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Observing the Sky

Lecture 8

Chapter 2 Opener

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Figure 2.1

Figure 2.2

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Figure 2.6

Figure 2.4 Annotated

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The Celestial Sphere

• The celestial sphere is the vast hollow sphere on which the stars appear fixed.

• The celestial equator is defined by extending the earth’s equator outward.

• The N & S poles of the celestial sphere correspond to the earth’s poles.

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The Ecliptic

• The ecliptic is the apparent path of the sun through the sky.

• It is also the plane of the earth’s orbit about the sun on the celestial sphere.

• Note: The ecliptic is tilted w.r.t. the earth’s equatorial plane by 23.5o.

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The Zodiac

• The zodiac is a band of celestial sphere which represents the path of the planets, the moon and the sun.

• Extends ~8o to either side of the ecliptic.

• In astrology the zodiac is divided into 12 equal parts called signs, each bearing the name of a constellation.

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Astrology is NOT a science!

• Propagates the claim that a person’s life is determined by the position of the sun, moon, and planets at birth.

• This notion is patently false, and potentially harmful.

• Astrology is neither a science nor a religion.

Figure 2.7B

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Figure 2.7A

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Zenith

• The zenith is the point on the celestial sphere that is directly above the observer.

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Meridian

• The meridian is the great circle passing through the two poles of the celestial sphere and the observer’s zenith.

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Equatorial Coordinates

• Astronomers use equatorial coordinates to locate objects on the celestial sphere.

• Right Ascension – Notation: RA or

– Equivalent to longitude

• Declination – Notation: Dec or

– Equivalent to latitude

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Defining RA and Dec.

• RA is measured in hours – The range is from 0 to 24 hours

increasing on sky towards the east. – The “zero point” is towards the

constellation Pisces (Vernal Equinox).

• Dec is measured in degrees. – The zero is on the equator – North Pole = 90o

South Pole = -90o

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Equatorial Coordinates (Cont’d)

• The equatorial (celestial) coordinate system is fixed on the sky.

• The coordinates (, ) of the stars and constellations do not change (ignoring precession).

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North

Equatorial Plane

23.5o

Ecliptic Plane

Vernal Equinox

0

6 hr

12

18

Autumnal Equinox

Equinoxes

Equinoxes at the intersection of the equatorial and ecliptic planes.

Sun here on first day of fall

Sun here on first day of spring

1st day of summer

1st day of winter

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Finding objects

• Circumpolar objects can be visible any time of the year

– For example, Polaris, the pole star.

• From Ithaca southerly objects are best observed during transit.

– Really, all objects are best observed when they transit (you look through the least atmosphere)

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Using RA to find an object

• Given two of RA, meridian transit time, and date

• Find remaining one

Method

• Always work with RA (RAmid) on the meridian at midnight

• Find closest reference date (via RA or date) – Sep 21 (0), Dec 21 (6), Mar 21 (12), Jun 21 (18 hr)

• Use fact sky changes by ~ 1 hour of RA per 2 weeks.

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Figure 2.20 Unannotated

Figure 2.20B Annotated

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Figure 2.5 Unannotated

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The Changing Sky

• At the same time each night, a different RA will be on the meridian at different times of the year.

• For instance at midnight, the RA’s on the meridian are:

– Sept. 21 0 hr , March 21 12 hr

– Dec. 21 6 hr , June 21 18 hr

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Fluxes and Magnitudes

• Flux is the power per unit area received from an object

– e.g. fsun = 1 kW/m2

• If two stars, A and B, have fluxes, fA and fB, their magnitudes are related by

)/log(5.2 BABA ffmm

Magnitude example

• Suppose fB/ fA = 10, then using

we have mA - mB = 2.5*log(10)

so that mA - mB = 2.5

)/log(5.2 BABA ffmm

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Converting between f and m

• We can also write our relation between magnitudes and fluxes as

So if mA = 5 and mB = 0, fB/fA = 100.

5.210BA mm

A

B

f

f

Flux example

• If mA = 5 and mB = 0, then using

we have fB/fA = 10(5-0)/2.5

so that fB/fA = 102 = 100

5.210BA mm

A

B

f

f

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Measuring distance from fluxes

• If we know the luminosity of an object (such as a star) and measure its flux

we can determine its distance!

f rL

r

Lf

4 42

Standard Candles

• Objects with known luminosity are called standard candles in astronomy.

• They are of fundamental importance.

• Astronomers use standard candles to measuring distances.

• There are very few standard candles and it is a problem to calibrate them (determine L).

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Viewed looking down from the north.

0 hr

6 hr

12 hr

18 hr

Fall

Sun

Midnight Sep. 21

Winter

Sun

Midnight Dec. 21

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Simulation 1: Yearly variation

• Earth moving around the sun.

• Why we see different parts of the sky at different times of the year.

Here the observer is out at midnight each night

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Simulation 2: Daily variation

• Rotation of earth as it moves around the sun.

• How we see different portions of the sky at night.

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Viewed looking down from the north.

0 hr

6 hr

12 hr

18 hr

Sun

Spring midnight 12 hr on meridian

4:00 AM 16 hr on meridian

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The Changing Sky (continued)

• Each night a given object will pass over the meridian 4 minutes earlier.

• This corresponds to 2 hours earlier each month, or 24 hours in one year.

• Objects rise and set earlier each day.

• At a given time, the RA crossing the meridian increases by 4 min. per day.

Motion of earth along orbit is exaggerated.

1 day along orbit

4 min.

mid

nig

ht

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On what date does Orion appear on the meridian at midnight?

• Orion Nebula

– RA = 5.5 hr Dec = -5.5 deg

• RA = 6 hr transits at midnight on Dec 21.

Orion transits at midnight on Dec 14.

Also

• Orion transits at 9:00 p.m. on Jan 28.

• Orion transits at 3:00 a.m. on Oct. 31.

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Example 1: What RA is on the meridian for a given date and time?

• What RA is on the meridian at 3:00 am on Feb. 21?

– Dec 21 -- 6 hr overhead at midnight

– Feb 21 -- 2 months later => add 4 hr => 10 hr overhead at midnight

– 3:00 am => 3 hr later => 13 hr overhead