LESSON 15: Celestial Coordinate Systems

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LESSON 15Celestial 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.

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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).

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1. Terrestrial Coordinate System

• A quick review

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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.

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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.

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Declination
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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

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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

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Hour Angles
GHA GHA(Aries) SHA
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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 observers position.
• This system is necessary because stars are
  sighted with respect to the observers position.

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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)

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Horizon Coordinate System
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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.

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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.

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The Celestial Triangle
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The Celestial Triangle

• Azimuth Angle (Z)
• Meridian angle (t)

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Coordinate System Comparison