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Celestial Navigation
Solar System
The Solar
System
The sun, the most visible celestial body in the sky,
is the centre of the solar system. Associated with it are at least nine
principal planets. Some planets like earth have moons/ satellites.
Motions Of Bodies Of The Solar System
The two principal motions of celestial bodies are
Rotation and Revolution.
Rotation is a spinning motion about an axis within the
body, whereas Revolution is the motion of a body in its orbit around another
body. The body around which a celestial object revolves is known as that body’s
primary.
The gravitational force of the sun holds the entire
solar system together
This gravitational force causes the planets to go
around the sun in nearly circular, elliptical orbits.
In each planet’s orbit, the point nearest the sun is
called the perihelion. The point farthest from the sun is called the aphelion.
The line joining perihelion and aphelion is called the
line of apsides.
In the orbit of the moon, the point nearest the earth is called the perigee,
and that point farthest from the earth is called the apogee.
The distance from the earth to the sun varies from
91,300,000 at perihelion to 94,500,000 miles at aphelion.
When the earth is at perihelion, early in January, the
sun’s diameter appears largest, 32.6’. At aphelion, in June the sun’s apparent
diameter is a minimum of 31.5’.
Planets
The principal bodies orbiting the sun are called
planets.
Nine principal planets are known: Mercury, Venus,
Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. Of these, only four
are commonly used for celestial navigation:
Venus, Mars, Jupiter, and
Saturn.
Except for Pluto, the orbits of the planets lie in
nearly the same plane as the earth’s orbit. This plane of the celestial sphere
is called the ecliptic.
The two planets with orbits smaller than that of the
earth are called inferior planets, and those with orbits larger than that of
the earth are called superior planets.
Planets can be identified in the sky because, unlike
the stars, they do not twinkle. The stars are so distant that they are
virtually point sources of light. Therefore the tiny stream of light from a
star is easily scattered by normal motions of air in the atmosphere causing the
affect of twinkling. The planets, however, are close enough to present
perceptible disks. The light from a planet is not easily distorted unless the
planet is low on the horizon or the air is especially turbulent.
The Earth
The earth rotates on its axis and revolves in its
orbit around the sun.
The above motions are the reason why the other
celestial bodies have apparent motions.
For most navigational purposes, the earth can be
considered a sphere. However, like the other planets, the earth is
approximately an oblate spheroid, or ellipsoid of revolution, flattened at the
poles and bulged at the equator.
The polar diameter is less than the equatorial
diameter, and the meridians are slightly elliptical, rather than circular.
Planets
useful for navigation
Inferior
Planets
Since Mercury and Venus are inside the earth’s orbit,
they always appear close to the sun. Over a period of weeks/ months, they
appear to go back and forth from one side of the sun to the other.
They are seen either in the eastern sky before sunrise
or in the western sky after sunset. For brief periods they disappear into the
sun’s glare.
At this time they are between the earth and sun (known
as inferior conjunction) or on the opposite side of the sun from the earth
(superior conjunction). On rare occasions at inferior conjunction, the planet
will cross the face of the sun as seen from the earth. This is known as a
transit of the sun.
When Mercury or Venus appears most distant from the
sun in the evening sky, it is at greatest eastern elongation.
(Although the planet is in the western sky, it is at
its easternmost point from the sun.) From night to night the planet will
approach the sun until it disappears into the glare of twilight. At this time
it is moving between the earth and sun to inferior conjunction. A few days
later, the planet will appear in the morning sky at dawn. It will gradually
move away from the sun to western elongation, and then move back toward the
sun. After disappearing in the morning twilight, it will move behind the sun to
superior conjunction. After this it will reappear in the evening sky, heading
toward eastern elongation.
Mercury is never seen more than about 28˚from
the sun.
For this reason it is not commonly used for
navigation. Near greatest elongation it appears near the western horizon after sunset, or the eastern horizon before sunrise. At these
times it resembles a first magnitude star.
The interval during which it appears as a morning or
evening star can vary from about 30 to 50 days. Around inferior conjunction,
Mercury disappears for about 5 days; near superior conjunction, it disappears
for about 35 days.
Venus can reach a distance of 47˚from the
sun, allowing it to dominate the morning or evening sky. At maximum brilliance,
about five weeks before and after inferior conjunction, it has a magnitude of
about –4.4 and is brighter than any other object in the sky except the sun and
moon.
At these times it can be seen during the day and is
sometimes observed for a celestial line of position.
Superior
Planets
They can pass behind the sun (conjunction), but they
cannot pass between the sun and the earth. Instead we see them move away from
the sun until they are opposite the sun in the sky (opposition). When a
superior planet is near conjunction, it rises and sets approximately with the
sun and is thus lost in the sun’s glare. Gradually it becomes visible in the
early morning sky before sunrise. From day to day, it rises and sets earlier,
becoming increasingly visible through the late night hours until dawn.
Approaching opposition, the planet will rise in the late evening, until at
opposition, it will rise when the sun sets, be visible throughout the night, and
set when the sun rises.
Observed against the background stars, the planets
normally move eastward in what is called direct motion.
Approaching opposition, however, a planet will slow
down, pause (at a stationary point), and begin moving westward (retrograde
motion), until it reaches the next stationary point and resumes its direct
motion.
The superior planets are brightest and closest to the
earth at opposition.
Mars can usually be identified by its orange color. It
can become as bright as magnitude –2.8 but is more often between –1.0 and –2.0
at opposition.
Jupiter, largest of the known planets, normally
outshines Mars, regularly reaching magnitude –2.0 or brighter at opposition.
Saturn, is at opposition becomes as bright as
magnitude +0.8 to –0.2.
The Moon
It revolves around the earth once in about 27.3 days,
as measured with respect to the stars. This is called the lunar month.
When the moon is in conjunction with the sun (new
moon), it rises and sets with the sun and is lost in the sun’s glare.
From day to day, the moon will rise (and set) later,
becoming increasingly visible in the evening sky, until (about 7 days after new
moon) it reaches first quarter, when the moon rises about noon and sets about
midnight. Over the next week the moon will rise later and later in the
afternoon until full moon, when it rises about sunset and dominates the sky
throughout the night.
During the next couple of weeks the moon will rise
later and later at night. By last quarter (a week after full moon), the moon
rises about
At full moon, the sun and moon are on opposite sides
of the ecliptic. Therefore, in the winter the full moon rises early, crosses
the celestial meridian high in the sky, and sets late; as the sun does in the
summer. In the summer the full moon rises in the southeastern part of the sky
(Northern Hemisphere), remains relatively low in the sky, and sets along the
southwestern horizon after a short time above the horizon.
At the time of the autumnal equinox, the part of the
ecliptic opposite the sun is most nearly parallel to the horizon. Since the
eastward motion of the moon is approximately along the ecliptic, the delay in
the time of rising of the full moon from night to night is less than at other
times of the year.
The Earth’s elliptical orbit, and Approximate
perihelion and aphelion distances and dates
The earth travels round the sun in an orbit, which is
slightly elliptical. Its plane being called the Ecliptic,
because eclipses happen only when the moon crosses it.
The above shows the earth in its orbit, viewed from an
elevation above the plane of the ecliptic, the sun is not exactly at the centre
of the ellipse and the earth is shown at the four extremities of the ellipse.
The ecliptic is thus an imaginary plane that cuts the
earth and the sun in halves.
The earths distance from the sun varies, It is maximum
when it is farthest away – aphelion (about 4th July) – about 93.5
million miles, and nearest – perihelion (1st January) - distance is
90.5 million miles.
Due to the above we see the sun as slightly larger at
perihelion and slightly smaller at aphelion. This is the reason that the semi
diameter of the sun changes from max. of 16.3’ to
15.8’ of the arc.
Eccentricity
of the earth’s orbit
The force of gravity determines the way the planets
and the sun move. As a result of gravity, bodies attract each other in
proportion to their masses and to the inverse square of the distances between
them. This force causes the planets to go around the sun in nearly circular,
elliptical orbits.
The sun is not exactly at the centre of the orbit of
the earth, which is an ellipse; this is the reason why the earth swings from
perihelion to aphelion.
The inclination of the earth’s axis to the plane of
the orbit and the stability of the axis (ignoring precession) – Cause of
seasons
If the earth’s axis were perpendicular to the plane of
the ecliptic the sun would be over the equator throughout the year and then we
would not have any seasonal changes.
But, the earths axis is not
perpendicular to the plane of the ecliptic, it is tilted at an angle of
23˚26’. The axis of the earth may be assumed to be pointing fixedly in one
direction in space, about the direction of the pole star.
Due to this tilting of the earths axis from the
perpendicular, the sun bobs up and along from the earths equator.
Thus when the sun reaches its maximum northerly travel
along the ecliptic, when the declination is 23.5˚N, it is summer in the
Northern Hemisphere. And when the sun reaches its maximum southerly travel,
when the declination is 23.5˚S, it is winter in the Northern Hemisphere.
At 23.5˚N the sun therefore is overhead on earth, the 23.5˚N latitude on earth where the sun is
overhead is called the Tropic of Cancer.
Similarly the Southern 23.5˚S latitude is called
the Tropic of Capricorn.
Please note that actually the sun does not travel but
it is the earth that does the travelling, but we from earth view the sun to be
moving apparently.
Declination may thus be defined as the angular
distance of the sun North or South of the equator.
Dates of the solstices
and equinoxes
The solstices are two points in the ecliptic where the
sun reaches its maximum (23.5˚) North or South declination. The summer
solstice is on June 21st and the winter solstice is on December 22nd.
Concept of
the earth’s axial rotation giving day and night
As the earth spins on its axis, only one half of the
earth’s surface faces the sun. Therefore only that half receives the light and
heat of the sun, this half is experiencing daylight and the half that is on the
other side - the dark side – it is Nighttime.
As the earth rotates more areas come within daylight
and other area on the day’s edge move into darkness or night.
Varying
length of daylight through the year
If the earths axis were not tilted, then the sun would
be always above the equator, in that case the sun would rise and set at the
same time everywhere throughout the year, However, when it is summer in the
Northern hemisphere the sun is overhead or nearly overhead at 23.5˚N, the
footprint of the sun therefore is more encompassing the Northern Hemisphere and
the days are longer in the Northern Hemisphere.
But when the sun moves down south and is at
23.5˚S the place in the Northern Hemisphere are not at the centre of the
footprint but at the edge of it, the days are therefore shorter.
Daylight and darkness conditions in various latitudes
at the solstices and equinoxes
Due to the tilt in the axis of the earth, the sun
apparently moves along the ecliptic and at 23,5˚N declination more of the
Northern Hemisphere is facing the sun, more heat and light are received by the
northern hemisphere, summer is then being experienced in the northern
hemisphere, with more daylight and less darkness.
But with the earth continuing its journey, the
apparent sun starts to move southward and on September 28th Autumnal
Equinox (equal nights), the sun is shining is overhead at the equator, the days
and night are of equal duration.
On the 22nd of December the sun is overhead
on the Tropic of Capricorn - latitude of 23.5˚S,
it is summer in the southern hemisphere and winter in the northern hemisphere.
The days are shorter and nights longer in the Northern Hemisphere.
After this the earth continues its journey and on
March 21st the sun again is overhead at the equator – Vernal Equinox
– and the days and night are of equal duration.
The
significance of the tropics of Cancer and Capricorn and of the
Due to the tilt in the axis of the earth, the sun’s
apparent motion in the sky during the year is from latitude 23.5˚N to
23.5˚S. Thus the sun is overhead at latitude 23.5˚N on June 21st
and overhead at latitude 23.5˚S on 22nd December. Between these
two latitudes lie the area which receives the maximum heat and light from the
sun and they are termed as the
The parallels about 23.5˚ from the poles, marking
the approximate limits of the circumpolar sun, are called polar circles, the
one in the Northern Hemisphere being the