Transcript Celestial Coordinate Systems

LESSON 15:
Celestial Coordinate
Systems
• Learning Objectives
– Know the ultimate goal of celestial
navigation.
– Know the definitions of terms and
components associated with the
terrestrial, celestial, and horizon
coordinate systems.
– Know the relationship between the
terrestrial, celestial, and horizon
coordinate systems.
– Apply correct procedures to
describe the location of a celestial
body in reference to the celestial
and horizon coordinate systems.
The Goal of Celestial
Navigation
• The solution of spherical
triangles of sides based on
the observed positions of
celestial bodies, in order to
determine the position of a
vessel.
• 100 years ago, this involved
some complicated spherical
trigonometry.
• Today, it requires the use of
tables or a navigational
calculator (HP makes one).
1. Terrestrial
Coordinate System
• A quick review:
Basic Assumptions
• First, assume the earth
does not move, but instead
the celestial bodies rotate
about it in a predictable
manner.
• The celestial sphere:
celestial bodies are
assumed to be on the inner
surface of a vast, hollow
sphere of infinite radius,
which has the earth at its
center.
2. Celestial
Coordinate System
• The celestial coordinate
system is best understood
as a projection of the
terrestrial coordinate
system, outward into
space onto the celestial
sphere.
Declination
Celestial Coordinate
System
•
•
•
•
•
Celestial Equator (Equinoctial)
Celestial Meridians
Hour Circles
Hour Circle of Aries
Declination
– celestial equivalent of latitude
• Hour Angles
– celestial equivalent of longitude
Hour Angles
• Three different references are
used:
• Sidereal Hour Angle (SHA)
– Hour Circle of a celestial body, as
referenced from the hour circle of
Aries (measured westerly)
• Greenwich Hour Angle (GHA)
– Hour circle of a celestial body, as
measured relative to Greenwich
Celestial Meridian
• Local Hour Angle (LHA)
– Hour circle of a celestial body, as
measured relative to the local
celestial meridian
Hour Angles
GHA
= GHA(Aries) + SHA
3. Horizon
Coordinate System
• In the terrestrial and celestial
coordinate systems, the basic
references are the poles and
the equator.
• The horizon coordinate
system, however, is based on
the observer’s position.
• This system is necessary
because stars are sighted with
respect to the observer’s
position.
Horizon Coordinate
System
• Zenith and Nadir
– analogous to north and
south poles
• Vertical Circle
– analogous to meridian
(terrestrial system) or hour
circle (celestial system)
• Prime Vertical (east and
west)
• Principal Vertical (north
and south)
Horizon Coordinate
System
Horizon Coordinate
System
• Celestial Horizon
– analogous to the equator
• True Azimuth (Zn)
– analogous to longitude
• Altitude
– analogous to latitude
• Sextant Altitude (hs)
– Measured altitudes of celestial bodies
• Visible or Sea Horizon
– Used as a reference for celestial body
altitude measurements
• Observed Altitude (Ho)
– Conversion of Sextant Altitude, since
sea horizon is not at celestial horizon.
The Celestial
Triangle
• These three coordinate
systems (TERRESTRIAL,
CELESTIAL, AND HORIZON)
are then combined to form
the celestial triangle, which
is used to determine our
position.
• One leg from each triangle
forms the new triangle on
the celestial sphere.
The Celestial
Triangle
The Celestial
Triangle
•Azimuth Angle (Z)
•Meridian angle (t)
Coordinate System
Comparison