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 - PowerPoint PPT PresentationTRANSCRIPT
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
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!!
Altitude-Azimuth coordinate systemBased on what an observer sees in the sky. Zenith = point directly above the observer (90o)Nadir = point directly below the observer (-90o) – can’t be seenHorizon = plane (0o)Altitude = angle above the horizon to an object (star, sun, etc)(range = 0o to 90o)
Azimuth = angle fromtrue north (clockwise)to the perpendicular arc from star to horizon(range = 0o to 360o)
Note: lines of azimuthconverge at zenith
The arc in the sky from azimuth of 0o to 180o
is called the local meridian
Point of view of the observer
LatitudeLatitude – angle from the equator (0o) north (positive) orsouth (negative) to a point on the earth – (range = 90o = northpole to – 90o = south pole). 1 minute of latitude is always = 1 nautical mile (1.151 statute miles)
Note: It’s more common to expressLatitude as 26oS or42oN
Longitude
Longitude = angle from the prime meridian (=0o) parallelto 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 longitudeis expressed as West, but this isinconsistent withmath conventions.Avoid confusion:40oW or 40o E
Comments on longitude
Location of prime meridian is arbitrary = Greenwichobservatory in UK
1 minute of longitude = 1 nautical mile * cosine(latitude)
Lines of longitude converge at the north and south poles
To find longitude typically requires a clock, although thereis a technique, called the lunar method that relies on the factthat the moon moves ½ of a degree per hour.
Celestial coordinates - some definitionsNorth celestial pole = point in sky directly above north poleon earth (i.e. zenith of north pole)South celestial pole = zenith of south pole on earth
Celestial equator – circlesurrounding equator on earth
Ecliptic – path followedby the sun through thesky over the course ofthe year against a “fixed” background ofstars
Declination – angle from celestial equator (=0o), positivegoing 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 expressedas a time going east – 0 to24 hours is 360o
“Prime meridian” – pointwhere sun is located at the vernal equinox (spring)(called vernal equinoctialcolure)
Declination and “star pillars”
Declination “maps” onto latitude – At some point a star of a given declination will pass over the zenithat a point on the earth at its corresponding latitude.
This happens once every24 hours
Alternative to Right Ascension
Sidereal Hour Angle (SHA) - same as RA, except measuredin degrees, going from 0 to 360o – conversion is straightforward
Note: RA is/was usefulfor navigation with clocks
As with longitude, the actual angular width between
lines of SHA shrinks with higher declination as
Cosine(declination)
John Huth’s alternative to SHA, RA
Use same convention as for terrestrial longitude, with positive and negative angles. Prime meridian correspondsto 0o for SHA
Same as SHA for 0o to 180o and (360o – SHA) for valuesof SHA from 180o to 360o
Why? Easy to remember, and allows you to associatestar coordinates with pointson earth. Makes it easier tovisualize and memorize. Also – declination and latitudego together.
New Delhi
CalcuttaDwarka
69oE 78oE 89oE
Example
Aldeberan (Taurus) = 69oERigel (Orion) = 78oEBetelgeuse (Orion) = 89oE
Aldeberan
Betelgeuse
Rigel
Sirius
Procyon Orion
Method – lie “on your back”look at the stars and visualizethe locations on the globe (otherwise, it’s a mirror image)
Dwarka
New Delhi
Calcutta
69oE78oE89oE
Aldeberan
Betelgeuse
Rigel
Orion
Example
Aldeberan (Taurus) = 69oE - DwarkaRigel (Orion) = 78oE – New DelhiBetelgeuse (Orion) = 89oE - Calcutta
Can associate star coordinates with latitude andLongitude of locations on earth
Note: don’t expect alignment with any star – this is justa way to memorize coordinates
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”!!
Mapping of three coordinate systems onto each other
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
Star paths in the sky form arcs in the sky
At the equator, stars rise and set atright angles to theHorizon.
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 arcsparallel to the celestialequator
Paths of stars as seenfrom the N. Arctic Circle66o N – few stars rise and set – most make completecircles
θ
Rising/setting angle is (90o – Latitude) dueeast/west – along celestial equator
Angles are smaller the further N/S one goes
Relation between Azimuth, Latitude and Declination ofrising and setting stars
)cos()sin()cos(
LdRz
Where Rz = rising azimuthd = declinationL = Latitude
So – at equator, L=0, cos(L) = 1, rising azimuth is thedeclination of the star – exploited by Polynesians instar compasses (near the equator cos(L) close to 1
Can use this to find latitude, if you’re willing to do the math, and find the azimuth of a rising star, knowingthe star’s declination.
Notes on azimuth – when )cos()sin( Ld Then star is either circumpolar or below the horizonExample – at latitude 45oN, cos(L)=0.707, the star Capella (declination = 46o) just becomes circumpolarThen cos(Rz) is just slightly greater than 1.
Largest rising/setting angles for Rz = 90/270 degrees(along celestial equator)
Circumpolar stars – never set
Knowing a star’s declination, can get latitudefrom horizon grazing stars.
Horizon (est)
Min. star height
Polar distance =(90o – Declination)
Latitude = (polar distance – minimum height)
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.
Big dipper
Arcturus
Spica
“Arc to Arcturus, spike to Spica”
After sunset: Spring/summer
Arcturus (Decl = 19oN)and Spica (Decl = 11oS)“alone” in this part of the sky (“longitude” = 146oW and 159oW respectively)
Deneb Vega
Altair
Antares
Scorpio
Summer triangle and Antares
Antares is only visible for a shortperiod (hours) in mid summer.Declination = 26oS
Good candidate for ahorizon grazing star inthe summer
Altair
Vega
Deneb
SummerTriangle
Cygnus/NorthernCross
Summer triangle, northern cross (Cygnus)
Vega (Decl = 39oN) and Deneb (Decl = 45o) straddle zenithin Boston (Latitude = 42o), Altair is 9o N
Dubhe
Schedar
Cassiopeia
Big dipper/Ursa major
Polaris
Finding Polaris from the big dipper
Schedar (Decl = 56o) and Dubhe (Decl = 62o)are circumpolar for Boston
Also can be used asthe basis for a “clock”(project)
Aldeberan
Betelgeuse
Rigel
Sirius
Procyon Orion
Constellation story about Orion
Pleiades
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), followedby hunting dogs Canis Minor (Procyon = 5N, 115E) andCanis Major (Sirius = 17S and 101E)
Mintaka – right starin belt is on the equator
Time lapse image of Orion
Sirius
Betelgeuse
Rigel
Arcturus
Regulus
Leo Pollux
Gemini
Procyon
Late winter/early spring constellations
Pollux/Procyon line (115E) forms good north-south arcPollux (28N, 115E) is readily recognized with twin Castor
Regulus (12N, 152E) marks start of sparsely populatedregion of stars in N. hemisphere –closest is Arcturus (142W)