Transcript The Navigation Triangle

LESSON 16:
The Navigation Triangle
• Learning Objectives
– Comprehend the interrelationships of
the terrestrial, celestial, and horizon
coordinate systems in defining the
navigation triangle.
– Gain a working knowledge of the
celestial and navigation triangles.
The Celestial Triangle
• The celestial, horizon, and terrestrial
coordinate systems are combined on
the celestial sphere to form the
astronomical or celestial triangle.
The Celestial Triangle
The Celestial Triangle
• The three vertices of the triangle:
– observer’s zenith
– position of the celestial body on the
celestial sphere
– celestial pole nearest the observer
(referred to as the elevated pole)
The Celestial Triangle
• Two of the angles are also of
concern:
– meridian angle (t)
– aximuth angle (Z)
• Meridian angle is simply a more
convenient way of expressing LHA
– if LHA<180o, t=LHA (west)
– if LHA>180o, t=360o-LHA (east)
The Celestial Triangle
• Likewise, azimuth angle is simply a
more convenient way of expressing
true azimuth (Zn)
• The third angle is known as the
parallactic angle and is not of use in
our discussion.
• Let’s take another look at the
triangle….
The Navigation Triangle
• When the celestial triangle is projected
downward from the celestial sphere
onto the earth’s surface, it becomes
the navigation triangle.
• The solution of this navigation triangle
is the purpose of celestial navigation.
• Each of the three coordinate systems
forms one side of the triangle.
The Navigation Triangle
The Navigation Triangle
• Now the vertices of the triangle are
– our assumed position (AP)
• Corresponds to the observer’s zenith on the
celestial triangle
– the geographic position (GP) of the
celestial body
• Corresponds to the star’s celestial position
– the earth’s pole (Pn or Ps)
• Corresponds to the elevated pole
The Geographic Position
(GP)
The Navigational Triangle
• The three sides of the triangle are used in
determining the observer’s position on the earth.
The length of each side is as follows:
– colatitude = 90 – latitude
• Connects observer’s position to pole’s
position
– polar distance = 90 +/- declination
• Connects pole to the star’s geographic
position
– coaltitude = 90 – altitude
• Connects star’s geographic position to
observer’s position
The Navigation Triangle
• Note that the polar distance may be
greater than 90 degrees (if the GP
and the elevated pole are on
opposite sides of the equator) but
coaltitude and colatitude are always
less than 90 degrees.
The Navigation Triangle
• The angles of the celestial and
navigational triangles are the same:
– meridian angle (t)
• measured 0o to 180o, east or west
• suffix E or W is used to indicate direction
– Azimuth angle (Z)
• measured 0o to 180o
• prefix N or S is used to indicate elevated pole
• suffix E or W used to indicate on which side of
the observer’s meridian the GP lies.
The Navigation Triangle
• Consider this scenario:
• Given:
• LHA = 040o
• Z = 110 oT
• Find:
• t
• Zn
Solution
• Since the LHA<180o, LHA and t are
equivalent, thus
t = LHA = 40oW
• To determine Zn, it is usually helpful
to draw a diagram, as shown on the
next slide….
• Zn is the angle
between the north
pole and the GP, as
seen by the observer.
• Since Ps is the
elevated pole and the
GP is west of the
observer, add 180
degrees to Z:
Zn = S 290o W
LHA, t, Zn, and Z
• Only four possible combinations
exist when you combine
– GP either east or west of the observer
– elevated pole either north or south pole
• It is simple enough to come up with
an equation for converting between
Zn and Z for each case, or you can
draw a picture as we just did.
– Just draw the picture.