Homework Assignment #1

Transcription

1 Homework Assignment #1 There will be 5 homework assignments. Each one will be handed out on Wednesday, and due the following Wednesday at the BEGINNING of class. You are free to work in groups, but make sure the final homework that you hand in is in your OWN words. If you want FULL credit, make sure you do the following: Be NEAT! If I can t read it, I can t give full credit Put a circle around each problem number Put a box around all numerical answers Put your name, the date, and the homework ksdljfkljsnumber in the upper right hand corner Staple multiple sheets together NO late homework!

2 Observing Projects What's the point of astronomy if you don't ever look in the sky? These observing projects are meant to be a fun and instructive way to get you outside to admire the beauty of the heavens--because really, that's what astronomy is all about. Due Monday, June 29nd at the beginning of class. It will not be accepted late! You must complete TWO observing projects. Each will be given equal weight to your course grade (12.5% each) Each project consists of a set of observations and a ~1 page write up. Please type your write up and stable any additional figures or other materials. Be sure to start working EARLY. Many of the projects take multiple days or weeks to complete, and you don t want to get stuck with bad weather!

3 Observing Projects List 1. The Setting Sun: How does the position of the Sun change each night? What does this tell you about the Earth-Sun configuration? 2. The Phases of the Moon: Learn about how the phases of the Moon change each night. 3. Stargazing at the Lawrence Hall of Science: Experience looking at objects through real telescopes. 4. The Sun s Path: Use a sundial to investigate the motion of the Sun each day. 5. Angles and Parallax: Learn how to measure the size of the Moon using angles and the distances to stars using parallax.

4 Light, Matter, and Energy Today s Lecture: What is light and why is it important for astronomy? Wavelength, frequency, and the speed of light Introduce the concept of black bodies The relation between color and temperature Show how we can measure a star s radius from its brightness and color.

5 What is light? When you pass white light through a prism you see a rainbow. Roy G. Biv - Unfortunately, indigo is somewhat obsolete

6 Qutb al-din Persian astronomer ( ) First to correctly explain rainbow as coming from light being refracted by water droplets. He tested his theory by filling glass sphere s with water.

7 Electric fields The electric field of a stationary positive charge. Magnetic fields Magnetic field of a stationary magnet.

8 Electromagnetic Waves Electromagnetic waves consist of self-propagating, oscillating electric and magnetic fields that are perpendicular to each other and to the direction of motion.

9 Wavelength and Frequency λ (Greek letter lambda ) = wavelength = distance from one crest to the next ν (Greek letter nu ) = frequency = number of times per second a crest passes some fixed point Note that ν -1 = 1/ν = P = Period

10 Wavelength, Frequency, and Speed λν = v = c, the speed of light! Since c is a constant, λ and ν are inversely proportional!

11 Spectrum of visible light Plot brightness (or intensity) as a function of color (or wavelength) for a quantitative analysis of a spectrum. Intensity V I B G Y O R Wavelength (in nanometers)

12 The Wavelength of Visible Light The typical unit of measurement for λ is the Ångstrom (Å) = m= 0.1 nanometer Red = 6500 Å Yellow = 5800 Å Green = 5300 Å Blue = 4800 Å

13 The Electromagnetic Spectrum γ (gamma) rays: l < 0.1 Å X-rays: Ultraviolet (UV): Visible (optical): Infrared (IR): Radio: ~ Å ~ Å ~ Å ~7000 Å - 1 mm ~1 mm - 10 km and more There is NO qualitative difference between different types of electromagnetic waves. They have different frequencies and wavelengths, but the SAME speed, c (independent of the observer or source s speed). But the the detection techniques can vary greatly!

14 Photons (wave or energy packets) Light also behaves like discrete particles called photons White light (sunlight) contains all of the colors Collectively, lots of photons with the same color (same wavelength) make an electromagnetic wave

15 A photon has no mass, but its energy is E = hν h = Planck s constant, which is a VERY small number (6.63 x in our units). Energy Frequency (ν) Photons of higher energy (E) have a higher frequency (ν) and shorter wavelength (λ) E = hν = hc/λ (since c = λν)

16 Wave/particle duality Photons are both a wave and particle! Sometimes they act like a wave, and sometimes they act like a particle. It depends on what kind of experiment you re doing. In fact, everything is both a wave and particle at the same time (for example, electrons). This is one of the fundamental discoveries of quantum mechanics. λ = h / (m v) Even YOU are both a particle and a wave. You just seem more like a particle because the wavelength is so small. The more momentum something has, the smaller the wavelength.

17 What composes a star s spectrum? Stars are huge, opaque, luminous balls of gas held together by gravity. Very hot inner parts emit continuous radiation. This gives the spectrum it s shape. Cooler outer layers absorb certain wavelengths, creating absorption lines. From this we derive the chemical composition.

18 The Color Indicates Temperature The wavelength at which the spectrum peaks (which determines the color) is a measure of the surface temperature. Ignoring the absorption lines, the spectrum of a star resembles a black body (a perfect absorber and emitted with no reflected or transmitted light). Thermal emitter Brightness λ peak Wavelength (λ) The hotter something is, the bluer it is. Blue stars are hotter than yellow stars, which are hotter than red stars.

19 Temperature Scales F C K Lowest temperature Water freezes Water boils K = C F = (9/5)C + 32 C = Celsius (Centrigrade) F = Fahrenheit K = Kelvin

20 Different Temperature Black Bodies A 5000 K star peaks in the red, while a 6000 K star peaks in the yellow. Even hotter stars are blue. Is this backwards to our intuition?!

21 Reflectors vs. Thermal Emitters Most of the light we see is due to reflection, which doesn t tell us about the temperature. Everything also emits thermally, it s just usually subdominant to the reflected visible light.

22 Hotter objects emit shorter λ Cooler objects emit longer λ T(K) λ peak (Å) Wien s Law λ peak T = constant 2.9 x 10 7 Å K

23 Stefan-Boltzmann Law The Stefan-Boltzmann Law tells you how much energy per unit area is emitted from a black body. ε = σ T 4 (σ = Greek letter sigma = constant) Energy per area per sec Because of the T 4 power, hotter object emit MUCH more energy per area than cold objects. Example: 6000 K 3000 K If a star is 2x as hot, it emits 16 times more power! (if the two stars have the same surface area)

24 Luminosity (or Power) This is the amount of energy emitted per second by the entire object. For a sphere of radius R, Surface Area = 4πR 2, so that If we know both L and T, then we can derive the radius, R!

25 Revisiting Orion The stars Betelgeuse and Rigel have about the same brightness and about the same distance, but are very different colors. What must be different between Betelgeuse and Rigel?

26 Revisiting Orion The radius (and thus surface area) of Betelgeuse must be larger to output the same power as Rigel! In fact, Betelgeuse is 1000x the size of the Sun, while Rigel is merely 62x the size of the Sun. Both have luminosities that are ~100,000x that of the sun!