth ples, and extend this line utwards until it reaches the Celestial Sphere, then the pints where it reaches the Celestial Sphere are knwn as the Celestial Ples. The Nrth Celestial Ple lies directly abve the Earth s nrth ple. It is the zenith fr an bserver standing at the Earth s nrth ple. Similarly, the Suth Celestial Ple is the zenith fr an bserver standing at the Earth s suth ple. Just as the Earth is divided int tw hemispheres by the equatr, the Celestial Sphere is als divided int tw by the Celestial Equatr. It is an imaginary line which runs arund the Celestial Sphere directly abve the Earth s equatr. Fr an bserver standing n the Earth s equatr the zenith wuld be a pint n the Celestial Equatr. Declinatin Nrth Celestial Ple First pint in Aries Declinatin Right Ascensin Celestial Equatr The declinatin plays the same rle n the Celestial Sphere as latitude des n the Earth s surface. It is a measurement Suth Celestial Ple f hw far, nrth r suth, a pint is frm the Celestial Equatr. It is defined as the angle between tw imaginary Right Ascensin and Declinatin lines, ne cnnecting the pint t the Earth, and the ther cnnecting the nearest pint n equatr t the center f the Earth. Designatins are made t define whether the pint is nrth f the equatr r suth f it. On the Celestial Sphere pints which are nrth f the Celestial Equatr has a psitive declinatin. Thse which are suth f the Celestial Equatr have a negative declinatin. There are sme general statements that can be made. C Any pint n the Celestial Equatr has a declinatin f 0. C The Nrth Celestial Ple has a declinatin f 90. C Any pint in the nrthern half f the Celestial Sphere has a declinatin which lies between 0 and 90. C The Suth Celestial Ple has a declinatin f -90. C Any pint in the suthern half f the Celestial Sphere has a declinatin which lies between 0 and Right Ascensin

5 Just as the declinatin is the equivalent f latitude, n the Celestial Sphere the right ascensin is the equivalent f lngitude. It measures hw far that pint lies east f a reference pint knwn as the first pint in Aries. The first pint in Aries is an imaginary pint in the sky crrespnding t the psitin f the Sun at the time f the Vernal equinx. All measurements are made in a directin east f this pint. Fr a pint which is just t the west f the first pint in Aries the right ascensin is measured almst arund the Celestial Sphere. Althugh the Right Ascensin can be defined as an angle equivalent t that fr lngitude, it is nrmally expressed nt as an angle but as a time. Remember that the stars (and ther bjects) appear t mve acrss ur sky because the Earth rtates n its axis thrugh 360 nce every 24 hurs, that is 15 per hur. C What is a declinatin f 3 h expressed in degrees? C 3 h * 15 per h = 45 C What is a declinatin f 120 expressed in hurs? C 120 / 15 per h = 8 h C What is a declinatin f 4 h 24 m expressed in degrees? C 4 h 24 m = 4 h + 24/60 h = 4.4 h C 4.4 h * 15 per h = 66 C What is a declinatin f 275 expressed in hurs? C 275 / 15 per h = h C h = 18 h +0.33*60 m = 18 h 20 m

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