Basics of Celestial Navigation stars

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Basics of Celestial Navigation - stars

• Coordinate systems
• Observer based azimuth and altitude
• Earth based latitude and longitude
• Celestial declination and right ascension (or
  sidereal hour angle)
• Relationship among three star pillars
• Motions of the stars in the sky
• Major star groupings

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Comments on coordinate systems

• All three are basically ways of describing
  locations on a sphere inherently two
  dimensional
• Requires two parameters (e.g. latitude and
  longitude)
• Reality three dimensionality
• Height of observer
• Oblateness of earth, mountains
• Stars at different distances (parallax)
• What you see in the sky depends on
• Date of year
• Time
• Latitude
• Longitude
• Which is how we can use the stars to navigate!!

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Altitude-Azimuth coordinate system
Based on what an observer sees in the sky.
Zenith point directly above the observer
(90o) Nadir point directly below the observer
(-90o) cant be seen Horizon plane
(0o) Altitude angle above the horizon to an
object (star, sun, etc) (range 0o to 90o)
Azimuth angle from true north (clockwise) to
the perpendicular arc from star to
horizon (range 0o to 360o)
Note lines of azimuth converge at zenith
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The arc in the sky from azimuth of 0o to 180o is
called the local meridian
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Point of view of the observer
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Latitude
Latitude angle from the equator (0o) north
(positive) or south (negative) to a point on the
earth (range 90o north pole to 90o
south pole). 1 minute of latitude is always 1
nautical mile (1.151 statute miles)
Note Its more common to express Latitude as
26oS or 42oN
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Longitude
Longitude angle from the prime meridian (0o)
parallel to the equator to a point on earth
(range -180o to 0 to 180o) East of PM
positive, West of PM is negative. Distance
between lines of longitude depend on latitude!!
Note sometimes positive longitude is expressed
as West, but this is inconsistent with math
conventions. Avoid confusion 40oW or 40o E
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Comments on longitude
Location of prime meridian is arbitrary
Greenwich observatory in UK 1 minute of
longitude 1 nautical mile cosine(latitude) Li
nes of longitude converge at the north and south
poles To find longitude typically requires a
clock, although there is a technique, called the
lunar method that relies on the fact that the
moon moves ½ of a degree per hour.
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Celestial coordinates - some definitions
North celestial pole point in sky directly
above north pole on earth (i.e. zenith of north
pole) South celestial pole zenith of south pole
on earth
Celestial equator circle surrounding equator on
earth
Ecliptic path followed by the sun through
the sky over the course of the year against a
fixed background of stars
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Declination angle from celestial equator (0o),
positive going north (north celestial pole
90o), negative going south (south celestial
pole - 90o)
Right ascension (RA) angle from celestial
prime meridian equivalent of celestial
longitude
RA typically expressed as a time going east 0
to 24 hours is 360o Prime meridian
point where sun is located at the vernal equinox
(spring) (called vernal equinoctial colure)
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Declination and star pillars
Declination maps onto latitude At some point
a star of a given declination will pass over the
zenith at a point on the earth at its
corresponding latitude.
This happens once every 24 hours
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Alternative to Right Ascension
Sidereal Hour Angle (SHA) - same as RA, except
measured in degrees, going from 0 to 360o
conversion is straightforward
Note RA is/was useful for navigation with clocks
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As with longitude, the actual angular width
between lines of SHA shrinks with higher
declination as Cosine(declination)
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John Huths alternative to SHA, RA
Use same convention as for terrestrial longitude,
with positive and negative angles. Prime
meridian corresponds to 0o for SHA
Same as SHA for 0o to 180o and (360o SHA) for
values of SHA from 180o to 360o
Why? Easy to remember, and allows you to
associate star coordinates with points on earth.
Makes it easier to visualize and memorize. Also
declination and latitude go together.
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Example Aldeberan (Taurus) 69oE Rigel (Orion)
78oE Betelgeuse (Orion) 89oE
69oE
78oE
89oE
New Delhi
Calcutta
Dwarka
Method lie on your back look at the stars and
visualize the locations on the globe (otherwise,
its a mirror image)
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Example Aldeberan (Taurus) 69oE - Dwarka Rigel
(Orion) 78oE New Delhi Betelgeuse (Orion)
89oE - Calcutta
69oE
78oE
89oE
New Delhi
Aldeberan
Betelgeuse
Calcutta
Dwarka
Orion
Rigel
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Can associate star coordinates with latitude
and Longitude of locations on earth
Note dont expect alignment with any star this
is just a way to memorize coordinates
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Important Point

• Mariners had to/have to rely on tables for star
  coordinates
• You can memorize major navigational star
  coordinates and eliminate tables
• Helps identify stars, too
• On a desert island, with only a watch, can
  identify latitude and longitude along with your
  memory!
• Tell that to the creators of Lost!!

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Mapping of three coordinate systems onto each
other
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How stars move through the sky

• Stars move in arcs that parallel the celestial
  equator angle perpendicular to celestial
  equator is the declination
• Star move across the sky at 15o per hour (4
  minutes per degree)
• Each day star positions move 1o west
• Stars on the celestial equator rise and set with
  angles of (90o Latitude)
• Some stars are circumpolar never set

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Star paths in the sky form arcs in the sky
At the equator, stars rise and set at right
angles to the Horizon.
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At Boston (41oN), stars due east will rise and
set at an angle (90o Latitude) 49o with
respect to the horizon (i.e. on celestial
equator) Stars always move in arcs parallel to
the celestial equator
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Paths of stars as seen from the N. Arctic
Circle 66o N few stars rise and set most
make complete circles
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Rising/setting angle is (90o Latitude)
due east/west along celestial equator Angles
are smaller the further N/S one goes
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Relation between Azimuth, Latitude and
Declination of rising and setting stars
Where Rz rising azimuth d declination L
Latitude
So at equator, L0, cos(L) 1, rising azimuth
is the declination of the star exploited by
Polynesians in star compasses (near the equator
cos(L) close to 1 Can use this to find latitude,
if youre willing to do the math, and find the
azimuth of a rising star, knowing the stars
declination.
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Notes on azimuth when
Then star is either circumpolar or below the
horizon Example at latitude 45oN, cos(L)0.707,
the star Capella (declination 46o) just
becomes circumpolar Then cos(Rz) is just slightly
greater than 1.

Largest rising/setting angles for Rz 90/270
degrees (along celestial equator)
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Circumpolar stars never set
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Knowing a stars declination, can get
latitude from horizon grazing stars.
Latitude (polar distance minimum height)
Polar distance (90o Declination)
Min. star height
Horizon (est)
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Some star groupings

• If you can locate stars and know the declination
  you can find your latitude.
• With a watch, and SHA (or stellar longitude),
  you can find your longitude (must know date).
• Clustering into constellations and their stories
  help locate stars by name.

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Arc to Arcturus, spike to Spica
After sunset Spring/summer
Big dipper
Arcturus
Arcturus (Decl 19oN) and Spica (Decl
11oS) alone in this part of the sky
(longitude 146oW and 159oW respectively)
Spica
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Summer triangle and Antares
Deneb
Vega
Altair
Antares is only visible for a short period
(hours) in mid summer. Declination 26oS Good
candidate for a horizon grazing star in the summer
Antares
Scorpio
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Summer triangle, northern cross (Cygnus)
Deneb
Vega
Summer Triangle
Cygnus/ Northern Cross
Altair
Vega (Decl 39oN) and Deneb (Decl 45o)
straddle zenith in Boston (Latitude 42o),
Altair is 9o N
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Finding Polaris from the big dipper
Schedar
Schedar (Decl 56o) and Dubhe (Decl 62o) are
circumpolar for Boston
Cassiopeia
Polaris
Also can be used as the basis for a
clock (project)
Dubhe
Big dipper/Ursa major
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Constellation story about Orion
Pleiades
Mintaka right star in belt is on the equator
Winter constellations Zeus daughters, Pleiades
(24N, 57E) are guarded by Taurus (Aldeberan
orange eye 17N, 69E), from Orion, the hunter
(Betelgeuse 7N, 89E, Rigel 8S,78E), followed by
hunting dogs Canis Minor (Procyon 5N, 115E)
and Canis Major (Sirius 17S and 101E)
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Time lapse image of Orion
Betelgeuse
Arcturus
Sirius
Rigel
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Late winter/early spring constellations
Pollux/Procyon line (115E) forms good north-south
arc Pollux (28N, 115E) is readily recognized with
twin Castor
Gemini
Leo
Pollux
Regulus
Procyon
Regulus (12N, 152E) marks start of sparsely
populated region of stars in N. hemisphere
closest is Arcturus (142W)