Lecture 2 Our Place in the Universe (Cont'd)
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Astronomy 110 –1 Lecture 2 Our Place in the Universe (Cont’d) 14/01/09 1 Copyright © 2009 Pearson Education, Inc. A few useful mathematical skills 14/01/09 2 Copyright © 2009 Pearson Education, Inc. Powers of ten 103 = 10 x 10 x 10 = 1000 102 = 10 x 10 = 100 101 = 10 100 = 1 10-1 = 1/10 = 0.1 10-2 = 1/10 x 1/10 = 0.01 10-3 = 1/10 x 1/10 x 1/10 = 0.001 Then: 300 = 3 x 100 = 3 x 102 2,500 = 2.5 x 1000 = 2.5 x 103 14/01/09 3 Copyright © 2009 Pearson Education, Inc. Multiplying & dividing 101 x 101 = 100 = 102 101 x 102 = 10 x 100 = 1000 = 103 102 x 102 = 100 x 100 = 10000 = 104 When multiplying two powers of ten, add the exponents 1000 ÷ 100 = 103 ÷ 102 = 10 = 101 10 ÷ 10 = 101 ÷ 101 = 1 = 100 10 ÷ 100 = 101 ÷ 102 = 1/10 = 10-1 When dividing, subtract exponent of divisor from exponent of numerator 14/01/09 4 Copyright © 2009 Pearson Education, Inc. Powers and roots (104)3 = 104 x 104 x 104 = 1012 Rule of thumb: when raising to a power, multiply exponents What about √(104)? √(104) = 102 taking roots is the same as raising to a fractional power, in this case 1/2 power: √(104) = (104)1/2 = 102 √ is the same as raising to 1/2 power 3√ is the same as raising to 1/3 power 4√ is the same as raising to 1/4 power 14/01/09 5 Copyright © 2009 Pearson Education, Inc. Summary To multiply powers of ten, add exponents: 10n x 10m = 10(n+m) To divide powers of ten, subtract exponents: 10n ÷ 10m = 10(n-m) To raise powers of ten to other powers, multiply exponents: (10n)m = 10(nxm) where m can be fractional for roots. 14/01/09 6 Copyright © 2009 Pearson Education, Inc. Scientific notation All numbers should be expressed as a number between 1 and 10 times whatever power of ten is required Radius of Earth = 6,400 km = 6.4x103 km. Galaxy diameter = 1,000,000,000,000,000,000,000 m = 1021 m. Size of H atom = 0.000,000,000,05 m =5x10-11 m. Rule of thumb: • number of places decimal is moved to the left is the positive power of ten; • number of places decimal is moved to the right is the negative power of ten. 14/01/09 7 Copyright © 2009 Pearson Education, Inc. Basic units used in Astronomy • astronomical unit (AU): average distance between Earth and Sun = 150 million km or 1.5 108 km (about 108 mi or 100 million miles) [Technically = semi-major axis of Earth’s orbit around Sun] • light year: distance that light travels in 1 year = 9.46 1012 km (about 6 1012 miles, or 6 trillion miles) 14/01/09 8 Copyright © 2009 Pearson Education, Inc. Calculating the distance equivalent of a light year [distance that light travels in 1 year] This distance is fixed because light in a vacuum always travels at the same speed = 300,000 km/s or 3 105 km/s (1.86 105 mi/s) Calculation: distance = velocity x time 1 light year = speed of light x 1 year = 3 105 km/s x 1 yr x 365 day/yr x 24 hr/1 day x 60 min/1 hr x 60 sec/1 min = 9.46 1012 km [do exercise by rounding off numbers] 14/01/09 9 Copyright © 2009 Pearson Education, Inc. Working with units A number without a unit has no physical meaning: For example, a salary of 1,000,000 is meaningless without units You cannot add or subtract numbers unless they have the same units. You can multiply units: area is feet x feet = (feet)2, or, volume is meter x meter x meter = (meter)3. You can divide units: speed = miles ÷ time = miles per hour 14/01/09 10 Copyright © 2009 Pearson Education, Inc. Converting Units 1. Converting speed of light from km/s to m/s We know that 1 km =1000 m So: 300,000 km/s = 300,000 km/s x 1000 m/1km = 3 108 m/s 2. Converting from m/s to km/hr 1 m = 10-3 km 1 hr = 60 min x 60 s = 3600 s = 3.6 103 s Or 1 s = 1 ÷ 3.6 103 hr ≅ 2.8 10-4 hr So: 1 m/s = 1 m x 10-3 km/m ÷ ( 1s x 2.8 10-4 hr/s) = 3.6 km/hr 14/01/09 11 Copyright © 2009 Pearson Education, Inc. Other examples How long is 1 light second? 1 light second = distance traveled by light in 1 second distance = speed x time speed of light = 3 105 km/s 1 light second = 3 105 km/s x 1s = 3 105 km In units of miles: 1 mi = 1.6 km 1 light second = 3 105 km x 1 mi/1.6 km ≅ 2 105 mi 14/01/09 12 Copyright © 2009 Pearson Education, Inc. Chapter 1 (Cont’d) 14/01/09 13 Copyright © 2009 Pearson Education, Inc. How did we come to be? Telescopic observations of distant galaxies show that the entire universe is expanding From observed rate, we estimate that it occurred about 14 billion years ago Here is how we think things happened … 14/01/09 14 Copyright © 2009 Pearson Education, Inc. 1. The Big Bang 14/01/09 15 Copyright © 2009 Pearson Education, Inc. 2. Stellar lives and galactic recycling 14/01/09 16 Copyright © 2009 Pearson Education, Inc. 3. Stars manufacture the elements of Earth and Life Stars are born in clouds of gas and Massive stars dust; planets may explode when form in surrounding they die, disks scattering the elements they have produced into space Stars shine with energy released by nuclear fusion, which ultimately 14/01/09 manufactures all elements 17 Copyright © 2009 Pearson Education, Inc. heavier than hydrogen and helium 4. Earth and Life 14/01/09 18 Copyright © 2009 Pearson Education, Inc. How can we know what the universe was like in the past? • Light travels at a finite speed (300,000 km/s). Destination Light travel time Moon 1 second Sun 8 minutes Sirius 8 years Andromeda Galaxy 2.5 million years • Thus, we see objects as they were in the past: The farther away we look in distance, the further back we look in time. 14/01/09 19 Copyright © 2009 Pearson Education, Inc. Quick study exercise: • Try to find the distance to these objects in km using scientific notation Remember: distance = speed x time speed of light = 3 105 km/s 14/01/09 20 Copyright © 2009 Pearson Education, Inc. Example: This photo shows the Andromeda Galaxy as it looked about 1/2 million years ago. Question: When will we be able to see what it looks like now? M31, the Great Galaxy in Andromeda 14/01/09 21 Copyright © 2009 Pearson Education, Inc. • At great distances, we see objects as they were when the universe was much younger. 14/01/09 22 Copyright © 2009 Pearson Education, Inc. Thought Question: Assume the universe is 14 billion years old. Why can’t we see a galaxy 15 billion light- years away? A. Because no galaxies exist at such a great distance. B. Galaxies may exist at that distance, but their light would be too faint for our telescopes to see. C. Because looking 15 billion light-years away means looking to a time before the universe existed. 14/01/09 23 Copyright © 2009 Pearson Education, Inc. Thought Question: Assume the universe is 14 billion years old. Why can’t we see a galaxy 15 billion light- years away? A. Because no galaxies exist at such a great distance. B. Galaxies may exist at that distance, but their light would be too faint for our telescopes to see. C. Because looking 15 billion light-years away means looking to a time before the universe existed. 14/01/09 24 Copyright © 2009 Pearson Education, Inc. What have we learned? • What is our place in the universe? — Earth is part of the solar system, which is in the Milky Way Galaxy, which is a member of the Local Group of galaxies in the Local Supercluster. • How did we come to be? — The matter in our bodies came from the Big Bang, which produced hydrogen and helium. — All other elements were constructed from H and He in stars and then recycled into new star systems, including our solar system. 14/01/09 25 Copyright © 2009 Pearson Education, Inc. What have we learned? • How can we know what the universe was like in the past? — When we look to great distances, we are seeing events that happened long ago because light travels at a finite speed. • Can we see the entire universe? — No. The observable portion of the universe is about 14 billion light-years in radius because the universe is about 14 billion years old. 14/01/09 26 Copyright © 2009 Pearson Education, Inc. 1.2 The Scale of the Universe Our goals for learning: • How big is Earth compared to our solar system? • How far away are the stars? • How big is the Milky Way Galaxy? • How big is the universe? • How do our lifetimes compare to the age of the universe? 14/01/09 27 Copyright © 2009 Pearson Education, Inc. How big is Earth compared to our solar system? Let’s reduce the size of the solar system by a factor of 10 billion; the Sun is now the size of a large grapefruit (14 cm diameter).