If the universe were infinite, static and full of stars, every line of sight should eventually hit a star, making the sky as bright as the Sun’s surface. It isn’t. Why?

1. The universe is not infinitely old — it is $\sim 13.8$ billion years old.
2. Light from galaxies beyond a certain distance has not yet reached us.
3. The universe is expanding, so light from distant galaxies is red-shifted toward lower energy and longer wavelengths — much of it shifted out of the visible range.
4. Both effects keep the night sky dark.

Key idea: even something as simple as the darkness of the night sky is evidence for a finite, expanding universe. Olbers saw this paradox in the 1820s — it was not fully resolved until the 20th century.

A light-year is the distance light travels in one year. Calculate it, given $c = 3.0 \times 10^8$ m/s.

1. Seconds in one year: $365.25 \times 24 \times 60 \times 60 \approx 3.156 \times 10^7$ s.
2. Distance: $3.0 \times 10^8 \times 3.156 \times 10^7 \approx 9.47 \times 10^{15}$ m.
3. That is roughly $9.5$ trillion km.

The nearest star to the Sun, Proxima Centauri, is $\sim 4.24$ light-years away — so we see it as it was in $2020$.

A galaxy is measured to be receding at $7\,000$ km/s. Estimate its distance using $H_0 = 70$ km/s per megaparsec.

1. $d = \dfrac{v}{H_0} = \dfrac{7\,000}{70} = 100$ megaparsecs.
2. One megaparsec $\approx 3.26$ million light-years, so $d \approx 326$ million light-years.

Key idea: we are seeing that galaxy as it was $326$ million years ago — light takes that long to reach us.

Describe the stages the Sun will go through from now to the end of its life.

1. Main sequence (current, $\sim 4.6$ Gyr old, $\sim 5$ Gyr remaining): fusing hydrogen to helium in its core.
2. Red giant ($\sim 5$ Gyr from now): core hydrogen exhausted; outer layers expand beyond Earth’s orbit.
3. Planetary nebula: outer layers puff off as a beautiful shell of gas.
4. White dwarf: the exposed core, about Earth-sized but half the Sun’s mass, slowly cooling over billions of years.

More massive stars end more violently: they collapse, trigger a supernova explosion, and leave behind a neutron star or (for the most massive) a black hole. Elements heavier than iron are made in supernovae and merging neutron stars.

A calcium atom in your bones was made billions of years ago in a different star. Describe the chain of events.

1. Calcium (atomic number 20) is made in massive stars by fusion of lighter elements during the red-giant phase.
2. The star eventually goes supernova, scattering the heavy elements into space.
3. A gas cloud enriched in these heavy elements forms a new solar system — ours, $\sim 4.6$ billion years ago.
4. Earth accreted from that enriched material; calcium became part of rocks, oceans, plants, and your skeleton.

Key idea: every atom heavier than lithium in your body was forged in a star. “We are all star-stuff.” — Carl Sagan.