General Astronomy

Astronomical Observations

Angles and Angular Measurement

Remember there are:360° in a circle 60' in a degree 60" in a minuteOr 2Π radians in a circle

60 min to an Hour60 sec to a minute

To try to keep confusion to a minimum, sometimes seconds refering to angular measurement is designated as arcsec (arc – seconds)

Also,

Getting a grip on AnglesSize of person is 5' 6"

Angle: 90º Conversational DistanceDistance: 3' 6"

Angle: 10º Across the RoomDistance: 31' 6"

Angle: 1º A football fieldDistance: 100 yds

Angle: 1'Distance: 3.5 miles

Angle: 1"Distance: 215 miles

Angular Separation

These two stars have an angular separation of 11' 49"

Being able to see both stars is a test of "perfect" vision

Rules of 'Thumb'It is difficult to measure the distances to the stars – as we will see

later on in the course, but it is relatively easy to measure the angles between objects and between the horizon and an object.

Even when 'just stargazing' it is common to hear directions such as

"find the first two stars in ---- then go 30° to find ---"

Some rough estimates are:

Using an outstreached arm,Thumb 1°Two knuckles 2°Fist 10°Extended hand 25°

Rules of 'Thumb'

Angular Size

Instruments for Angles

British Navy SextantCirca 1840

16th century Quadrant used in navigation

True versus Apparent SizeThe Sun has an angular size of about 30' of arc.

And it appears to be about the size of a quarter as we view it. We can relate the angular size of an object to its true size if we know the distance to the object

Angular Size =

True SizeDistance

Radians

=180 True Size

Π Distance

Degrees

ExamplesLunar Angular Diameter:

Angular Diameter = 180 3475 Km

Π 385000 Km= 0.517° =31.2 arcminutes

Solar Angular Diameter:

149.6x106 KmAngular Diameter = 180 1.39x106 Km

Π=0.532° =31.9 arcminutes

Even though the Sun is much larger than the moon the distances are such that they subtend nearly the same angle.

Review: Measuring Distance• Miles/Kilometers

Distances on the surface of a object

• Astronomical Unit (AU)Distances within the Solar System1 AU = 93,000,000 Miles

• Lightyear (Ly)Distances to nearby stars and other objects1 Ly = 65,000 AU = 6,000,000,000,000 Miles

• Parsec (pc)Distances in the ‘local neighborhood’1 pc = 3.26 Ly

• Megaparsec (Mpc)Distances to distant galaxies1 Mpc = 1,000,000 pc

Review: Brightness• Apparent Magnitude

How bright does it appear?

• Absolute MagnitudeHow bright would it appear from 10 pc?

• Sometimes either magnitude may be further identified as visual (MV) or photographic (MB)

Finding our wayBefore we can find our way amongst the stars, it

would be good to find our way here on Earth.

Where are you? (AQHNA This may not help much)

We need to precisely define our position on the surface of the earth (airplanes and submarines also need position with respect to the surface)

Москва

ירושליםالقد北京س

Location, Location, Location

Let's take a look at:1. The shape of the Earth2. Zenith & Nadir3. Meridian4. Equator5. Latitude6. Longitude

http://fxb.worth1000.com/entries/396292/great-a-tuin

The Shape of the Earth

This is close, but it's really more 'pear shaped'

Flat?

A disk? Where's the elephants and the great turtle?

A sphere?

Defining the Earth

• The North and South Poles• The Parallels of Latitude

The Equator

• The Meridians of LongitudeThe Prime MeridianThe International Date Line

• Your position:1. Zenith … The point above your head2. Nadir … The point beneath your feet3. Meridian … The line over your head and the

poles

The Earth Reference System

L 39° 33' 09“ N

074 ° 29' 08“ W

So Where is this?

The Taylor ObservatoryLatitude 39° 33' 09“ NLongitude 074 ° 29' 08“ W

北京 39º 55’N 116º 24’E

AQHNA 37º 58’N 023º 43’E

Москва 55º 45’N 037º 27’E

Finding our way

القدس

ירושלים

31º 47’N 035º 13’E

31º 47’N 035º 13’E

New York 40º 40’N 073º 56’W

London 51º 30’ 26N 000º 07’ 39”W

Now it’s easy to see that there are two the same…

Finding our way in the Night Sky

The Celestial Sphere1.A projection of the Earth's coordinates onto

the sky2.The poles are extended to become the

celestial poles3.The equator is projected to become the

celestial equator4.The Latitude lines (parallels) are projected

onto the celestial sphere and given the name 'Declination'

5.The Longitude lines (meridians) are projected out and are now called 'Right Ascension'

The Celestial Sphere• The North Celestial Pole appears to be near a

star, Polaris. As the evening passes, the stars appear to rotate clockwise about Polaris.

• For a given latitude of an observer, some stars never set - these are known as circumpolar stars

• If you were at the North Pole, Polaris would be nearly on your zenith and the motion of the stars would be parallel to the horizon.

• If you were at the Equator, Polaris would be on the horizon; The stars would appear to move vertically: "up" to the East, "down" to the West

The Celestial Sphere

StarTrails

Polar

The motion of the stars as seen from the North Pole

Star Trails: Equatorial

The motion of the stars as seen from the Equator

The Celestial Coordinates• Declination

1. Measured in degrees2. '+' or '-' from the celestial equator

• Right Ascension– Measured in hours, minutes and

seconds– From 0h 0m 0s to 23h 59m 59.999s

Celestial Coordinates

0

061218

Right Ascension

-45

+45

Declin

atio

n

+90

-90

For convenience, stars are assumed to be fixed to the celestial sphere and can be located on the coordinatechart:

Using the Coordinates

Alkaid 13h 47m 42s +49º 17' 20"

Merak 11h 02m 01s +56º 21' 52"

Dubhe 11h 03m 55s +61º 43' 58"

Meridian & Right Ascension