- The document discusses three main celestial coordinate systems used to define positions on the celestial sphere: the celestial equinoctial system, celestial horizon system, and celestial ecliptic system. - It provides details on the key components that make up each system, such as declination circles and hour angles in the equinoctial system, and altitude, azimuth, and zenith distance in the horizon system. - A combination of the equinoctial and horizon systems is represented by the PZX spherical triangle, known as the nine-point diagram, which relates celestial positions to latitude, longitude, and other coordinates.

1. Celestial Sphere &
Coordinate Systems
Cdr VR – BSc 19 – Nov 2021

2. Celestial Sphere

3. Celestial Sphere
- There are 3 Main Systems of defining
a Position (Coordinates) on the Celestial
Sphere, they are
- Celestial Equinoctial System
- Celestial Horizon System
- Celestial Ecliptic System
(Not commonly used in Navigation)
Plane of the Ecliptic Tilted on Celestial Sphere - YouTube

4. Earth
Coordinates

5. Celestial Sphere
All Celestial bodies (Sun, Moon, Stars & Planets are assumed
to lie on the surface of the celestial sphere
All calculations are based on angular measurements (radius of
celestial sphere is irrelevant)
Earth is assumed to be stationary while the celestial bodies
are assumed to move on the surface of the celestial sphere
Two Main Systems used for defining a Position on the
Celestial Sphere are Celestial Equinoctial System & Celestial
Horizon System

6. Celestial Sphere
Various Reference points / lines on the earth have equivalent
points / lines on the surface of the celestial sphere
EARTH Coordinates Equinoctial system
 Geographic Poles Celestial Poles
 Equator Equinoctial (Celestial
Equator)
 Meridians Celestial Meridians
 Parallels of Latitude Declination Circles
 Latitude Declination
 Longitude Greenwich Hour Angle

7. Celestial Equinoctial
System Coordinates
Declination GHA (Hour
Angle)

8. Earth &
Celestial
Equinoctial
Coordinates

9. - Celestial Poles - Two points where the axis of rotation of
the earth cuts the surface of the celestial sphere are called
celestial poles
- Equinoctial (Celestial Equator) - The equinoctial is a Great
Circle which is equidistant from the Celestial poles and therefore
are at 90 deg away from the celestial poles. It is also referred to as
the celestial equator
- Declination - Is the arc of a celestial meridian or the
angle at the centre of the celestial sphere measured between the
equinoctial and the declination circle passing through that body.
Declination is expressed in degrees and minutes North or South of
the Equinoctial. (90 deg N or S)
Celestial Equinoctial System

10. - Declination Circles - They are Small Circles on the
celestial sphere parallel to the equinoctial
- Celestial Meridians - They are Great Circles that
pass through the celestial poles. Celestial Meridians cross
the equinoctial and all declination circles at right angles.
Celestial Equinoctial System

11. Greenwich Hour Angle - GHA of a celestial body is the
arc of the equinoctial or the angle at the celestial pole,
measured westerly from the celestial meridian of
Greenwich to the celestial meridian passing through
that body.
GHA is expressed in degrees from 0 to 360 deg &
GHA would be 0 when the body is on the Greenwich
Meridian, increase steadily until it is 360 deg when it
would again be on the Greenwich Meridian
Celestial Equinoctial System

12. LHA of Celestial Body is the arc of the Equinoctial or the
angle at the Celestial Pole contained between the
Celestial Meridian of the Observer and that through the
Body measured Westward from the Observer’s Meridian
GHA of the body – contained between Greenwich and
Celestial Body
LHA of the body – contained between Obs Celestial
Meridian and Celestial Body
Celestial Equinoctial System

13. Relationship of Hour Angles and Longitude
Celestial Sphere
- Local Hour Angle (LHA) - LHA of a celestial body is the Arc of the equinoctial
or the angle at the celestial pole measured westerly from the observer’s celestial
meridian to the celestial meridian passing through that body.
LHA of a celestial body would increase steadily from 0 to 360 deg. LHA would
be 0 when the body is on the observer’s meridian and increase steadily.
At any instant, for any celestial body
GHA = LHA - Long (East) / + Long (West) of Observer
GHA is measured from 0 to 360 westwards from Greenwich, while the
Longitude is measured from 0 to 180 E & 0 to 180 W from Greenwich.
The GHA of the celestial body if it is less than 180 deg then it will be equal to the West
Longitude of its GP. If the GHA is more than 180 deg, the Longitude of its GP will be (360 –
GHA) East.

14. Relationship of Hour Angles & Longitude
Relationship between LHA & GHA
-

15. The First Point of Aries
First Point of Aries. In astronomy, we need a celestial coordinate system for
fixing the positions of all celestial bodies in the celestial sphere. To this end, we
express a celestial body’s position in the celestial sphere in relation to its angular
distances from the Celestial Equator and the celestial meridian that passes
through the ‘First Point of Aries’. This is similar to the way in which we use
latitude and longitude to identify a position on the Earth’s surface in relation to its
angular distances from the Equator and the Greenwich Meridian.
The First Point of Aries is usually represented by the ‘ram’s horn’ symbol shown
below:

18. The First Point of Aries
Just as the Greenwich meridian has been arbitrarily chosen as the zero point for
measuring longitude on the surface of the Earth, the first point of Aries has been
chosen as the zero point in the celestial sphere. It is the point at which the Sun
crosses the celestial equator moving from south to north along the ecliptic (at the
vernal Equinox in other words). This point is known as the ‘First Point of Aries’
because in 150 B.C. when Ptolemy first mapped the constellations, Aries lay in
that position. However, although still named the ‘first point of Aries’, due to
precession, the vernal equinox now lays in the constellation Pisces.
Right Ascension (RA). This is used by astronomers to define the position of
a celestial body and is defined as the angle between the meridian of the First
Point of Aries and the meridian of the celestial body measured in an Easterly
direction from Aries. RA is not used in astro navigation; Sidereal Hour Angle is
used instead:
Sidereal Hour Angle (SHA). This is similar to RA in as much that it is
defined as the angle between the meridian of the First Point of Aries and the
meridian of the celestial body. However, the difference is that SHA is measured
westwards from Aries while RA is measured eastwards.

19. First point of Libra
(≏) The point on the celestial sphere diametrically opposite the first point
of Aries. It is the same as the autumnal equinox. It has right ascension
12h and declination zero. It is the point at which the Sun passes from
north to south of the celestial equator, which happens on September 22
or 23 each year. Because of precession, it no longer lies in Libra but in
neighbouring Virgo.
Earth's precessional wobbling causes the vernal equinox point to migrate
around the ecliptic once every 26,000 years. This point was once in Aries
the Ram, hence the term "First Point of Aries." The vernal equinox point
is now in Pisces and in the late 26th century will shift into the Aquarius
region. Note that the symbol designating the vernal equinox point is the
astrological sign of Aries.

22. Relationship of Hour Angles
Celestial Sphere
- Sidereal Hour Angle (SHA) - SHA of a celestial body is the Arc of the
equinoctial or the angle at the celestial pole contained between the celestial meridian
of the First Point of Aries and to the celestial meridian passing through that body,
measured Westward from Aries.
Right Ascension (RA) - RA of a celestial body is the arc of equinoctial or the
angle at the celestial poles contained between the celestial meridian of the First point of
Aries and that through the body, measured Eastward from Aries.
Note: Since SHA is measured Westward and RA is measured Eastwards from the same
point (First point of Aries), the SHA and RA of any body will together always add up to
360 deg.

23. Position of a Celestial Body at any instant is indicated by its Declination
and GHA at that instant
Geographical Position (GP) of a celestial body is the point on the surface
of the Earth, vertically beneath that body (ie, the point at which a
straight line from the centre of the Earth to the celestial body meets the
Earth’s surface)
GP being on the Earth’s surface, is always expressed in terms of Latitude
and Longitude.
Since the Centre of the celestial sphere is the Earth’s centre, and as the
Equator & the Equinoctial are in the same plane, the Latitude of a
celestial body’s geographical position (GP) is equal to the body’s
Declination. The Longitude of its GP corresponds to its GHA.
Celestial Equinoctial System

24. Celestial Horizon System

25. Observers’ Zenith – The
point on the Celestial
sphere vertically above
the Observer, ie, the
point at which a straight
line from Centre of Earth
through the observer
meets the celestial
sphere
Observers’ Nadir – The
point on the celestial
sphere vertically
opposite his Zenith
Horizon System Coordinates
Nadir

26. Celestial / Rational
Horizon – The
observer’s Celestial
Horizon (rational
horizon) is a great circle
on the celestial sphere,
every point on which is
90 degree away from
his zenith / nadir
Horizon System Coordinates
Nadir

27. Vertical Circles – They are great circles on the celestial sphere
passing through the observer’s Zenith and Nadir
Principal Vertical Circle – Principal Vertical circle is a great circle
passing through Observer’s Zenith and Nadir and through the
North and South Celestial Pole
Prime Vertical Circle – Prime Vertical circle is a great circle passing
through Observer’s Zenith and Nadir and through the East & West
points of his Celestial Horizon
Horizon System Coordinates

28. Celestial
Horizon
Coordinates

29. Altitude – Altitude of a celestial body is the arc of the Vertical
circle through that body contained between the celestial horizon
and the center of the celestial body
Zenith Distance – Zenith Distance of a celestial body is the arc of
the vertical circle through the body contained between the
observer’s Zenith and the centre of the celestial body
Since every point on the celestial horizon is 90 degree from the
observer’s zenith, the Zenith Distance = 90 – Altitude
Azimuth – The Azimuth of a celestial body is the arc of the
observer’s celestial horizon or the angle at his Zenith contained
between the Principal Vertical Circle and the vertical circle
through that celestial body
Horizon System Coordinates

30. Celestial
Horizon
Coordinates

31. Altitude and Azimuth

32. Comparison of Systems
Earth Coordinates Celestial Equinoctial System
Coordinates
Horizon System
Coordinates
Equator Celestial equator Celestial Horizon
Poles Celestial poles Zenith/nadir
Meridians Hour Angles Celestial meridians Vertical circles
Prime meridian Greenwich Hour Angle (GHA) Principal / Prime vertical
circle
Parallel of Latitude Parallel of declination Circle of Equal altitude
Latitude Declination Altitude
Co-altitude Polar distance Zenith distance
Longitude GHA = LHA +/- Long Azimuth/ Amplitude

33. PZX Spherical Triangle
(9 Point diagram)

34. Combination of Equinoctial & Horizon System –
PZX Spherical Triangle
LATITUDE
Declination
Co LAT
ZD
Prime
Vertical
Cel Mer of C.Body
Principal Vertical Circle /
Celestial Meridian of
Observer
Equinoctial
Altitude
Celestial
Horizon
<P

35. 9 Point diagram PZX Spherical Triangle NHS
Convenient to draw Circle using a radius
of 9 Units to represent 90 deg from Z
and Rational Horizon
ZQ – Latitude (North Lat)
Q is marked South or North of Zenith, as
per Obs Lat
NP – Altitude of Elevated Pole (NCP)
Equal to ZQ, the Lat of Obs
PZ = 90 – Lat (Co-Lat)
PX = 90 – Dec (Polar Dist)
ZX = 90 – True Altitude (Zenith Dist)
Major Angle P = LHA (Measured
Westward from Obs Cele Meridian)
<P

36. This Picture shows for an Observer in
South Lat & the Body’s Dec is North.
Pl note that LHA, which is Westward
measurement, is measured counter
clock-wise from the Observer’s Celestial
Meridian, as the measurement is being
made around the South Pole
9 Point diagram PZX Spherical Triangle SHS

37. Thank you