Chapter 2:

The Sky

Common Units we will use

Common Conversions

Standard Prefixes

Review Notation• 1,000,000,000 = 109

• 1,000,000 = 106

• 1,000 = 103 • 1 = 100

• .001 = 10-3 • .000001 = 10-6 • .000000001 = 10-9

Celestial Sphere• When we look at the sky, we see stars but

have no actual clue as to how far away they are. Therefore it is as if they were all on a sphere out a long distance from us. This conceptual device is known as the celestial sphere.

• Distances between objects then are measured in angles since all objects appear to be at the same distance.

• This is an example of the use of a model.

Celestial Sphere Attributes

• North and South Celestial Poles.• Zenith (point directly overhead.• Nadir (point directly below – through earth)• Celestial equator (extension of plane through

the earth at equator and extended to sphere.

The Celestial Sphere• Zenith = Point on

the celestial sphere directly overhead

• Nadir = Point on the c. s. directly underneath (not visible!)

• Celestial equator = projection of the Earth’s equator onto the c. s.

• North celestial pole = projection of the Earth’s north pole onto the c.s.

Discussion

• If the Earth did not rotate about its axis, could we define a celestial sphere as we do now?

• Could we even define a set of poles and equator?

• What is the difference between a constellation and an asterism? Examples?

• What does the word apparent mean in the context of “apparent visual magnitude”?

More discussion

• Where on Earth can you see both the North and South Celestial poles simultaneously?

Stars are named by a Greek letter () according to their relative brightness within a given constellation + the possessive

form of the name of the constellation:

Betelgeuse = Orionis,

Rigel = Orionis

Betelgeuse

Rigel

OrionConstellations

The Magnitude ScaleFirst introduced by Hipparchus

(160 - 127 B.C.)• Brightest stars: ~1st magnitude

• Faintest stars (unaided eye): 6th magnitude

More quantitative:Now that we have instrumentation:

• 1st mag. stars appear 100 times brighter than 6th mag. stars

• 1 mag. difference gives a factor of 2.512 in apparent brightness (larger magnitude =>

fainter object!)

Where did 2.512 come from?

• There are 5 magnitudes difference between magnitude 1 and magnitude 6 stars.

• The magnitude 1 star is defined to be 100 times as bright as a magnitude 6 star.

• The steps are equal brightness factor.• Therefore each one of the steps is equal to

(100) 1/5 = 2.512 (fifth root of 100)

Example:

Betelgeuse

Rigel

Magnitude = 0.41 mag

Magn. Diff. Intensity Ratio

1 2.512

2 2.512*2.512 = (2.512)2 = 6.31

… …

5 (2.512)5 = 100

Magnitude = 0.14 magFor a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512)0.27 =

1.28

The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint objects):

Sirius (brightest star in the sky): mv = -1.42

Full moon: mv = -12.5

Sun: mv = -26.5

The Magnitude Scale

More standard values

The Celestial Sphere

On the sky, we measure distances between objects as angles:The full circle has 360o (degrees)1o has 60’ (arc minutes)1’ has 60” (arc seconds).