4 Solar System and Time
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1 4 olar ystem and Time 4.1 The Universe Introduction The Universe consists of countless galaxies distributed throughout space. The bodies used in astro navigation belong to the Galaxy known as the Milky Way. The Milky Way appears to the observer as a luminous belt of stars encircling the heavens. The Milky Way is shaped like a disc, the olar ystem lying near its central horizontal plane, the Galactic Plane. Relatively few stars are found in directions at 90 to this plane tability of the Galactic ystem The stars apparently maintain constant relationships to each other, forming the characteristic patterns known as Constellations. However, the rate of rotation of the Galactic ystem is not constant; stars at the centre rotate more rapidly than those at the periphery, and consequently, stars lying at different distances from the centre slowly change their relative positions with time. This change is too slow to influence the problems of navigation on the Earth s surface. The un s orbital velocity is shared by the Earth and the other bodies of the olar ystem tellar Magnitude tars were originally categorised by the Greek astronomer Ptolomy according to Fig. G 4.1 ideview of the Milky Way (AA) their relative brightness to an observer. This brightness, or magnitude, was originally based on the order in which the stars appear; magnitude 1 stars appear as darkness falls, while magnitude 6 stars are just visible to the naked eye in total darkness. This crude method was later modified as observation techniques improved. Magnitude 1 stars were reclassified to the extent that some were allocated negative values e.g. irius -l.6. The lower the number the brighter the body. This was then extended to include other bodies in the sky. For example Venus has a olar ystem and Time 4-1 General avigation E5 Proof 2.in :21:10
2 un Venus Mars Mercury Earth aturn Jupiter Uranus eptune Fig. G 4.2 The solar system magnitude of -4, the full moon a magnitude -12 and the un a magnitude olar ystem The main bodies of the olar ystem are the un, Moon, and the Planets. The un is the central figure of the olar ystem; being distinguished by its size and as a radiator of heat and light. The Moon and the Planets are not self-luminous but shine by reflecting sunlight. The Planets revolve round the un in elliptical orbits. The Moon, Earth s only natural satellite, revolves about the Earth, see fig. G 4.2 and G 4.3. The Planets in order of their distances from the un are: Mercury, Venus, Earth, Mars, Jupiter, aturn, Uranus and eptune. A un Fig. G 4.3 The Moon orbits the Earth Moon Earth rhyme may help you remember this order: My Vet Eyes May Just ee U ow. Venus, Mars, Jupiter and aturn are sufficiently bright to be observed through 4-2 olar ystem and Time General avigation E5 Proof 2.in :21:10
3 Aphelion Equal areas P 1 A A 1 Radius vector P One of the foci of the elipse Perihelion Time from A to A 1 = time from P to P 1 Fig. G 4.4 Kepler's laws a sextant. There are also about 2000 minor planets and asteroids Kepler s Laws Kepler defined the following laws of planetary motion: The orbit of each planet is an ellipse, with the un at one of the foci The line joining the planet to the un, known as the radius vector, sweeps out equal area in equal time The square of the siderial (annual) period of a planet is proportional to the cube of its mean distance from the un In fig. G 4.4, the orbit of the Earth is represented by the ellipse, the un is at one of the foci. AP is the major axis or lapse line. The point P, where the Earth is closest to the un, in early January, is known as Perihelion. Point A, where the Earth is farthest from the un (), in early July, is called Aphelion. The Earth takes the same amount of time to travel from A to A 1 as from P to P 1. By Kepler s laws, the areas AA 1 and PP 1 are equal. ince the distance PP 1 is greater than AA 1 it follows that the Earth s orbital speed varies, being greatest at Perihelion and least at Aphelion. As the Earth is closest to the un in January and farthest away in July, the summer is longer than the winter in the orthern Hemisphere. In the outhern Hemisphere, the winter is longer than the summer. olar ystem and Time 4-3 General avigation E5 Proof 2.in :21:10
4 Equator orthern summer orthern winter 66 33' 23 27' Equator outhern winter outhern summer Fig. G 4.5 The Ecliptic The Earth s Orbit The Earth completes one orbit round the un in approximately days. The orbital plane is called the ecliptic, the Earth s - axis being inclined at 66.5 (actual angle ) to the ecliptic. The plane of the ecliptic makes an angle of 23.5 (actual angle ) with the plane of the Earth s equator; this angle is known as the obliquity of the ecliptic, see fig. G 4.5. The tilting of the Earth s axis causes the annual cycle of seasons. The projection of the un s apparent annual path on the Earth is a great circle inclined at 23.5 to the equator. About 21 December the orth Pole is inclined directly away from the un, which is overhead the 23.5 outh parallel. Known as the December solstice, this is mid winter in the orthern Hemisphere and mid summer in the outhern Hemisphere, see fig. G 4.6. eptember Equinox (Autumn H) 23 27' December solstice (Winter H) Ecliptic CP CP Fig. G 4.6 The un's annual path Celestial Equator June solstice (ummer H) 23 27' March Equinox (Vernal H) As the Earth travels around its orbit its axis always points in the same direction. On 21 June, the un is vertically overhead the 23.5 orth parallel. Known as the June olstice, this is mid-summer in the orthern γ East 4-4 olar ystem and Time General avigation E5 Proof 2.in :21:10
5 Hemisphere and mid-winter in the outhern Hemisphere. Between these dates the un, moving along its annual path, crosses the equator from south to north and again from north to south. These crossings occur on or near 21 March and 23 eptember. These are known as the March (vernal) equinox and eptember equinox respectively. The vernal equinox is also known as the First Point of Aries. The Tropic of Capricorn is the parallel of latitude at 23.5 outh of the Equator, and is the farthest southern latitude that the sun can appear directly overhead, occurring on the December solstice. The Tropic of Cancer is the parallel of latitude that lies 23.5 orth of the Equator, and is the farthest northern latitude that the sun can appear directly overhead, occurring on the June solstice. A Polar Circle is either the Arctic Circle or the Antarctic Circle. On Earth, the Arctic Circle is located at a latitude of 66.5, and the Antarctic circle is located at a latitude of Areas between each polar circle and its associated pole (north pole, or south pole) will annually experience at least one 24 hour period when the sun is continuously above the horizon and at least one 24 hour period when the sun is continuously below the horizon The Earth s Rotation The Earth rotates from west to east on its axis as it orbits the un. The un s apparent daily path over the Earth is along a parallel of latitude, the particular latitude depending on the position of the un along its apparent annual path. ince the Earth rotates from west to east the apparent daily movement of the un and all other astronomical bodies is east to west. The daily paths of the stars also follow parallels of latitude. Because their movement is small over long periods the stars appear to traverse the same parallel throughout the year. The planets have independent orbits around the un. The planes of these orbits are inclined to the Earth s equatorial plane, and consequently the paths of the Planets over the Earth vary. 4.2 The Celestial phere Introduction An observer on the Earth has no indication that any particular star is farther from the earth than its neighbour i.e. all stars appear to be the same distance from the earth. The stars are therefore considered to be positioned on the inner surface of a sphere whose centre is the centre of the Earth. This imaginary sphere is known as the Celestial phere, on which all celestial bodies are imagined to be projected Position on the Celestial phere Position on the celestial sphere is located by: The declination and hour angle system. The altitude and azimuth system. olar ystem and Time 4-5 General avigation E5 Proof 2.in :21:10
6 4.2.3 Declination and Hour Angle ystem The equinoctial and the Earth spin axis, projected onto the celestial sphere, provide the framework for the declination and hour angle co-ordinate system, which is similar to the latitude and longitude system used to define position on the Earth. Declination Declination is the co-ordinate analogous to latitude. Circles of declination are small circles parallel to the equinoctial, declination being defined as the angular distance to a body on the celestial sphere measured north or south through 90 from the equinoctial along the hour circle of the body, see fig G 4.7. between a datum hour circle and the hour circle of the body, measured westwards from 0 to 360 (fig. G 4.8). (ote: At any instant, hour circles are coincident with particular celestial meridians). of aries GHA HA LHA of observer of star mall circle of declination CP HA Body pecified celestial GHA of Greenwich Fig. G 4.8 Measurement of hour angles Dec Three hour angles are recognised: idereal Hour Angle (HA) Greenwich Hour Angle (GHA) Local Hour Angle (LHA) Celestial of body CP Fig. G 4.7 Declination and hour angle Equinoctial Hour Angle Hour angle is the celestial co-ordinate corresponding to Longitude, and is defined as the arc of the equinoctial intercepted idereal Hour Angle ince the stars maintain their relative positions on the celestial sphere for long periods, declination and sidereal hour angle position them. The hour circle of the first point of Aries (γ) is used as the datum. The First Point of Aries is the point of intersection of the ecliptic and the equinoctial at which the un is moving from south to north declination. 4-6 olar ystem and Time General avigation E5 Proof 2.in :21:11
7 idereal Hour Angle (HA) is defined as the arc of the equinoctial between the celestial meridian of the First Point of Aries (i.e. The hour circle of Aries and the celestial meridian of the body. HA and declination therefore define the position of a star on the celestial sphere without reference to Earth co-ordinates. (Fig G 4.8) tar's vertical circle C CP Altitude Azimuth Z Observer's celestial Greenwich Hour Angle Greenwich Hour Angle (GHA) is the arc of the equinoctial measured westwards through 360 from the celestial meridian of Greenwich to the hour circle of the body. GHA of Aries relates the position of the hour circle of Aries to the Greenwich celestial meridian. By combining GHA of Aries and HA of the body the positions of the stars at any instant are related to the Greenwich celestial meridian, see fig G 4.8. Local Hour Angle Local Hour Angle is the arc of the equinoctial measured westwards through 360 from the observer s celestial meridian to the hour circle of the body, see fig G Altitude and Azimuth ystems Positioning a Body A body can be positioned on the celestial sphere by altitude and azimuth as shown in fig. G 4.9. Zenith and adir The Zenith is the point on the celestial sphere overhead an observer. The adir is the diametrically opposite point. Fig. G 4.9 Altitude and azimuth Altitude Altitude is the smaller arc of the vertical circle through the body, intercepted between the celestial horizon and the body. Azimuth Azimuth is the angle at the zenith measured clockwise from the observer s celestial meridian to the vertical circle through the body. Azimuth is therefore the great circle bearing of the body from the zenith, and is always measured clockwise through 360 from true north. 4.3 Time Introduction CP From the earliest days, time has been measured by observing the recurrence of astronomical phenomena. The Earth s rotation on its axis produces the apparent rotation of the celestial sphere, allowing time to be measured from the relative positions H olar ystem and Time 4-7 General avigation E5 Proof 2.in :21:11
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