A Modern View of the Universe — Chapter 1 (PHYS 405/406, Spring 2015)

Quick Tour of the Universe

  • The Earth is one of several major planets orbiting the Sun.

  • The Sun sits near the outer edge of a huge collection of stars called the Milky Way Galaxy.

  • The Milky Way is similar to many other galaxies we see in the night sky; examples include the Andromeda Galaxy.

  • The Milky Way is just one of billions of other galaxies in the Universe.

  • Our cosmic address follows a hierarchy: Planet → Solar System → Galaxy → Galaxy Cluster (a collection of galaxies) → Universe.

Distances and Units in Astronomy

  • Distances in astronomy are extremely large. To manage these, astronomers define their own units of distance.

  • The Earth–Sun distance is about ext1AU≈1.5×108 km.ext{1 AU} \approx 1.5\times 10^{8}\ \rm{km}.

  • Mercury ≈0.4 AU\approx 0.4\ \rm{ AU}, Earth = 1 AU1\ \rm{ AU}, Mars  ≈1.5 AU\,\approx 1.5\ \rm{ AU}, Saturn  ≈9.6 AU\,\approx 9.6\ \rm{ AU}, Pluto  ≈39.2 AU.\,\approx 39.2\ \rm{ AU}.

  • The speed of light is the ultimate speed limit: c≈3.0×105 km s−1.c\approx 3.0\times 10^{5}\ \rm{km\,s^{-1}}.

  • Light travel times within the solar system: Moon  ≈1.5 s\,\approx 1.5\ \rm{ s}, Sun  ≈8 min\,\approx 8\ \rm{min}, Saturn \,\approx 1\ \rm{hour}}.

The Light Year and Nearby Distances

  • A light year is the distance that light travels in one year, not a unit of time.

  • 1 ly≈9.46×1012 km.1\ \text{ly} \approx 9.46\times 10^{12}\ \rm{km}.

  • Nearest star to the Sun, Alpha Centauri, is about 4.3 ly.4.3\ \text{ly}.

How Big is a Trillion?

  • If you counted one number every second, how long would it take to reach a given N?

  • Seconds per year (based on a schedule of 8 h/day, 5 days/week, 50 weeks/year):
    extsecondsperyear=8×3600×5×50=7.2×106.ext{seconds per year} = 8\times 3600 \times 5 \times 50 = 7.2\times 10^{6}.

  • Time to count N numbers (in years):
    extyears=N7.2×106.ext{years} = \frac{N}{7.2\times 10^{6}}.

  • Example times for powers of ten (rounded):

    • N=102N=10^{2}  ⇒\,\Rightarrow about 1 min 40 s.

    • N=103N=10^{3}  ⇒\,\Rightarrow about 16 min 40 s.

    • N=106N=10^{6}  ⇒\,\Rightarrow about 6.9 weeks.

    • N=109N=10^{9}  ⇒\,\Rightarrow about 139 years.

    • N=1012N=10^{12}  ⇒\,\Rightarrow about 139{,}000 years.

The Scale of the Universe: Number of Stars

  • The Milky Way contains about 101110^{11} stars.

  • There are roughly 101110^{11} galaxies in the observable Universe.

  • Total number of stars in the observable Universe is therefore on the order of 102210^{22} stars.

Scale of the Solar System (1:10101:10^{10} Model)

  • A 1:10101:10^{10} scale model of the Solar System means real sizes/distances are divided by 1010.10^{10}.

  • Example mapping using an approximate 1.39×1061.39\times 10^{6} km Sun diameter:

    • Sun diameter: real DSun=1.39×106 km⇒scaled=13.9 cm.D_{\text{Sun}} = 1.39\times 10^{6}\ \rm{km} \Rightarrow \text{scaled} = 13.9\ \text{cm}.

  • Planets (diameter, scaled):

    • Mercury: D≈4.88×103 km⇒0.05 cmD\approx 4.88\times 10^{3}\ \rm{km} \Rightarrow 0.05\ \rm{cm}; distance from Sun: 58×106 km⇒5.8 m.58\times 10^{6}\ \rm{km} \Rightarrow 5.8\ \rm{m}.

    • Venus: D≈1.21×104 km⇒0.12 cmD\approx 1.21\times 10^{4}\ \rm{km} \Rightarrow 0.12\ \rm{cm}; distance: 108×106 km⇒10.8 m.108\times 10^{6}\ \rm{km} \Rightarrow 10.8\ \rm{m}.

    • Earth: D≈1.28×104 km⇒0.13 cmD\approx 1.28\times 10^{4}\ \rm{km} \Rightarrow 0.13\ \rm{cm}; distance: 150×106 km⇒15.0 m.150\times 10^{6}\ \rm{km} \Rightarrow 15.0\ \rm{m}.

    • Mars: D≈6.79×103 km⇒0.07 cmD\approx 6.79\times 10^{3}\ \rm{km} \Rightarrow 0.07\ \rm{cm}; distance: 228×106 km⇒22.8 m.228\times 10^{6}\ \rm{km} \Rightarrow 22.8\ \rm{m}.

    • Jupiter: D≈1.43×105 km⇒1.43 cmD\approx 1.43\times 10^{5}\ \rm{km} \Rightarrow 1.43\ \rm{cm}; distance: 778×106 km⇒77.8 m.778\times 10^{6}\ \rm{km} \Rightarrow 77.8\ \rm{m}.

    • Saturn: D≈1.21×105 km⇒1.21 cmD\approx 1.21\times 10^{5}\ \rm{km} \Rightarrow 1.21\ \rm{cm}; distance: 1427×106 km⇒142.7 m.1427\times 10^{6}\ \rm{km} \Rightarrow 142.7\ \rm{m}.

    • Uranus: D≈5.11×104 km⇒0.51 cmD\approx 5.11\times 10^{4}\ \rm{km} \Rightarrow 0.51\ \rm{cm}; distance: 2870×106 km⇒287.0 m.2870\times 10^{6}\ \rm{km} \Rightarrow 287.0\ \rm{m}.

    • Neptune: D≈4.95×104 km⇒0.49 cmD\approx 4.95\times 10^{4}\ \rm{km} \Rightarrow 0.49\ \rm{cm}; distance: 4500×106 km⇒450.0 m.4500\times 10^{6}\ \rm{km} \Rightarrow 450.0\ \rm{m}.

    • Pluto: D≈2.32×103 km⇒0.023 cmD\approx 2.32\times 10^{3}\ \rm{km} \Rightarrow 0.023\ \rm{cm}; distance: 5900×106 km⇒590.0 m.5900\times 10^{6}\ \rm{km} \Rightarrow 590.0\ \rm{m}.

Driving to the Planets (at 100 km/h)

  • Travel time estimates (driving from the Sun):

    • Mercury: 66 years66\ \text{years}

    • Venus: 123 years123\ \text{years}

    • Earth: 170 years170\ \text{years}

    • Mars: 259 years259\ \text{years}

    • Jupiter: 888 years888\ \text{years}

    • Saturn: 1,630 years1{,}630\ \text{years}

    • Uranus: 3,300 years3{,}300\ \text{years}

    • Neptune: 5,100 years5{,}100\ \text{years}

    • Pluto: 6,700 years6{,}700\ \text{years}

The Scale of the Universe (California-sized Alpha Centauri)

  • On this scale, the nearest star (Alpha Centauri) would be located roughly somewhere in California. This illustrates how vast interstellar distances are compared to familiar terrestrial geography.

Look-Back Time: Seeing the Past

  • At great distances, we see objects as they were in the distant past because light takes time to reach us.

  • The Andromeda Galaxy (and other distant galaxies) are seen as they were long ago, not as they are today.

Spaceship Earth: Our Motion Through Space

  • The Earth rotates on its axis once every day.

  • The Earth orbits the Sun once every year.

  • The Sun itself orbits the center of the Milky Way roughly every 2.30×1082.30\times 10^{8} years (≈\approx 230 million years) at a speed of 8.0×105 km/h.8.0\times 10^{5}\ \rm{km/h}.

The Expanding Universe and Look Back to the Big Bang

  • Observations show that all galaxies are moving away from us, with more distant galaxies receding faster (Hubble expansion).

  • Extrapolating backward in time leads to the Big Bang, the origin of the expansion.

  • This fosters the idea that the Universe has a finite age and a finite size in the past, with expansion evolving over cosmic time.

The Expanding Universe: Local Raisin Analogy

  • Local Raisin model: As the universe expands, all raisins (galaxies) move away from each other.

  • In the baking analogy, raisins farther away move faster, illustrating that expansion is uniform on large scales but produces recession speeds that differ with distance.

  • Key takeaway: Expansion is a property of space itself, not merely objects moving through space.

Cosmic Calendar: The History of the Universe on One Year

  • A convention to visualize cosmic history by compressing the 13.8–billion-year history of the Universe into one ordinary year.

  • Milestones (approximate):

    • Jan 1 — Big Bang

    • Sep 3 — Earth forms

    • Dec 26–30 — Dinosaurs present on Earth

    • Dec 31 11:58 — Modern humans appear

    • 11:59:49 — Pyramids rise

    • 11:59:59 — Galileo and Kepler

Powers of Ten: Scale Across the Universe

  • A visual scale showing orders of magnitude in meters, from the largest (observable universe) to the smallest (fundamental limits):

    • 1026 m10^{26}\ \mathrm{m} — Observable universe

    • 1021 m10^{21}\ \mathrm{m} — Milky Way galaxy

    • 1013 m10^{13}\ \mathrm{m} — Solar System

    • 107 m10^{7}\ \mathrm{m} — Earth

    • 10−2 m10^{-2}\ \mathrm{m} — Insect

    • 10−10 m10^{-10}\ \mathrm{m} — Atom

    • 10−15 m10^{-15}\ \mathrm{m} — Atomic nucleus

    • 10−18 m10^{-18}\ \mathrm{m} — Smallest distance probed by particle accelerators

    • 10−18 to 10−35 m10^{-18} \text{ to } 10^{-35}\ \mathrm{m} — Typical size of fundamental strings and extra dimensions

    • 10−35 m10^{-35}\ \mathrm{m} — Minimum meaningful length in nature

Powers of Ten Video

  • https://www.wimp.com/powers-of-ten-the-amazing-scale-of-the-universe/