Astro Pre-SG Final

1 kiloparsec (kpc)

1,000 parsecs ≈ 3,000 light years

1 megaparsec (Mpc)

1 million parsecs ≈ 3 million light years

1 gigaparsec (Gpc)

1 billion parsecs ≈ 3 billion light years

“Thousand million” equals…

A billion (10⁹). Example: 14 thousand million years = 14 billion years.

“Million million” equals…

A trillion (10¹²)

How many km in a light year?

About 10 trillion km (10¹³ km)

How many AU in a light year?

About 63,000 AU

How many AU in a parsec?

About 206,000 AU (≈ 200,000)

Sun → Galactic center, in three units

27,000 ly ≈ 8.2 kpc ≈ 1.7 billion AU

Nearest star (Proxima), in three units

4.25 ly ≈ 1.3 pc ≈ 270,000 AU

Andromeda, in two units

2.5 million ly ≈ 0.7–0.8 Mpc (about 700–770 kpc)

Virgo cluster, in two units

~16 Mpc ≈ 50–55 million ly

Cosmological horizon, in two units

~14 Gpc ≈ 46 billion ly

Sun → Neptune, in three units

30 AU ≈ 4.5 billion km ≈ 4 light hours

Earth → Moon, in three units

384,000 km = 60 Earth radii = 1.3 light seconds

Sun → Earth, in three units

150 million km = 1 AU = 8 light minutes

30 km/s as a fraction of the speed of light

1/10,000 (300,000 ÷ 30 = 10,000)

200 billion written two other ways

200,000 million = 2·10¹¹

Spotting a disguised number

Convert it to the unit you know. Close (within ~2×) → probably true. Off by 1,000× or more, or the right number with the wrong unit → trap.

Threshold temperatures for hydrogen and helium burning

~10 million K for hydrogen; ~100 million K for helium

Which stars never ignite helium?

Very-low-mass stars, under ~0.5 M☉. They end as helium white dwarfs.

Which stars burn helium into carbon and oxygen?

Stars above ~0.5 M☉

Which stars do NOT make planetary nebulae?

Very-low-mass stars (under 0.5 M☉) and high-mass stars (over 8 M☉, which explode instead)

Minimum starting mass to explode as a type II supernova

~8 solar masses

The Sun's density: center and average

Center ~150 g/cm³ (150× water); average ~1.4 g/cm³. Water = 1; densest Earth materials (osmium) ~22 g/cm³

Range of stellar radii

Main sequence: 8% of the Sun's to ~60 R☉. Giants and supergiants: hundreds to ~2,000 R☉.

What does fast rotation do to a star?

Centrifugal force flattens it at the poles (ellipsoid). Achernar's equator is 35% wider than its poles.

How is energy carried out of a star?

By radiation or by convection. Sun: radiative zone inside, convective zone outside.

Chemical enrichment: who makes what?

Planetary nebulae → carbon, nitrogen · type I supernovae → iron · type II supernovae → oxygen

Tycho (1572) and Kepler (1604) supernovae

Type I supernovae in our Galaxy, seen with the naked eye

The stars-gas cycle

Gas clouds → stars → gas returned (planetary nebulae, supernovae, winds) with heavier elements → new stars

Compact vs large-scale stellar remnants

Compact: white dwarf, neutron star, black hole. Large-scale: planetary nebula, supernova remnant (gas).

What are stars made of?

Ionized gas (plasma): ions + free electrons, not atoms or molecules

When will the Sun become a giant, and how will it change?

In ~5 billion years: ~200× bigger (≈ 1 AU), thousands of times more luminous, cooler and redder surface

Rigel, Deneb, Betelgeuse

Blue supergiant · white supergiant · red supergiant

Aldebaran

Orange giant in Taurus, 65 ly away, 45× the Sun's diameter

What do giant stars burn?

First hydrogen in a shell around a dead helium core; later helium → carbon + oxygen in the core

Speed of light in glass and in water

Glass ~200,000 km/s, water ~225,000 km/s. Slower than in vacuum; red is faster than violet.

Dispersion

A prism splits white light into colors because each wavelength travels at a different speed in glass

Planck (1900)

Light is emitted and absorbed in quanta: E = h·f. h is a fundamental constant, like c and G.

Einstein (1905)

E = mc², and light travels as quanta (photons)

Mass of a photon (course version)

m = h·f / c² = h / (λ·c). Light has mass, so gravity bends its path.

Why is the sky blue? What about on the Moon?

Air scatters blue light more than red. The Moon has no air, so its day sky is black.

The Sun's true color

White. It looks yellow (and red at sunset) only through Earth's atmosphere.

Wave-particle duality

Light acts both as a wave and as particles (photons)

Speed of light

300,000 km/s = 3·10⁸ m/s (same for all wavelengths in vacuum)

1 AU

150 million km ≈ 8.3 light minutes (average Sun–Earth distance)

1 light year

≈ 10¹³ km (10 trillion km) ≈ 63,000 AU

1 parsec

3.26 ly ≈ 206,000 AU

Earth–Moon distance

384,000 km = 60 Earth radii ≈ 1.3 light seconds

Light travel time: Sun → Neptune

~4 hours (Neptune is at 30 AU)

Edge of the Solar system (Oort cloud)

~100,000 AU ≈ 1.5 light years

Nearest star and its distance

Proxima Centauri, 4.25 ly (270,000 AU, 1.3 pc)

Sun → center of the Galaxy

27,000 ly = 8.2 kpc = 1.7 billion AU

Distance to Andromeda (M31)

2.5 million ly

Distance to the Virgo cluster

~55 million ly

Distance to the cosmological horizon

46.5 billion ly (≈ 50 billion)

Age of the Universe

~14 billion years (= 14 thousand million)

Age of the Solar system

4.6 billion years ≈ ⅓ of the Universe's age

Number of stars in the Milky Way

~200 billion = 200,000 million = 2·10¹¹

Number of galaxies in the observable Universe

~2 trillion

Earth's orbital speed around the Sun

30 km/s = 1/10,000 of the speed of light

Sun's speed around the Galaxy, and the Galactic year

230 km/s; one orbit takes 230 million years (~20 orbits so far)

Earth's 1st, 2nd and 3rd cosmic speeds

7.9 km/s (circular), 11.2 km/s (escape Earth), 16.7 km/s (escape Solar system)

Earth's surface gravity

9.81 m/s²

Diameter ratios: Sun : Jupiter : Earth, and Sun vs Moon

≈ 100 : 10 : 1. The Sun is ~400× the Moon's diameter.

Mass ratios: Sun:Earth, Sun:Jupiter, Earth:Moon

333,000 · ~1,000 · 81

Size of an atom / an atomic nucleus

10⁻¹⁰ m / 10⁻¹⁵ m (ratio 100,000)

Luminosity of the Sun

4·10²⁶ W

Sun: surface and core temperature

5,800 K surface / 15 million K core

When was the CMB released, and how hot is it?

~400,000 years after the Big Bang (~3,000 K then); 2.7 K today

Milky Way disk size / dark matter halo size

Disk 100,000–200,000 ly / halo over 1 million ly

Local Group size and membership

~10 million ly across, 130+ members (mostly dwarf galaxies)

Hubble constant

~68 km/s per megaparsec (≈ 21 km/s per million ly)

Solar flux at Earth

~1,400 W/m²

Range of stellar masses

0.08 to ~150 solar masses

Low-, intermediate- and high-mass stars

0.08–2 · 2–8 · 8–150 solar masses

Range of stellar surface temperatures

~2,000 K to ~50,000 K (Wolf-Rayet stars and central stars of planetary nebulae exceed 200,000 K)

Spectral classes, hot → cool

O B A F G K M (“Oh Be A Fine Girl/Guy, Kiss Me”)

Luminosity classes I–V

I supergiant · II bright giant · III giant · IV subgiant · V main sequence (dwarf)

What is a G2V star?

A main-sequence star like the Sun (a yellow dwarf; the Sun's true color is white)

What is a B8I star?

A hot blue supergiant

What is a K1III star?

An orange giant

What is Sirius A's spectral class?

A1V: a white main-sequence star, 10,000 K, 2 M☉, 25 L☉, 9 ly away

Axes of the Hertzsprung-Russell diagram

Luminosity (up) vs surface temperature, which increases to the LEFT

What fraction of stars are on the main sequence?

~95%

Red dwarfs

M-type main-sequence stars under 0.6 M☉; ~80% of all stars; live up to trillions of years

Blue dwarfs

A hypothetical late stage of very-low-mass stars. None exist yet.

Black dwarfs

Cooled-down white dwarfs. None exist yet: cooling takes longer than the age of the Universe.

Largest stars? Most luminous stars?

Largest: red supergiants. Most luminous: blue supergiants.

Lifetime of the Sun

~12 billion years

Lifetime of a 150 M☉ star vs a 0.08 M☉ star

~3 million years vs ~11 trillion years

Initial Mass Function (IMF)

Distribution of masses at birth: low-mass stars dominate, median ~0.1 M☉, under 1% are high-mass

Composition of a newborn star

~¾ hydrogen, ~¼ helium, a few % heavier elements

Hydrostatic equilibrium

Gravity pulling in is balanced by gas and radiation pressure pushing out

Proton-proton cycle

4 protons → 1 helium-4 nucleus; 0.7% of the mass becomes radiation. The Sun's main energy source.

CNO cycle

Hydrogen burning with carbon as a catalyst. Dominates above ~17 million K (massive stars); only 0.8% of the Sun's energy.

Triple-alpha process

3 helium-4 → carbon-12, at ~100 million K, only in stars above ~0.5 M☉

Why does fusion stop at iron?

Iron has the highest binding energy per nucleon, so fusing it costs energy instead of releasing it

Onion-skin structure

Shells of H, He, C, Ne, O, Si around an iron core in a high-mass star near the end of its life