Lesson 16: Coordinate Systems

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Lesson 16 Coordinate Systems

• Learning Objectives
• Know the definitions associated with the
  celestial coordinate system.
• Apply correct procedures to describe the location
  of a celestial body in reference to the celestial
  coordinate system.
• Know the definitions associated with the horizon
  coordinate system.
• Comprehend 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 horizon
  coordinate system.
• Applicable reading Hobbs pp. 281-305.

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Humor
A Charlotte, North Carolina man, having purchased
a case of rare, very expensive cigars, insured
them against ... get this ....fire. Within a
month, having smoked his entire stockpile of
fabulous cigars, and having yet to make a
single premium payment on the policy, the man
filed claim against the insurance company. In his
claim, the man stated that he had lost the cigars
in "a series of small fires." The insurance
company refused to pay, citing the obvious reason
that the man had consumed the cigars in a normal
fashion. The man sued...and won.
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Humor
In delivering his ruling, the judge stated that
since the man held a policy from the company in
which it had warranted that the cigars were
insurable, and also guaranteed that it would
insure the cigars against fire, without defining
what it considered to be "unacceptable fire," it
was obligated to compensate the insured for his
loss. Rather than endure a lengthy and costly
appeal process, the insurance company accepted
the judge's ruling and paid the man 15,000 for
the rare cigars he lost in "the fires."
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Humor
This is the funny part After the man
cashed his check, however, the insurance company
had him arrested on 24 counts of arson. With his
own insurance claim and testimony from the
previous case being used as evidence against him,
the man was convicted of intentionally burning
the rare cigars and sentenced to 24 consecutive
one year terms.
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The Celestial Coordinate System

• The celestial coordinate system Just as any
  position on the earth can be located by
  specifying its terrestrial coordinates, any
  heavenly body can be located by specifying its
  celestial coordinates.
• Celestial equator (also known as the
  equinoctial) The basis for the celestial
  coordinate system. It is formed by projecting
  the terrestrial equator outward onto the
  celestial sphere .
• Celestial meridians Terrestrial meridians can be
  projected outward to the celestial sphere to form
  celestial meridians. Because of the apparent
  rotation of the celestial sphere with respect to
  the earth, these projected celestial meridians
  appear to sweep continuously across the inner
  surface of the sphere, making them inconvenient
  to use as a basis for lateral measurements of
  position on the celestial sphere. Hence, a
  separate set of circles are inscribed on the
  surface of the celestial sphere perpendicular to
  the celestial equator for use in describing the
  position of one point on the sphere relative to
  another. These great circles are called hour
  circles.

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The Celestial Coordinate System

• Hour circle A great circle on the celestial
  sphere perpendicular to the celestial equator and
  passing through both celestial poles. Every point
  on the celestial sphere has an hour circle
  passing through it.
• Hour Circle of Aries The hour circle passing
  through the First Point of Aries ( ) which
  forms the reference for the lateral coordinate of
  a point on the celestial sphere. It is
  analogous to the meridian passing through the
  observatory at Greenwich, which serves as the
  reference for the lateral coordinate of a point
  on the terrestrial sphere.

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The Celestial Coordinate System

• Declination (Dec) The celestial equivalent of
  terrestrial latitude. It is the angular distance
  of a point on the celestial sphere north or south
  of the celestial equator measured through 90
  degrees. Declination is labeled with the prefix N
  (north) or S (south) to indicate the direction of
  measurement prefixes are used to differentiate
  declination from latitude. The figure below
  depicts the declination of a star located 30
  degrees off the celestial equator.

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The Celestial Coordinate System

• Hour angle The celestial equivalent of
  longitude. It is the angular distance measured
  laterally along the celestial equator in a
  westerly direction through 360 degrees.
• Sidereal hour angle (SHA) Hour angles measured
  in a westerly direction from the hour circle of
  Aries to the hour circle of a particular body.
• For the purposes of celestial navigation, it is
  not only desirable to locate a body on the
  celestial sphere relative to Aries but also to
  locate a body relative to a given position on
  earth at a given time. To do this, two
  terrestrial meridians are projected onto the
  surface of the celestial sphere for use as
  references for hour angle measurements - The
  Greenwich meridian and the observers meridian.
  The celestial meridians thus projected are termed
  the Greenwich celestial meridian and the local
  celestial meridian.

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The Celestial Coordinate System

• Greenwich hour angles (GHA) Hour angles measured
  relative to the Greenwich meridian.
• Local hour angles (LHA) Hour angles measured
  with respect to the local celestial meridian.
• Both Greenwich hour angles and local hour angles
  are measured westward from a projected
  terrestrial meridian to a celestial hour circle
  moving ever westerly with the rotating celestial
  sphere. Consequently, both GHA and LHA values
  are constantly growing larger with time,
  increasing from 0 to 360 degrees once each 24
  hours. They relate the rotating celestial sphere
  to the meridians of the earth.
• Sidereal hour angles are measured between two
  hour circles on the celestial sphere although
  the value of the SHA of the star changes with
  time as the stars move through space relative to
  one another, the rate of change is extremely
  slow. Hence for purposes of celestial
  navigation, sidereal hour angles are considered
  to remain constant.

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The Celestial Coordinate System

• The hour circle of Aries and the projected
  Greenwich and observers meridians are shown in
  the following figure. The resulting sidereal,
  Greenwich, and local hour angles (SHA, GHA, AND
  LHA) of the star at a given time are indicated.
• It can be seen from the figure below that the GHA
  of the star (GHA ) is equal to the sum of the
  GHA of Aries (GHA ) plus the SHA of the star
  (SHA )
• GHA GHA SHA

Aries
star
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The Celestial Coordinate System
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The Celestial Coordinate System

• For some applications in celestial navigation, it
  is advantageous to use an alternative angle to
  LHA to express the angular distance from the
  observers meridian to the hour circle of a body.
  This is called the meridian angle (t). The
  meridian angle is defined as the angular distance
  between 0 degrees and 180 degrees, measured at
  the pole nearest the observer, from the
  observers meridian either easterly or westerly
  to the hour circle of the body. The meridian
  angle is always labeled with the suffix E (east)
  or W (west) to indicate the direction of
  measurement. The significance of the meridian
  angle will be discussed later when solving the
  celestial triangle.

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The Horizon Coordinate System

• The Horizon coordinate system In order to
  obtain a celestial line of position by
  observation of a celestial body, a third set of
  coordinates, called the horizon system, is
  required. This coordinate system differs from
  the celestial coordinate system in that it is
  based on the position of the observer, rather
  than on the projected terrestrial equator and
  poles.
• Celestial horizon A plane passing through the
  center of the earth perpendicular to a line
  passing through the observers position and the
  earths center. This reference plane corresponds
  with the plane of the equator in the terrestrial
  and celestial systems .

ZENITH
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The Horizon Coordinate System

• Zenith The line passing through the observer
  and the center of the earth perpendicular to the
  celestial horizon extended outward from the
  observer to the celestial sphere defines a point
  on the sphere directly over the observer called
  the observers zenith.
• The observer's zenith is always exactly 90
  degrees of arc above the celestial horizon.
• Nadir The extension of the line through the
  center of the earth and the observer to the
  opposite side of the celestial sphere defines a
  second point directly below the observer is
  called the observers nadir .
• The observers zenith and nadir correspond to the
  terrestrial and celestial poles, while the
  zenith-nadir line connecting the observers
  zenith and nadir corresponds to the axis of the
  celestial and terrestrial spheres.

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The Horizon Coordinate System

• Vertical circle A great circle on the celestial
  sphere passing through the observers zenith and
  nadir, perpendicular to the plane of the
  celestial horizon. It is the equivalent of a
  meridian in the terrestrial system and an hour
  circle in the celestial system.
• Prime vertical The vertical circle passing
  through the east and west points of the
  observers horizon.
• Principal vertical The vertical circle passing
  through the north and south points the
  observers horizon. It is always coincident with
  the projected terrestrial meridian (i.e. the
  local celestial meridian) passing through the
  observers position.
• Altitude The angular distance of a point on the
  celestial sphere above a designated reference
  horizon, measured along the vertical circle
  passing through the point. It is the horizon
  systems equivalent of latitude.

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The Horizon Coordinate System

• The reference horizon for the horizon coordinate
  system is the celestial horizon of the observer,
  defined previously as the plane passing through
  the center of the earth perpendicular to the
  zenith-nadir line of the observer.
• Observed Altitude (abbreviated HO) Altitude
  measured relative to the celestial horizon. It
  is the angle formed at the center of the earth
  between the line of sight of the body and the
  plane of the observers celestial horizon.
• Visible or Sea Horizon The other horizon used as
  a reference for altitude measurements. It is the
  line along which the sea and sky appear to meet.
  In practice, sextant altitudes must be converted
  to observed altitudes (Ho) to obtain an accurate
  celestial LOP.

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The Horizon Coordinate System

• True Azimuth (abbreviated Zn) The horizontal
  angle measured along the celestial horizon in a
  clockwise direction from 0000T to 3600T from the
  principle vertical circle to the vertical circle
  passing through a given point or body on the
  celestial sphere. True azimuth can be thought
  of as the true bearing of a celestial body from
  the observers position. It is the equivalent of
  longitude in the horizon system
• The figure below illustrates the horizon
  coordinate system.

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The Horizon Coordinate System
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Homework

• Chapter 15 Section 1- 2,5,6,7,9,11
• Section 2- 1,2,5,6,7,8,9,10
• Handout of Tides/Current