Navigation ( Part 4 )

 

Navigation ( Part 4 )

 

Celestial or Rational Horizon

The observer’s rational horizon is a great circle on the celestial sphere every point on which is 90 degree away from his zenith. The plane of the observers rational horizon passes through the center of the earth.

 

True Altitude

True Altitude of a body is the arc of the vertical circle through that body contained between the rational horizon and the center of the body .

 

Zenith Distance

Zenith Distance of a body is the arc of the vertical circle through the body contained between the observers zenith and the center of the body 

Since every point on the rational horizon is 90 degree from the observers zenith ,then the zenith distance = 90 degree – altitude.

 

Azimuth

Azimuth of a celestial body is the arc of the observers rational horizon or the angle at his zenith contained between the observer’s celestial meridian and the vertical circle through that body

 

Prime Vertical

It is the vertical circle through the east and west points of the observers rational horizon.

 

Amplitude

Amplitude of a celestial body is the arc of the observers rational horizon or the angle at his zenith contained between the observers prime vertical and the vertical circle through the body , when the body is on the observer’s rational horizon

The theoretical rising and setting amplitude is therefore measured N or S from the observers East point when the body is rising and from his West point when setting

 

Vertical Circle

These are the great circle on the celestial sphere passing through the observer’s zenith and nadir.

 

Summer Solstice

On 21^st June , the sun attains its maximum declination north and the sun’s rays fall vertically over the tropic of cancer. The sun is then said to be at the summer solstice.

 

Autumnal Equinox

On 23^rd Sep the tilt of the earth’s axis is in a direction at right angles to the direction from earth to sun . The sun’s rays fall vertically over the equator and the sun’s declination is o degree .

The circle of illumination passes through the two poles . All places on the earth have equal day and night . The sun is now said to be at the Autumnal equinox.

 

Winter Solstice

On 22^nd December the south end of the earth’s axis , the south pole is titled towards the sun by the maximum amount of 23 ½ degree . on this date the sun is said to be at the winter solstice attains its maximum declination south. Sun’s rays then fall vertically over the tropic of capricorn.

 

Vernal Equinox

On the 21^st march the earth axis is tilted in a direction at right angles to the direction from earth to sun. The sun’s rays again fall vertically over the equator and the declination of sun is zero . The sun is said to be vernal equinox .

 

Aphelion

A planet is said to be aphelion when its orbit , it is farthest from the sun.

 

Perihelion

A planet is said to be perihelion when in its orbit , it is nearest to the sun.

 

Perigee and Apogee

The moon in its orbit around the earth is nearest to the earth , they are said to be perigee and when farthest from the earth they are said to be apogee .

 

Conjunction

A planet or the moon is said to be in conjunction with the sun , when as viewed from the earth it is in the same direction as the sun . ie ) their celestial longitudes are same.

 

Opposition

A planet or the moon is said to be in opposition with the sun when as viewed from the earth , it is opposite in direction to the sun. Ie) their celestial longitudes are 180 degree apart.

Quadrature

A planet or the moon is said to be in quadrature when its elongation is exactly 90 degree east or west.

 

Sidereal Period of Moon

Its the time taken by the moon to complete one revolution of 360 degree around the earth. The sidereal period is of constant duration equal to 27 days 07 hours 43 minutes and 12 seconds ie ) approximately 27.33 days .

 

Synodic Period of Moon

Its the period of time between two consecutive new moons or two consecutive full moons. The sunodic period has an average length of about 29 days 12 hours 44 minutes  This period may also be called Lunar month or lunation.

 

Nodes

The points at which the moons orbit intersects the ecliptic are called the moon’s nodes. That node at which the moon crosses the ecliptic from south to north is called the ascending node and the node at which it crosses the ecliptic from north to south is called the descending node.

 

Solar Eclipse

When the moon is in conjunction with the sun and the center of the three bodies are nearly in a line . The moon appears directly over the sun as viewed from the earth. Blocking of sun’s disc wholly or partly such an occurrence is called solar eclipse.

 

 

Lunar Eclipse

A lunar eclipse takes place when the moon passes through the earth’s shadow. This can happen only when the moon is in opposition with the sun.

 

 Day

Is the interval in time between two successive meridian passage of a heavenly body over the same meridian.

 

Sidereal day

Is the interval in time between two successive meridian passage of the first point of aries over the same meridian.

 

Apparent solar day

Is the interval in time between two successive transit of the true sun across the same meridian .

 

Mean sun

Is an imaginary body assumed to move along the equinoctial at a uniform rate , equal to the average rate of motion of the true sun on the ecliptic.

 

Mean solar day

Is the interval in time between two successive meridian passage of the mean sun across the same meridian.

 

 

Greenwich Sidereal Time (GST)

Is the westerly hour angle of first point of aries measured from the Greenwich merdian

 

Local Sidereal Time (LST)

Is the westerly hour angle of the first point of aries measured from observer’s meridian.

 

Greenwich Apparent time (GAT)

Is the westerly hour angle of the true sun measured from the inferior meridian of Greenwich.

 

Local Apparent time (LAT)

Is the westerly hour angle of the true sun measured from the observer’s inferior meridian.

 

 

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will revert back,types of horizon shortly.

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Navigation ( Part 3 )

 

Navigation ( Part 3 )

 

Parallel Sailing

Sailing between two positions on the earth’s surface involves calculating the course and distance between them . the shortest distance between any two points on the earth is the shortest arc of the great circle through that points. The great circle track crosses the various meridians at different angles .Thus a ship following a great circle track would have to continuously alter her course throughout the passage . Therefore in navigating from one place to another the usual method is to sail along a rhumb line track.

 

Rhumb Line

A Rhumb line is a line on the earth’s surface crossing all meridians at the same angle . it can thus be seen that the rhumb line is the most convenient track to follow as the course of the ship remains constant for the entire passage .

On Mercator chart however , a rhumb line appears as a straight line as the meridians on a Mercator chart are represented as straight lines parallel to each other.

 

Plane Sailing

Plane sailing is sailing along a rhumb line from one position to another , which are not situated on the same latitude.

Dep / d’long = Cos lat

 

Dep / d’lat  = Tan .course

 

Distance = d’lat X Sec. Course

 

Departure 

On a Mercator chart , the E – W distance between two places , measured along the latitude scale ( in minutes of latitude ) is the departure between them in nautical miles . but if measured along the longitude scale it is the d’long.

 

DMP or d’ long – Difference in Meridian latitude

On a Mercator chart the N – S diatance between two places , measured  along the latitude scale , is the d’lat between them ( in minutes or nautical miles ) but if measured along the longitude scale ( in minutes of longitude ) it is the DMP between them.

 

Meridional Parts

Meridional parts for any latitude is the arc of the meridian , or the angle at the center of the earth , contained between the equator and that parallel of latitude expressed in minutes of longitude is called the meridional parts for that latitude.

 

Natural Scale

The Natural scale of a chart is the ratio that the distance between two points on the chart bears to the actual distance between them on the earth.

Natural scale = chart distance / earth distance

 

  Mercator sailing

  Where the distance exceeds 600 miles. It is recommended that calculation be done by Mercator sailing in order to get more accurate results than by plane and parallel sailing methods .

D’long / DMP  = Tan course

 

Gnomonic charts – Great circle chats

If a navigator is to follow the shortest route between two positions , he must sail along a great circle . it would therefore be convenient to have charts on which great circles are represented by straight lines.

 

Plan chart

Plan charts are representations of very small areas of the earth’s surface .such as an  anchorage , a port or a harbour

 

Different types of charts

Star charts

Magnetic variation charts

Co – Tidal and Co – range charts

Instructional charts

Time zone charts

 

Ecliptic

Is a great circle on the celestial sphere in the same plane as the plane of the earth’s orbit around the sun . Thus the sun’s apparent annual path on the celestial sphere is the ecliptic . It is so called because the sun , moon and earth must must be on this plane for a solar or lunar eclipse to occur.

 

Ellipse

The sun’s apparent orbit around the earth is an ellipse. Ecliptic is a projection of this ellipse on to the celestial sphere.

 

Obliquity of the Ecliptic

Is the angle between the plane of the equinoctial and that of the ecliptic . It’s value is approximately 23 ½ degree .

 

  Zodiac

                       Is a belt on the celestial sphere extending 8 degree on each side of ecliptic within which the sun , the moon and the planets are always found . The belt of the zodiac is divided into 12 equal parts of the length 30 degree each . These are named after groups of stars or constellations within them . they are Aries , Taurus , Gemini , Cancer , Leo , Virgo , Libra , Scorpio , Sagittorius , Capricorn , Aquarius and Pisces.

 

Observer’s zenith

Is the point on the celestial sphere vertically above the observer ie) the point at which a straight line from the center of the earth through the observer meets the celestial sphere.

 

Observer’s Nadir

Is the point on the celestial sphere vertically opposite his Zenith.

 

Vertical Circles

Are great circles on the celestial sphere passing through the observer’s Zenith and Nadir.

 

Position on the Celestial sphere

A position on a sphere may be defined by the angle at the center of the sphere or the great circular co ordinates of that position with respect to two reference great circles which are at right angles to each other.

Position on the earth’s surface for instance are defined by stating such angles or co ordinates with respect to two reference great circles the equator from which latitudes are measured and the prime meridian from which longitude are measured . 

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