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19Celestial Distances

19.1 Fundamental Units of Distance

Radio telescope can send and

receive radar waves, and thus

measure the distances to planets,

satellites, and asteroids

Distance to the planets

• Kilometers

• Solar system: Astronomical Unit

– Earth-to-Sun = 1 AU

How do astronomers know?

19.1 Fundamental Units of Distance

Distances to the stars (and beyond)

• Light year (LY)

– Mega-light year (MLY) = 1,000,000 light years

• Parsec (PC)

– Mega-parsec (MPC) = 1,000,000 parsecs

How do astronomers know?

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19.2 Surveying the Stars

• Distance to the stars

– Triangulation: parallax

• Surveying

• Astronomy

– Friedrich Bessel: 1838

– He found angles were << 1°

Sky as

seen

from

point B

Sky as

seen

from

point A

BA

Earth’s

orbit

S

u

n

Parallax angle

19.2 Surveying the Stars

• Distance to the stars

– Parsec

• Term origin: parallax of one arcsecond

• Distance = inverse of parallax

– d = 1/p

• 1 parsec = 3.26 LY

– With ground-based telescopes, accurate

measurements feasible out to about 60 light-years

P

Parallax angle

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19.2 Surveying the Stars

• Distance to the stars

– HIPPARCOS satellite: High

Precision Parallax Collection

Satellite

• Launched by ESA

• Accurate distances out to

about 300 light-years

• Generated two catalogs

1. Parallax angles of 120,000

stars to an accuracy of

0.0001”

• about the diameter of a golf

ball in NYC as viewed from

Europe

2. >1 million stars w/ parallax

angles measured to 0.03”

Mission: 1989 - 1993

19.2 Surveying the Stars

• Distance to the stars

– New ESA mission: Gaia

(Hipparcos successor)

– 200 times more

accurate

– 1 billion stars out to

30,000 LY!

Video: May 3, 2018

https://www.youtube.com/watch?v=lxgdcG_NQyA

19.2 Surveying the Stars

• The Nearest Stars

– Winner: Sun

• 8 light-minutes away = 93 x 106 miles

– No known star is within 1 light-year or even 1 parsec of Earth.

– Closest is Proxima Centauri (only visible below ~30° N latitude)

• Low-mass red M dwarf

• Closest member of the Alpha (α) Centauri triple-star system

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19.2 Surveying the Stars

• Closest star system:

Proxima Centauri

– Measured parallax = 0.77”

– Distance = inverse of parallax

d = 1/p

d = 1/0.77 = 1.3 pc = 4.3 LY

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formula???

19.2 Surveying the Stars

• The Nearest Stars

– Closest star visible from Long Island: Sirius

• aka Alpha (α) Canis Major

• 8.3 light-years away

= 4.879 x 1013 miles

• Binary system: white main-

sequence star orbited by a

faint white dwarf

19.2 Surveying the Stars

Three accepted ways of naming stars

• International Star Registry is NOT one of them!

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19.2 Surveying the Stars

19.2 Surveying the Stars

• Naming Stars

– Set by the International Astronomical Union (IAU)

– Proper names

• Arabic translations of Greek and Roman astronomy

• Winter examples:

– Betelgeuse: The Armpit of the Giant

– Rigel: The Left Leg of the Giant

– Aldebaran: The Follower

– Procyon: Before the Dog

– Capella: The Little She-goat

Orion

19.2 Surveying the Stars

• Naming Stars

– Johann Bayer: German

• 1603

• Labeled stars with

letters from the Greek

alphabet

• Betelgeuse = α Orion

Name Symbol Name Symbol

Alpha α Nu ν

Beta β Xi ξ

Gamma γ Omicron ο

Delta δ Pi π

Epsilon ε Rho ρ

Zeta ζ Sigma σ

Eta η Tau τ

Theta θ Upsilon υ

Iota ι Phi φ

Kappa κ Chi χ

Lambda λ Psi ψ

Mu μ Omega ω

α

?

?

?

Orion

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19.2 Surveying the Stars

• Naming Stars

– John Flamsteed: English

• 1725

• Numbers from west

to east in a given

constellation

• Betelgeuse

= α Orion

= 58 Orion

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Orion

19.2 Surveying the Stars

• Naming Stars

– Other general catalogs

• HD: Henry Draper

Catalog

• SAO: Smithsonian

Astrophysical

Observatory BD:

Bonner

Durchmusterung

(German)

• USNO-B1.0: US

Naval Observatory

• HGSC: Hubble

Guide Star Catalog

19.3 Variable Stars: One Key to Cosmic Distances

Chapter 17 review: What is “luminosity”?

Refers to the inherent brightness of a star (more correctly, its

energy output), but not how bright a star appears in the night

sky.

Why do some stars appear brighter than others in the sky?

Answer: Either because:

a) More luminous (different "wattage");

b) Closer to us (remember the inverse-square law?);

or

c) Both

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19.3 Variable Stars: One Key to Cosmic Distances

• Breakthrough in measuring distances to the stars came from

the study of variable stars

– These strange stars actually change in light output

• Three types of variable stars

– Pulsating variables

– Erupting variables

– Eclipsing binaries

3.4

3.6

3.8

4.0

4.2

4.42 4 6 8 10 12 14 16 18

Time (days)

MagnitudeLight

Curve

Diagram

Period

19.3 Variable Stars: One Key to Cosmic Distances

• Cepheid pulsating variables

– Named for Delta (δ) Cephei

– Periodically expand and

contract: “breathing”

– Large, yellow stars

– Periods = 3 to 50 days

– Luminosities = 1,000 to

10,000 times the Sun

CASSIOPEIA

CEPHEUS

Polaris

URSA

MINOR

19.3 Variable Stars: One Key to Cosmic Distances

• Cepheid variables

– Period-Luminosity relationship

• Discovered by Henrietta Leavitt

(1868-1921)

• Worked at Harvard Observatory

• Studied Cepheids in the Magellanic

Clouds

– Satellite galaxies of Milky Way

– Stars within considered to be the

same distance away

– Found that the longer its period,

the greater the star’s luminosity

– Period-Luminosity Relationship

https://www.youtube.com/watch?v=XQv03YqEPNM

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19.3 Variable Stars: One Key to Cosmic Distances

19.3 Variable Stars: One Key to Cosmic Distances

• Cepheid variables

– Period-Luminosity relationship

• Knowing distances to nearby Cepheids by parallax,

astronomers calibrated the system

19.3 Variable Stars: One Key to Cosmic Distances

• Cepheids are visible in more distant galaxies, as well

• Ejnar Hertzsprung and Harvard’s Harlow Shapley, and Edwin

Hubble (Mount Wilson Observatory) immediately saw the

potential of the new technique

– 1920s: Hubble made one of the most significant

astronomical discoveries of all time using cepheids

– He discovered that the universe is expanding

Hertzsprung Shapley Hubble

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19.3 Variable Stars: One Key to Cosmic Distances

• RR Lyrae stars

– Another class of pulsating variables

– Named for prototype star in constellation Lyra

– Similar in behavior to Cepheids

• Period-luminosity relationship

– Very short periods

• Always less than one day

– More common but less luminous

• Can be detected to 2 million LY

• Cepheids to 60 million LY

Cepheids versus RR Lyrae stars

• Note the differences

19.3 Variable Stars: One Key to Cosmic Distances

• RR Lyrae stars

– Visible in star clusters

• All stars within are at the

same distance from Earth

• All RR Lyrae stars in a

given cluster shine at

same magnitude, so they

must have same

luminosity: like a

“standard bulb”

• Once we know

magnitude and

luminosity, we can

calculate distance using

the inverse-square law

Globular star cluster M15

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19.4 H-R Diagram and Cosmic Distances

• So far, we have seen how to measure the distance to a:

– Nearby stars: parallax

– Cepheid/RR Lyrae variables: Period-luminosity

relationship

– Cluster stars: Use Cepheids or RR Lyrae

• But what if the star we want to measure is not variable or in

a star cluster?

Chapter 5 review: Inverse-Square Law

• Light intensity will decrease by the square of the change in

distance

– Double the distance, four times fainter

– Triple the distance, nine times fainter

– Ten times the distance, 100 times fainter

19.4 H-R Diagram and Cosmic Distances

• Once we know a star’s luminosity and magnitude, we can use

the inverse-square law to figure out the distance from its

spectral type.

• But how do you know the luminosity??

– Well, you could examine the star’s spectrum to figure out

the spectral class

– Example: Let’s say you’re examining a type G2 star, with an

identical spectrum as our Sun

– But…

• It could be a main-sequence star with a luminosity of 1 Lsun

• or it could be a giant with a luminosity of 100 LSun,

• or even a supergiant with a still higher luminosity.

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19.4 H-R Diagram and Cosmic Distances

• We can use the H-R Diagram from chapter 18

• What did it show?

O B A F G K M

19.4 H-R Diagram and Cosmic Distances

• The H-R Diagram classifies stars by spectral type and

temperature based on spectral analysis

• Astronomers can also tell:

– Diameters using differences in pressure

• Giant stars - lower pressures

• Dwarf stars - higher pressures

• From this, astronomers created luminosity classes

Class Description Typical Luminosity (LSun)

Ia Bright supergiants 500,000

Ib Supergiants 8,000

II Bright giants 1,300

III Giants 100

IV Subgiants 25

V Main-sequence stars/dwarfs Entire range of values

19.4 H-R Diagram and Cosmic Distances

• Luminosity classes

O B A F G K M

Ia

Ib

IIIII

IV

V

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19.4 H-R Diagram and Cosmic Distances

By knowing a star’s spectral and luminosity classes, we know itsposition on the H–R diagram, and therefore read the star’s luminosity.

Examples of luminosity classes

1. A1 V

• Description: main sequence, white star

• Example: Sirius

2. G2 V

• Description: main sequence, yellow star

• Example: Sun

3. M2 Ib

• Description: Red supergiant

• Example: Betelgeuse

4. B8 Ia

• Description: Blue supergiant

• Example: Rigel

Cosmic Distance Ladder

Table 19.1 Techniques for measuring distances to the stars

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