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Unit 6 Celestial Sphere and Equinoctial System of Coordinates

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Unit 6 Celestial Sphere and Equinoctial System of Coordinates Celestial Sphere and UNIT 6 CELESTIAL SPHERE AND EQUINOCTIAL Equinoctial System of SYSTEM OF COORDINATES Coordinates Structure 6.1 Introduction Objectives 6.2 Celestial Sphere and References 6.3 Apparent Annual Motion of the Sun and the Concept of the Ecliptic and the ‘Obliquity of the Ecliptic’ 6.4 The Equinoctial System of Coordinates 6.4.1 Reference Great Circles – Equinoctial, Celestial Meridians of Greenwich and Celestial Meridian of the First Point of Aries 6.4.2 Coordinates – Declination, Greenwich Hour Angle (GHA), Local Hour Angle (LHA), Sidereal Hour Angle, Right Ascension 6.5 Relationship between GHA, LHA and Longitude 6.6 The Concept of the Earth’s Axial Rotation Causing Change in the Hour Angle of Bodies 6.7 Summary 6.8 Key Words 6.9 Answers to SAQs 6.1 INTRODUCTION In order to use celestial bodies (the Sun, Planets, Moon, and stars) for position fixing it is required that we know their position in the sky. The position of a celestial body is defined on the celestial sphere by using different coordinate systems based on their purpose. The coordinate systems used are equinoctial system, Horizon system and ecliptic system. In this unit we will discuss the equinoctial coordinate system of defining position of the body in the sky, which is used in the Nautical Almanac. Objectives After studying this unit, you should be able to • define the celestial sphere, celestial poles, celestial meridians, equinoctial, declination circles, • explain the apparent annual motion of the sun and the concept of the ecliptic and the ‘obliquity of the ecliptic’, • explain the equinoctial as a fixed reference plane and the direction of the First Point of Aries as a reference direction (ignoring the effect of precession), • describe the equinoctial system of co-ordinates, • define ‘Greenwich Hour Angle (GHA)’, ‘Local Hour Angle (LHA)’ and longitude, and explain their relationship, • define sidereal hour angle, declination, and right ascension, and • describe the concept of the earth’s axial rotation causing change in the hour angle of bodies. 29 Celestial Navigation 6.2 CELESTIAL SPHERE AND REFERENCES In celestial navigation, the earth is assumed to be a perfect sphere, located at the center of the universe. At night when we look at the sky we see all heavenly bodies located on a hemispherical dome called the celestial sphere. The earth is assumed to be stationary due to which all celestial bodies appear to move on the celestial sphere. The grid for pin pointing position of a celestial body may be imagined to be created by projecting the earth’s grid on the celestial sphere with light source at the center of the earth. North Celestial Poles (NCP) Declination Circles Earth’s North Pole Earth’s Meridian Equator Equinoctial Celestial Meridians Celestial Sphere South Celestial Poles (SCP) Figure 6.1 6.2.1 Definitions Celestial Sphere It is a sphere of immense radius whose centre is same as centre of the earth. It is the sphere on which all celestial bodies appear to lie. As calculations in celestial navigation are based on angular measurements, the radius of the earth is irrelevant. It can be also defined as sphere of infinite radius concentric with the earth. Celestial Poles The earth’s poles extended to meet the celestial sphere are called celestial poles (north celestial pole and south celestial pole). They can also be defined as outward projection of the earth’s poles on the celestial sphere. Equinoctial or Celestial Equator Equinoctial is a great circle on the celestial sphere whose plane is same as plane of the earth’s equator. It can be also defined as projection of the equator on the celestial sphere. Celestial Meridians The semi-great circles on the celestial sphere joining the celestial poles or projection of the earth’s meridians on the celestial sphere. Celestial meridians cut the equinoctial and the declination circles at 90º. Declination Circles / Parallels of Declination These are small circles on the celestial sphere parallel to the plane of equinoctial. Declination circles may also be defined as projection of parallels of latitude on the celestial sphere. 6.3 ANNUAL APPARENT PATH OF THE SUN The solar system consists of the Sun, the planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto), the planetary satellites (moons), asteroids, comets and meteors. The most important member of the Solar system is the Sun. All the planets 30 revolve eastward in elliptical orbits around the sun. The earth also rotates eastward on its Celestial Sphere and Equinoctial System of axis. Coordinates For the purposes of celestial navigation the earth is assumed to be stationary. Therefore due to eastward revolution of the Earth, the Sun appears to move eastwards on the celestial sphere, in the plane of the Earth’s orbit. CelestialError! Sphere Ecliptic Earths Orbit Figure 6.2 Figure 6.2 shows the apparent motion of the Sun along the great circle on the celestial sphere, due to the eastward motion of the earth in its orbit. The great circle on the celestial sphere in the plane of the earth’s orbit is called Ecliptic. It is so called because the Sun, Moon and Earth must be on this plane for a solar or lunar eclipse to occur. The projection of the Sun on the ecliptic from successive positions of the earth in its orbit, appears to constantly move eastwards. The earth’s axis is inclined to its orbiting plane by about 23° 26.7′. Therefore the equinoctial also makes the same angle with the plane of ecliptic. The angle at which the plane of ecliptic cuts the equinoctial plane is called Obliquity of Ecliptic. First Point of Aries γ The ecliptic intersects the equinoctial at two points called the equinoctial points. The equinoctial point when the Sun appears to cross the Equinoctial from South to North is called first point of Aries and is denoted by symbol γ. This occurrence takes place on 21st March, at Vernal Equinox. The first point of Aries is considered as fixed point on the celestial sphere (ignoring precession of equinoxes will be discussed in later units). First Point of Libra Ώ The equinoctial point when the Sun appears to cross the Equinoctial from North to South is called first point of Libra, and is denoted by the symbol K. The First point of Aries and the First point of Libra were named after the constellations in which they once lay. These points are however moving westward slowly, along the Ecliptic. Due to this, the 1st point of Aries is no longer in the constellation of Aries. It is now in the constellation of Pisces. 31 Celestial Navigation 6.4 THE EQUINOCTIAL SYSTEM OF CO-ORDINATES The coordinates used to define the position of a celestial body on the celestial sphere in the equinoctial system are Declination and Greenwich Hour Angle. This system of coordinates is used in Nautical Almanac to define the position of celestial body at any instant of the year. For determining these coordinates reference used are as follows. 6.4.1 The Reference Great Circles Used in the Equinoctial System Equinoctial Equinoctial is the great circle on the celestial sphere which is equidistant from the celestial poles or whose plane is same as the plane of equator. This is the reference plane from which declination of astronomical bodies is measured north or south. Celestial Meridian Passing of Greenwich It is the celestial meridian that passes through Greenwich. Greenwich Hour Angle (GHA) of all celestial bodies is measured westward from this reference great circle. Celestial Meridian of First Point of Aries It is the celestial meridian that passes through first point of Aries. Sidereal Hour Angle of all celestial bodies is measured with reference to this great circle. 6.4.2 The Coordinates in the Equinoctial System Declination It is the arc of celestial meridian passing through the body contained between the Equinoctial and the body. It may be also defined as arc of celestial meridian or the angle at the centre of the earth contained between the Equinoctial and the declination circle passing through the body. If the body is North of the equinoctial the declination is North and if the body is South of the equinoctial declination is named South. As it is angular measure it is expressed in degrees and minutes and its value is in between 0º to 90º N or S. Hour Angle (HA) Hour Angle is arc of the Equinoctial or the angle at the celestial poles contained between two celestial meridians. Greenwich Hour Angle (GHA) GHA of a celestial body is the arc of the Equinoctial or the angle at the celestial poles contained between the celestial meridian of Greenwich and celestial meridian passing through the body, measured westward from celestial meridian of Greenwich. It is expressed in degrees and minutes and its value is in between 0º to 360º. Sidereal Hour Angle (SHA) SHA of a celestial body is an hour angle the arc of the Equinoctial or the angle at the celestial pole contained between the celestial meridian of the First point of Aries and that through the body, measured westward from Aries. Right Ascension (RA) RA of a celestial body is an hour angle contained between the celestial meridian of the First point of Aries and the celestial meridian passing through the body, measured eastward from Aries. RA is generally expressed in hours, minutes and seconds, instead of, in arc. Since SHA is measured westward and RA eastwards from the same point, the SHA and RA of any body will together always add up to 360°. SHA* + RA* = 360º 32 Local Hour Angle (LHA) Celestial Sphere and Equinoctial System of LHA of a celestial body is an hour angle contained between the observer’s Coordinates celestial meridian and the celestial meridian through that body, measured westward from the observer.
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