Section 9: Cosmology
1. Cosmic Chronology
Place the following events of the early universe in chronological order (from earliest to latest): Recombination (formation of neutral atoms), Big Bang Nucleosynthesis, Inflation, Formation of first galaxies, Quark-gluon plasma era.
2. Cosmic Temperatures
Order temperatures of objects in the universe from hottest to coldest: the core of the Sun, the surface of the Sun, the present Cosmic Microwave Background (CMB) radiation, interstellar space, temperature of the Univeres at the nucleosynthesis era, human body temperature, temperature of the Universe at the recombination era, temperature of black hole with 10 solar masses, ionization temperature of hydrogen.
3. Cosmic Sizes
Order the following objects in the universe from smallest to largest: Earth, Milky Way galaxy, Solar System, observable universe, Sun, Andromeda galaxy, human, Moon, Pluto, Jupiter, Ceres, Local Group of galaxies
4. Hubble's Law
According to Hubble's Law \(v = H_0 d\), and using the value of \(H_0 \approx 70 \text{ (km/s)/Mpc}\), at what distance would a galaxy be receding from us at the speed of light? This defines the approximate size of the observable universe.
4. Galactic Year
Our Solar System orbits the center of the Milky Way (a distance of about 27,000 light-years) at a speed of about 220 km/s. How long does it take to complete one orbit (a "galactic year")?
5. Galactic Collision
The Andromeda galaxy is about 2.5 million light-years away and is moving towards our Milky Way at about 110 km/s. Estimate how long it will be until the two galaxies collide.
6. Galactic Communication
How much time would it take to exchange mutual greetings between two civilizations located at opposite ends of the Milky Way, assuming they can communicate at the speed of light?
7. Galactic Trivia
a) What is the Milky Way galaxy's ratio of diameter to its thickness?
b) If 200 billion stars constituting the Milky Way were distributed equally among the present Earth's people, how many stars would each person get?
c) How much time would it take to count all the stars in the Milky Way if you counted one star per second without stopping?
8. Cosmic Expansion
If the universe is expanding at a rate of 70 km/s per megaparsec, how much will the distance between two galaxies that are currently 100 million light-years apart increase after 1 billion years? Assume that the expansion rate remains constant over this time period. (1 Mpc \(\approx 3.26\) million light-years).
9. Doppler Effect
A galaxy is receding from Earth at a speed of \(5 \times 10^6 \text{ m/s}\). It emits light with a wavelength of 486 nm (blue-green). What wavelength will be observed on Earth? Assume non-relativistic Doppler shift for light: \(\lambda_{observed} = \lambda_{emitted} \left(1 + \frac{v}{c}\right)\), where \(v\) is the recession speed and \(c\) is the speed of light. Then use the relativistic Doppler shift formula to find the observed wavelength: \(\lambda_{observed} = \lambda_{emitted} \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}\), and compare the results.
10. Cosmic Microwave Background
The Cosmic Microwave Background (CMB) radiation now has the temperature of about 2.7 K. When it was emitted during the recombination era, it had a temperature of about 3000 K. What was the wavelength of the peak intensity of the CMB radiation at the time of recombination, and what is its wavelength now? Use Wien's displacement law: \(\lambda_{peak} = \frac{b}{T}\), where \(b \approx 2.898 \times 10^{-3} \text{ m K}\) is Wien's constant.