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Midterm

AS101 Midterm Study Guide

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Department
Astronomy
Course
AS101
Professor
Victor Arora
Semester
Summer

Description
A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 1 Scale of the Universe The Cosmos - Mostly vacuum (empty space) - Everything we can possibly see if a tiny fraction - Why does it seem like there are so many objects in space? - “dark matter” = means not visible - We only really know what atoms are (the 5%), we don’t even know what dark matter/energy is, it’s invisible The Sun is our Star - Massive ball of glowing gas that generates energy through nuclear fusion - About 100x as wide as the Earth - Source of almost all energy on Earth - Mostly of hydrogen gas - The thing that’s holding the sun together is gravity Planets are less massive than stars (their difference) - Planets are either rocky or gaseous (Earth is a rocky planet) - How are planets different from stars o Planets are less massive o Non-luminous (don’t glow on their own) and spherical  Reflect light instead from the sun  Can only see the planets and moon from reflected light o In orbit around a star (Need to be in orbit) o “Cleared the neighbourhood” of other objects  You kind of dominate the neighbourhood  All of the little objects go away, disappear  Why Pluto is not a planet anymore, hasn’t cleared the neighbourhood  There are several hundred objects out there that’s the same size as Pluto o At least that’s what we think Exoplanets - Over 800 planets confirmed to be orbiting other stars - Thousands of “candidate” exoplanets, observed by the Kepler Space Telescope - Kepler Space telescope is the most recent telescope - Several methods have to have access to a theory before it can be confirmed Some planets have satellites - Satellite – an object in orbit around a planet, anything that orbits around a planet - Natural satellites are also known as “moons” - Saturn doesn’t have the most, Jupiter has more Other objects in the solar system - Asteroid: a small, rocky object orbiting a star - Comet: a small, icy object that orbits the sun - Comets can grow tails near the Sun - If a thing isn’t quite spherical, then gravity didn’t form it o Gravity pulls on all sides equally, so therefore should be a sphere - Comet’s tails can be very long, ironic to call it a small icy object Eris - The planet that knocked Pluto out of being classified as a planet - Slightly bigger than Pluto Planets - Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune - Earth is the massive out of the terrestrial planets - Venus is the sister planet of Earth o Just because almost the same size (just a little bit smaller) A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 2 Galaxies: “cities” of the Cosmos - A large system of dark matter, stars, gas, and dust, all bound together by their combined gravity - Pictured is the spiral galaxy M83 - Not all galaxies are spirals - Galaxy – where a star is born and dies Nebulae - Nebulae – Clouds of gas and/or “dust” within galaxies - Raw materials for new stars from previous generations - They recycle; stars die, the matter erupts, the same material is used again for others stars Star clusters - Different types of clusters: open and global - Open clusters: 1000s of stars - Globular clusters: 100000s of stars - Our Sun probably formed in an open star cluster but has since “moved out” Galaxy groups and clusters - A group of galaxies (a few dozen up to thousands) all held together gravitationally - Galaxies go with each other Many clusters form a supercluster which make up the cosmic web - Supercluster – from a bunch of clusters Summary: we are the 5% - The Universe is mostly made of invisible matter and energy - The Universe if mostly empty space - But the Universe is a very big place - Walls – made up of cluster of galaxies - We are the 5%, we are the atoms - Galaxies made up of stellar systems, nebulae, and star clusters - Walls SuperclustersGalaxy clustersGalaxies(Nebulae, star clusters) Stellar systems stars, planets, small objects Powers of 10 Models in science - In general, a model is something that represents reality - A scientific model is a hypothesis that describes reality and has withstood observational/experimental tests - We can also develop conceptual models to help us think about how nature works - We will be looking at some scale models (miniature or shrunk down versions) Scale model: the solar system - How do the sizes of the planets compare to the distances between them? - What if we shrunk the solar system by a factor of about 45 billion? - Sun  radius = 15mm - Earth  radius = 0.1mm - Jupiter  radius = 1.6mm - Neptune  radius = 0.5mm - At this scale, from the Sun: Earth is 3m away, Jupiter is 17m away, Neptune is 99m away - The sizes of the planets are tiny compared to the distances between them The astronomical unit - We can specify distances in the solar system by comparing them to the average Earth-Sun distance - 1AU = 150,000,000km = 150,000,000,000m - A planet twice as far from the Sun would be 2AU away There has to be a better way - What if we just specified how many zeroes a number has? 1 2 3 - This is known as scientific notation. For example: 10 = 10 , 100=10x10=10 , 1000=10x10x10=10 - 1 Googol = 10 100 A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 3 Representing large numbers - The Earth is on average 150,000,000,000m from the Sun - In scientific notation we would write this as a coefficient between one and ten, multiplied by the appropriate power of ten - Hint: just count the numbers of places the decimal would move - 150,000,000,000m=1.5x10 11 Doing math with exponents - To multiply two (or more) numbers written in scientific notation, just 1. Multiply the coefficients (if there are any) 2. Add the exponents 1 1 2 - For example: 10x10=10 x10 =10 10 x10 =10 5 Clicker - There are an estimated 100 billion galaxies in the universe with, on average, 100 billion stars per galaxy. How many stars are there in the universe? o 10 22 Clicker - Eta Carinae is a massive star located 10 000 light years away and is expected to undergo a violent explosion known as a supernova. If this star went supernova in 2000 BCE, how long would it be from today until we know about it? o 6000 years How far away are the stars? - The nearest star system is Alpha Centauri: 4.1x10 km 13 - Using our scale from our model solar system: 60 billion actual km = 1 scale km, puts Alpha Centauri at 683km away, in NYC Light-travel and look-back time - But light has a finite speed: 300,000km/s - In other words, this star is so far away that we are seeing it as it looked in the past - Imagine you can walk at rate of 3km/hr; in one hour, you will walk 3km o Let’s call this a “walk-hour” - In one year (8760 hours), you will walk 26280km o Let’s call this a “walk year” 13 - A light year (is the distance light travels in one year) is about 10 km (ten trillion km!) - So Alpha Centauri is about 4 light years away Distances in the universe - The further an object appears to be in space, the further we are looking back in time o The Sun: about 8 light minutes o Alpha Centauri: 4 light-years o Andromeda Galaxy: 2 million light years o Observable universe: 13.82 billion light-years - Galaxy is 2 million light-years from the Earth - This means that it takes 2 million years for its light to reach us - This means that this picture shows this object as it was 2 million years ago Summary - The stars, planets, and galaxies are separated by fantastic distances - We can use models, scientific notation, and appropriate distance units to tame these large numbers - We see the stars and galaxies as they were, not as they are Observing Part 1 Recap and preview - There are different objects at different scales in the visible universe, but it is mostly invisible - Objects in the universe are separated by astronomical distances - Our place in the cosmos is our observatory of the universe A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 4 How the earth is moving - Perihelion: nearest points to the Sun (147.1 million km) - Aphelion: furthest point from the Sun (152.1 million km) - Average distance: 1AU = 149.6 million km - Two basic motions: 1. Revolves around (“orbits”) the Sun 2. Rotates on its (tilted) axis - Rotation is responsible for rising and setting of the sun The rotating Earth and you! - The Sun rises in the East and sets in the West - To a moving observer, stationary objects appear to move in the opposite direction as the observer’s motion - The Earth rotates from west to east - The Earth rotates counter-clockwise when viewed from the North Pole (you’re on Earth) The celestial sphere - A conceptual model of the sky: o An imaginary sphere of very large radius surrounding the Earth o A very large crystal sphere that completely surrounds the Earth - Assumptions: every model has ssumptions o Objects in the sky appear to be attached to the rotating celestial sphere - Allows us to specify the direction to an object in the sky and how it moves from night to night The celestial sphere model - From the inside, we can see exactly one-half of the entire sky at any given time, from the horizon up to the zenith (directly overhead) - The North and South Celestial Poles are directly above with the Earth’s North and South poles - The Meridian is the line passing through the North point on the horizon, through the Zenith, and to the South point - All of the points don’t move on the celestial sphere as long as you don’t move Celestial sphere: inside view - In the northern hemisphere, stars that never appear to set are located near the: North celestial pole - These are called circumpolar stars because they appear to circle the pole - Stars go in a circle motion o Some appear to set and rise because they go below the horizon - The North Celestial pole is near the star Polaris - Stars reach their highest points when they cross the: meridian o True for any star even the Sun o Called the high noon o Where am and pm comes from o Am is when the sun is before the meridian and pm is when after Terrestrial coordinates - We specify locations on Earth using latitude and longitude - Longitude: in degrees East or West of the Prime Meridian - Latitude: in degrees North or South of the Equator - On the Earth, intersecting lines of longitude and latitude form a grid - Imagine this grid projected outward onto the celestial sphere - Prime meridian = the dotted line in the middle of diagram Celestial coordinates - We specify positions in the sky using Right Ascension (RA) and declination (Dec) - Right ascension: in hours East of the Vernal Equinox (from 0h to 24h) - Declination: in degrees North (+) or South (-) of the Celestial equator (from +90 degrees to -90 degrees) - Vernal equinox – right ascension is 0 A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 5 Latitude affects what you can see - Recall: we can only see one-half of the sky at one time - The half that we see at a given time of night changes depending on: o The position of the Earth along its annual orbit o The latitude of the observer Clicker - Which of the following positions is closest to the South celestial pole? o RA = 14h, Dec = -88 degrees - You’re stranded on a deserted island and forgot your astronomy textbook! You locate the pole star Polaris at 15 degrees above the northern horizon. What is your latitude? o 15 degrees north o If you see Polaris (north star), you must be in the north Summary: part one - Objects in the night-sky rotate due to the Earth’s rotation on its axis - The celestial sphere is a model that helps us map out the relative positions and the nightly motions of these objects - What we see in the night-sky depends on our latitude Observing Part 2 Recap - The Earth’s rotation on its axis causes objects in the night-sky to rotate as well - We can specify the positions of these objects and visualize their motion using the celestial sphere model - The stars that we can see, and how they move over the course of a night, both change with latitude Precession: a slow wobble - The sun and moon are unevenly pulling on the slight (43km) bulge around the Earth’s equator - This causes a very slow but regular wobble of the Earth’s axis o The orientation of the axis changes but it remains tilted at 23.5 degrees - The star Polaris will trace the circle that Earth slowly makes (26 000 years to complete one full circle) Precession changes the NCP - This very slowly changes the position of the NCP, and all the other coordinates - Catalogues of stellar coordinates are slightly adjusted only every 50 years The constellations: then - The constellations are arbitrary patterns of stars invented, mostly, by ancient cultures The constellations: now - Today, astronomers officially recognize 88 constellations - The sky is divided into parcels that each contain the constellation and other stars of objects in the same part of the sky Stars in the constellations - The stars in a constellation are not at the same distance from the Earth, just in the same direction Measuring angular distances - You can measure the angular sizes and separations on the celestial sphere using degrees - The angular size of an object decreases the further you are separated from it - The Meridian spans a distance of 180 degrees - Rule of pinky: pinky held at arm length = 1 degree - Rule of first: fist held at arm length 10 degrees Measuring apparent brightness - Astronomers sometimes specify how bright an object would appear the naked eye using the magnitude scale - For historical reasons, the scale runs backwards - Our eyes are non-linear detectors: each step is a factor of 2.5x brighter - The professional astronomers measure the “flux” (the rate of light energy collected per unit area) A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 6 - If we don’t know how far away the star is, its apparent brightness does not tell us about its true (absolute) power output - The smaller the number is, the brighter the star is - The dimmest thing you can see with the naked eye is 6 magnitude - We can’t tell the star’s brightness power if we don’t know the distance Sidereal and solar days - Recall: the two basic motions of the Earth are rotation and revolution - How can we define what a “day” should be? Two ideas o Solar day: the average time between successive Meridian crossings for the Sun (24h) o Sidereal day: the time between successive Meridian crossings for any other star (23h 56m) - A solar day is longer than a sidereal day because the Earth has moved along its orbit so it takes a bit longer for the observer on the Earth to line up with the Sun again - Sun and stars are the highest when they cross the meridian - For any other star, it takes shorter than the Sun to cross the meridian Yearly variation - This slight difference means that the stars rise about 4 min earlier each night - Over the course of a year, the constellations we see at night time change - The underlying cause of the change is the Earth’s revolution around the Sun - The stars are moving each night - Have to go through one year for the constellations to go back to the same spot (the same view of the night sky) Clicker - What is the brightest star in the night sky? o Sirius (It is “seriously” bright) - Sirius is further away than Alpha Centauri; which star has a greater absolute power output? o Sirius Summary: Part 2 - Constellations are invented patterns used to help demarcate and find our way around the sky - The apparent brightness of stars is measured using a non-linear scale that runs backwards - The Earth’s revolution causes different constellations to be visible through the year Seasons Recap: - Objects in the sky move in circles around the celestial poles due to the Earth’s rotation on its axis - What we see in the night-sky depends on our latitude Recall: the orbit of the Earth - The Earth’s orbit is nearly-circular - By what percent does the distance from the Sun vary through the year? - (152.1-147.1)/147.1=0.034 or 3.4% - Is that enough to make a difference? Compare ideas to “real-world” - In January, the average daytime high temperature in o Waterloo (latitude 43 degrees North) is: -3 degrees C o Christchurch, New Zealand (latitude 43 degrees South) is: 23 decrees C - What might we conclude about the seasons in opposite hemispheres of the Earth? o At the same time (and, therefore, distance from the Sun), opposite hemisphere have opposite seasons - Also: since the Earth’s orbit is pretty much a circle, the distance is almost the same year round anyways - Conclusion: distance from the Sun does not cause the seasons Annual motion of the Earth - The Earth revolves once around the Sun in 365.25 days and remains tilted at 23.5 degrees - The ecliptic is the plane of the Earth’s orbit around the Sun - The amount of solar energy received in either hemisphere varies through the year due to the tilt A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 7 - The Earth’s orbit is more of like a circle rather than an oval Northern summer solstice: 6/21 - Northern hemisphere: sunlight hits the surface at a nearly perpendicular angle o Energy is more concentrated o Start of summer, first day of summer o The longest day of the year o When the sun shines on Earth at a perpendicular angle (less likely for shadows) - Southern hemisphere: sunlight hits the surface at a grazing angle o Energy is spread out o Start of winter Northern winter solstice: 12/21 - Northern hemisphere: sunlight hits the surface at a: grazing angle o Energy is spread out o Start of winter, first day of winter o South is more faced on compared with the Sun - Southern hemisphere: sunlight hits the surface at a: nearly perpendicular angle o Energy is more concentrated o Start of summer The equinoxes: 3/21 or 9/21 - Days with roughly equal amounts of daylight and darkness, everywhere on Earth o The same amount of day time hours and night time hours anywhere on Earth - Summer = shorter shadows, winter = longer shadows - Mark the beginning of Spring (vernal) or fall (autumnal) - On the equinox, the sun is crossing the celestial equator Apparent annual motion of Sun - Recall: the stars rise 4 min earlier every night  they move westward - On the celestial sphere, the Sun moves Eastward with respect to the “background stars” - We can also think of the ecliptic as the apparent yearly path of the Sun amongst the stars - The Sun spends half the year north of the celestial equator (CE) and half the year south of the CE o Vernal equinox: Sun crosses CE heading North o Summer solstice: Sun at furthest point north from CE o Autumnal equinox: Sun crosses CE heading south o Winter solstice: Sun at furthest point south from CE Length of days - The Sun rises and sets at different times through the year - In the Northern hemisphere, there are more daylight hours when the Sun is further North - More daylight hours in the summer means more energy from the Sun is received at the surface per day Summary - Observations: o Earth keeps nearly the same distance from the Sun o The seasons are opposite in opposite hemispheres - Model: the Sun is higher in the sky in Summer o More efficient warming when the sunlight is nearly perpendicular to the Earth’s surface o More daylight hours means more time for warming - The longest day of the year is the Summer solstice - As the Earth now revolves around the Sun, the Sun migrates southward in the sky and the amount of daylight decreases - On the autumnal equinox, the amount of daylight is equal to the amount of darkness - On the winter solstice, the sun is the furthest south in the sky; it is the shortest day of the year - As the Earth continues to revolve around the Sun, the Sun migrates northward in the sky and the amount of daylight increases - On the Vernal Equinox the amount of daylight is equal to the amount of brightness A S 1 0 1 M i d t e r m E x a m N o t e s E d w i n a C h e u n g | 8 Lunar Phases and Eclipses The Earth-Moon system - The moon orbits the Earth in a slightly elliptical path once in approximately one month (“moon-th”!) How does the moon shine? - The moon shines by reflected light from the Sun - Only half of the spherical moon is illuminated at any given time (just like the Earth) Describing the phases The moon rotates - This must be the case since we only ever see same side of moon o There is no permanently “dark side” of the moon, only a near-side and a far-side - The moon’s librations allow us to see 59% of the surface over the course of a lunar cycle How long is a moon-th? - How long does the moon take to orbit the Earth once? o Reference point: background stars o Time: 27.32 days  sidereal month - How long does the lunar phase cycle take? o Reference point: the Sun o Time: 29.53 days  synodic month Summary so far - The phases of the Moon are a consequence of its position along its orbit with respect to the Sun - Different parts of the near-side of the Moon become illuminated at different times in its orbit - The Earth’s shadow plays no role o Consider the shape of the line dividing day and night Earth-Moon system and the Sun - Both orbits lie in
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