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

Dubhe

Schedar

Cassiopeia

Big dipper/Ursa major

Polaris

Finding Polaris from the big dipper: Example computer!!

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 seenHorizon = plane (0o) where the sky meets the earth

Azimuth = the cardinal directions or the circle around you (range = 0o to 360o)

North = 0 degreesEast = 90 degreesSouth = 180 degreesWest = 270 degrees

Point of view of the observer leads to problems:

1. Coordinates change when you change location2. Coordinates of stars change as they move across the sky3. 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 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, moon, and planets through the sky over the course ofthe year

Meridian: the imaginary line that extends from the NCP through the zenith to the SCP

Declination – latitude of stars, positivegoing 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

Horizon (est)

Min. star height

Polar distance =(90o – Declination)

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…a sidereal hour maps declination perfectly onto the latitude of earth btw

ANGLES

OBJECTS WITH LARGE ANGULAR SIZES(ROUGHLY TO SCALE)

Andromeda Galaxy (M31)180’ x 63’.

M54, extragalatic globular star cluster, 12’

M4, globular star cluster, 36’

Orion Nebula (M42), 85’ x 60’.

Pleiades, open star cluster, 180’.

Moon, 30’.

Sun, 30’.

MORE EXAMPLES

Hubble Deep Field, ≈ 1.5’.

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°.

Io, Jovian satellite,

1”.

Crab Nebula Supernova

remnant, 6’x4’.

Ring nebula,

planetarynebula,

1.4’ x 1’.

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

θ

Rising/setting angle is (90o – Latitude) dueeast/west – along celestial equator

Angles are smaller the further N/S one goes

Circumpolar stars – never set

Relation between Azimuth, Latitude and Declination ofrising and setting stars

)cos(

)sin()cos(

L

dRz

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.

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.

Altair

Vega

Deneb

SummerTriangle

Cygnus/NorthernCross

Summer triangle, northern cross (Cygnus)…are part of Lyra and Aquila too

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?