BELLWORK 9/2
• Describe what you learned in your lab yesterday in
15 words or less.
BASICS OF CELESTIAL NAVIGATION - STARS
• Coordinate systems
• Earth based – latitude and longitude
• Observer based – azimuth and altitude
• Celestial – declination and right ascension
• Motions of the stars in the sky and night sky observations
• 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
• Stars at different distances
• What you see in the sky depends on
• Date of year
• Time
•
Latitude
• Longitude
• Which is how we can use the stars to navigate!!
WHEN YOU LOOK AT THE SKY
• Stars: celestial object that is self-illuminated due to fusion, twinkle
• Constellation: formal name for a grouping of stars (88 total)
• Example: Ursa Major
• Asterism: common name for a grouping of stars
• Example: Big Dipper
• Planets: object that orbits a star and reflects light; don’t usually twinkle
• Seeing: the stability of the sky
• Bad = lots of twinkle
• Observation: to look at something and take detailed information about it
Finding Polaris from the big dipper: Example computer!!
Schedar
Cassiopeia
Polaris
Dubhe
Big dipper/Ursa major
CELESTIAL SPHERE
• The celestial sphere is an imaginary
sphere that surrounds the earth
and is used to discuss star locations
• The celestial sphere appears to
rotate around the earth, thus most
stars rise and fall daily.
Altitude-Azimuth coordinate system (Horizon System)
Based on what an observer sees in the sky, the horizon, and the directions (NSEW)
Altitude = angle above the horizon to an object (star, sun, etc)
(range = -90o to 90o)
Zenith = point directly above the observer (+90o)
Nadir = point directly below the observer (-90o) – can’t be seen
Horizon = plane (0o) where the sky meets the earth
Azimuth = the cardinal directions
or the circle around you
(range = 0o to 360o)
North = 0 degrees
East = 90 degrees
South = 180 degrees
West = 270 degrees
Point of view of the observer leads to problems:
1. Coordinates change when you change location
2. Coordinates of stars change as they move across the sky
3. Requires time and location for other people to determine the stars you were
looking at
BELLWORK: WHY DO STARS APPEAR TO RISE IN THE EAST
AND SET IN THE WEST?
WHAT DOES THIS MEAN FOR WHEN YOU READ A STAR MAP?
Equatorial System-
based on latitude and longitude of earth extended to the sky
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, moon, and planets
through the sky over the course of
the year
Meridian: the imaginary line that
extends from the NCP through the
zenith to the SCP
Declination – latitude of stars, positive
going north (north celestial pole = + 90o), negative going
south (south celestial pole = - 90o)
• This means you can determine latitude on earth by measuring the angle to Polaris
Right ascension (RA) – longitude of stars
RA – typically expressed as a time going
east – 0 to 24 hours, 0h is the vernal
equinox
Polar distance =
(90o – Declination)
Min. star height
Horizon (est)
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…a sidereal hour maps
declination perfectly onto the latitude of
earth btw
ANGLES
OBJECTS WITH LARGE ANGULAR SIZES
(ROUGHLY TO SCALE)
Sun, 30’.
Andromeda Galaxy (M31)
180’ x 63’.
Orion Nebula (M42), 85’ x 60’.
Moon, 30’.
M54, extragalatic
globular star cluster, 12’
Pleiades, open star cluster, 180’.
M4, globular star cluster, 36’
Ring nebula,
planetary
nebula,
1.4’ x 1’.
MORE EXAMPLES
Crab Nebula
Supernova
remnant,
6’x4’.
Io, Jovian
satellite, 1”.
Polaris A’s apparent size = 0.002”.
Polaris A to Polaris Ab is 0.2”;
Polaris A to Polaris B is 20”;
Polaris A to Dubhe ≈ 30°.
Hubble Deep Field, ≈ 1.5’.
HOW STARS MOVE THROUGH THE SKY
• Stars seem to move across the sky at 15o per hour (4 minutes per
degree)
• It’s actually a bit faster because the earth is moving too, but no
worries
• Some stars are “circumpolar” – never set
Rising/setting angle is (90o – Latitude) due
east/west – along celestial equator
Angles are smaller the further N/S one goes
θ
Circumpolar stars – never set
Relation between Azimuth, Latitude and Declination of
rising and setting stars
sin( d )
cos( Rz ) 
cos( L)
Where Rz = rising azimuth
d = declination
L = Latitude
So – at equator, L=0, 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 you’re willing to do the
math, and find the azimuth of a rising star, knowing
the star’s declination.
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.
Summer triangle, northern cross (Cygnus)…are part of Lyra and Aquila too
Deneb
Vega
Summer
Triangle
Cygnus/
Northern
Cross
Altair
Vega (Decl = 39oN) and Deneb (Decl = 45o), Altair is 9o
BIG DIPPER AS STAR GUIDE
BELLWORK:
• You’re lost in the woods without a watch or phone.
How can you figure out how much daylight you
have left to build a shelter and fire?