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Astronomical Size and Time Scales: The Vastness of It All... Brief math review The SIZE of the Universe The AGE of the Universe The FUNKINESS of the Universe Reading assignment: Chapter 1

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Radius(Jupiter) ~ 10x Radius(Earth) Radius(Sun) ~ 10x Radius(Jupiter) Radius(Sun) ~ 100x Radius(Earth)

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Ch.1: Our Place in the Universe 15,000,000,000,000,000,000 miles!

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Brief review of some math... (see Appendix C in Cosmic Perspective) 1. Powers of 10: number of times to multiply 10 by itself. e.g., 10 2 = 10 x 10 = 100 e.g., 10 4 = 10 x 10 x 10 x 10 = 10, Negative powers of 10: reciprocal of positive power e.g., = 1/10 2 = 1/100 = 0.01 Rules of thumb: A positive power indicates the number of zeros that follow the 1. A negative power indicates the number of places to the right of the decimal point.

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Multiplying & Dividing Powers of x 10 2 = 10,000 x 100 = 1,000,000 = x = 100,000 x 0.1 = 10,000 = 10 4 Rule of thumb: Multiplication: 10 n x 10 m = 10 n+m Division: 10 n 10 m = 10 n-m THERE ARE NO SIMPLE RULES FOR ADDING OR SUBTRACTING POWERS OF 10.

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Scientific Notation: expressing large numbers with powers of 10 Two steps: 1. Move the decimal to appear after the first non-zero digit 6,000,000,000.0 = 6.0 x ,112 = x = 4.0 x Count the number of places that the decimal point moved; this is the power of 10. The power is negative if the decimal moved to the right; positive if moved to the left. Shortcuts: Multiplication: (6 x 10 3 ) x (2 x 10 4 ) = (6 x 2) x (10 3 x 10 4 ) = 12 x 10 7 Division: (6 x 10 3 ) (2 x 10 2 ) = (6 2) x (10 3 10 2 ) = 3 x 10 1 EVERY NUMBER CAN BE EXPRESSED AS A NUMBER BETWEEN 1 AND 10 x POWER OF 10

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Scientific notation rules of thumb

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Do not be a perfectionist! Approximations can be a good thing. Consider Jupiter vs. Sun size comparison: Jupiter radius = 71,492 km Sun radius = 695,000 km, i. e., 9.7x larger Jupiter radius ≈ 70,000 km Sun radius ≈ 700,000 km Therefore, the Sun is about 10x larger

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Units of Measurement Distance can be measured in km, cm, miles, yards, furlongs, etc. Units are extremely helpful, but you must get them right!! In this course, we will encounter a variety of units, and we’ll have to make conversions.

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“You’ve never heard of the Millennium Falcon? It’s the ship that made the Kessel Run in less than 12 parsecs. She’s fast enough for you, old man.” Bzzzzt. A parsec is a unit of distance, not time! A light year is a unit of distance, not time!

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Converting Units: a worked example Question: How many cm are there in 3 km?

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Start by writing down what you know. There are 100 cm in a meter: so 100cm = 1m 100cm 1m = 1 There are 1000 m in a kilometer: so 1000m = 1km 1m 100cm = 1and 1000m 1km = 1 1km 1000m = 1and Now we multiply by 1 until we get our desired units. 3km = 3km x 1000m 1km x 100cm 1m = 3 x 1000 x 100 cm = 3 x 10 5 cm

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What about light years? Sounds like a unit of time... is ??

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What about light years? Sounds like a unit of time... Nothing can travel at infinite speed. Light is the fastest thing in the universe, but even light travels at a finite speed. Speed of light = 186,000 miles secondminute 60 seconds 60 minutes hour = 6.7 x 10 8 mph! Speed = Distance Time Distance = Speed x Time

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One light year is the distance that light travels in one year. Distance = Speed x Time 1 light year = (speed of light) x (1 year) 1 light year = (3.0 x 10 5 km/s) x (3.15 x 10 7 seconds) 1 year = 3.15 x 10 7 seconds Speed of light (in metric units) = 3.0 x 10 5 km/s 1 light year = 9 x km

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Looking back in time: astronomers have a time machine! Sort of. Light, although fast, travels at a finite speed. It turns out that it takes: – 8 minutes to reach us from the Sun – 8 years to reach us from Sirius (8 light-years away) – 1,500 years to reach us from the Orion Nebula The farther we look out in the Universe, the farther back in time we see.

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Finding the Orion Nebula

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Your ancestors may surprise you In the early history of the Universe, there was nothing but hydrogen and helium. All other elements were manufactured deep in the cores of stars by nuclear fusion reactions, or in nuclear reactions that occur when a massive star ends its life in a violent explosion called a supernova. Seek to be one with the cosmos? You already are!

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The size of things in astronomy Terrestrial planets Gas giants

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The Solar System, scaled to the size of the Massachusetts Turnpike If the Earth is a 12” globe at Boston University, the Sun would be a 10-story building at South Station in Boston. If the speed of light were reduced to 16 mph, after a ray of light leaves the sun, it would take: 3 minutes to get to Mercury 6 minutes to get to Venus (which would be near Fenway Park) 8 minutes to get to Earth at BU 3 seconds past BU, the Moon 12.5 minutes to arrive at Mars 43 minutes to reach Jupiter 1 hour & 17 minutes to reach Saturn (Framingham exit) 1 hr & 38 min: Uranus 2 hours & 9 minutes to make it out to Neptune (Palmer exit) 5 hr & 28 min: last stop in the Solar System, Pluto Nearest star to the Sun (alpha Centauri): 4.4 years! Nearest big galaxy (the Andromeda galaxy): 2.2 million years!!

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The Age of the Universe If the entire age of the Universe were 1 calendar year, then 1 month would be equivalent to roughly 1 billion years

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The Age of the Universe If the entire age of the Universe were 1 calendar year, then 1 month would be equivalent to roughly 1 billion years (Figure 1.12)

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The funkiest bit of all: the expansion of the Universe! Mostly all galaxies appear to be moving away from us. The farther away they are, the faster they are moving. –Just like raisins in a raisin cake; they all move apart from each other as the dough (space itself) expands.

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The funkiest bit of all: the expansion of the Universe! Mostly all galaxies appear to be moving away from us. The farther away they are, the faster they are moving. –Just like raisins in a raisin cake; they all move apart from each other as the dough (space itself) expands. Raisin NumberDistance before bakingDistance after bakingSpeed 1 1 cm 3 cm 2 cm/hr 2 2 cm 6 cm4 cm/hr 3 3 cm 9 cm 6 cm/hr

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How can we sleep when the earth is turning? The many ways the Earth moves... Contrary to our perception, we are not “sitting still.” We are moving with the Earth. – and not just in one direction The Earth rotates around it’s axis once every day

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The Earth orbits around the Sun once every year The Earth’s axis is tilted by 23.5 º

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Our Sun moves relative to the other stars in the local Solar neighborhood Our Sun and the stars of the local Solar neighborhood orbit around the center of the Milky Way Galaxy every 230 million years Reading assignment for next lecture: Chapter 2

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