Astronomy 100

 



Lectures Table of Contents Astro 100

Course Overview and the Scale of the Universe


Outline

  1. Course Format, Philosophy and Requirements

 

1. Course Format, Philosophy, and Requirements

  • Motivation and Goals
  • Lectures and Reading
  • WWW Pages
  • Homework
  • Exams and Grades
  • What is Astronomy?

Powers of 10 


Outline

  1. The Scale of the Universe
  2. Powers of 10 and Scientific Notation
  3. The Speed of Light

    Terms to know

    order of magnitude
    exponent
    scientific notation

1. The Scale of the Universe: How Big is Astronomy?

    Your address in the Universe

Person: 2 meters (~ 6 feet)
Earth radius: 6378 km (~4000 miles)
Average Earth <--> Sun Distance: 1 Astronomical Unit (AU)~ 150,000,000 km
Average Pluto <--> Sun Distance: 39.44 AU ~ 5,900,000,000 km (size of Solar System)
Sun <--> Proxima Centauri (nearest star): 4.2 light year (l.y.) ~ 265,000 AU ~ 42,000,000,000,000 km
Sun <--> Center of Milky Way Galaxy: 25,000 l.y. ~ 1,500,000,000 AU ~ 240,000,000,000,000,000 km
Milky Way <--> Andromeda Galaxy: 2 million l.y.
Size of Observable Universe: 14 billion l.y.




...And that's ONLY THE BEGINNING!

Two ways to express very large (or very small) numbers:

  • Define NEW UNITS (AU, l.y., etc.); or
  • Use Powers of 10 and Scientific Notation

2. Powers of 10 and Scientific Notation

The range of sizes, time, temperature, pressure, density, radiation, etc. etc. in astronomy and physics is so huge that some special techniques are required to keep track of it all.

one 1 = 100 1 = 100 one
ten 10 = 101 0.1 = 10-1 tenth
hundred 100 = 102 0.01 = 10-2 hundredth
thousand 1000 = 103 0.001 = 10-3 thousandth
million 1,000,000 = 106 0.000001 = 10-6 millionth
billion 1,000,000,000 = 109 0.000000001 = 10-9 billionth
etc. ...

bigger

etc. ...

smaller




Names for scales:

Trillion Tera (T) 1012
Billion Giga (G) 109
Million Mega (M) 106
Thousand Kilo (K) 103
...
thousandth milli (m) 10-3
millionth micro (mu) 10-6
billionth nano (n) 10-9
trillionth pico (p) 10-12

Examples:
thousand = 1,000 103 = 10 x 10 x 10 = 101 x 101 x 101 = 101+1+1

million = 1,000,000 106 = 103+3 = 103 x 103 "a million" = "a thousand thousand"

Lengths Expressed as Powers of 10 (VERY round numbers):

atomic nucleus 10-16 m
Hydrogen atom 10-10 m
your height 100 m
earth radius 107 m
earth-sun distance 1011 m
solar system 1013 m
nearest star 1016 m

~ one light year (lyr)

sun to galactic center 1020 m
nearest galaxy 1022 m

106 lyr, or 1,000,000 lyr, or "million" lyr



Scientific Notation is just a way of expressing numbers in two parts:
  • A power of 10 (gives the approximate scale, or "Order of Magnitude"), multiplied by...
  • A number somewhere between 1 and 10 (gives the precise value)
For Example: 15 = 1.5 x 10 = 1.5 x 101 100 = 1.0 x 102 1500 = 1.5 x 103 39466.98 = 3.946698 x 104 1 = 1.0 x 100 0.1 = 1. x 10-1 0.035 = 3.5 x 10-2
Can you see that the power of ten tells you how many digits the decimal place should be moved over?
Examples of some astronomical scales in scientific notation:   1 AU = 150 million km = 150 x 106 km = 1.5 x 108 km 1 yr = 3.15 x 107 s 1 l.y. = (3 x 105 km/s) x 3.15 x 107 s = 9.45 x 1012 km (~ 1.0 x 1013 km) 1 Gyr = 109 yr = 3.15 x 1016 s Your Age (roughly) = 20 yr = (20) x (3.15 x 107 s) = 6.3 x 108 s Age of Universe = 20 Gyr = 20 x 109 yr x (3.15 x 107 s/yr) = 6.3 x 1017 s
 

3. The Speed of Light and Units


speed = distance / time = meters / seconds = m / s


c = speed of light = 3 x 108 m/s

c is constant finite fastest speed there is

Consequences:

It takes time for light to travel over distance

time = distance / speed



Light travel times:

Distance Light Travel Times
earth to sun 1.5x1011 m 5x102s 8.3 minutes
nearest star ~1016 m 3x107s 1 year
nearest galaxy ~1022 m 3x1013s 1 million, or 106 years
"Event Horizon" 2x1026 m 6x1017s 20 billion, 2x1010 years, or 20 Gyr


Lectures Table of Contents Astro 100

Houjun Mo Astronomy 100