demoquiz 5

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University of Washington *

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101

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Astronomy

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Jan 9, 2024

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Demoquiz 5 [Doppler Shifts & Making the Cosmic Microwave Background] Astronomy 101 University of Washington The first light from the Big Bang, the cosmic microwave background, is believed to be the relic radiation from the era of “recombination” when the hydrogen nuclei had formed and captured the electrons so that the light went free. Measurements of Hubble’s constant is currently a hot area of research since measurements of Hubble’s constant from the CMB are statistically different than measurements from local objects like supernovae. In this Demoquiz you will explore how these calculations work and you will explore painting pinecones to remind yourself of the significance of patterns in nature. 1. (5pts) Explore what are three ways we use shifted spectra to understand physics of the universe? Shifted spectra can tell us what elements are present in distant celestial objects. We can measure the redshift to determine something’s velocity and distance from Earth. We can use shifted spectra to study the CMB which tells us about physics in the early universe. 2. (5pts) Calculate Cosmic Microwave Background. The cosmic microwave background (CMB) radiation is a thermal quasi-uniform black body radiation which peaks at 2.725 K in the microwave regime. Using the perfect black body radiation formula (Wien’s law) what is the wavelength associated with this light? Wein ’ s λ_max = b / T b = 2.898 × 10^(-3) m·K) λ_max = (2.898 × 10^( -3) m·K) / 2.725 K λ_max ≈ 1.06 × 10^( -3) m or 1.06 millimeters 3. (5pts) Calculate You measure the CMB to be shifted by 1.3E-5 meters, what relative velocity does this correspond to? HINT: use 𝑣 𝑐 = 𝛥𝜆 𝜆 𝑜 v / (3.00 × 10 ^8 m/s) = (1.3E-5 m) / (1.06 × 10^(-3) m) 3.73 × 10^(-2) * (3.00 × 10^8 m/s) v ≈ 1.12 × 10^7 m/s relative velocity of 11.2 million meters per second
Demoquiz 5 [Doppler Shifts & Making the Cosmic Microwave Background] Astronomy 101 University of Washington 4. (5pts) Calculate If you assume that Hubble’s constant is 𝐻 𝑜 = 70 𝑘𝑚/(𝑠𝑒𝑐 ∗ 𝑀𝑝𝑐) , how far away is this patch of CMB you observed? HINT: use 𝑣 𝑟 = 𝐻 𝑜 𝐷 𝐻 𝑜 = 70 km/(sec * Mpc) * (1000 m/km) * (1 Mpc / 3.09 × 10^19 km) 𝐻 𝑜 = 2.27 × 10^(-18) s^(-1) 𝑣 𝑟 = 𝐻 𝑜 𝐷 𝐷 = 𝑣 𝑟 /𝐻 𝑜 D = (11.2 × 10^6 m/s) / (2.27 × 10^(-18) s^(-1)) D ≈ 4.93 × 10^24 meters 5. (10pts) Painting Find 2 pinecones of the same type and distinction, with the end part intact (where the pinecone attached to the tree). Using white-out or a sharpie or other marking type thing, identify the two different sets of spirals, one set on each of the pinecone. Include your thumb or finger in each picture, and under the picture indicate which Fibonacci number each picture represents. Fibonacci 3 Fibonacci 5
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