# Course Overview and the Scale of the Universe

## Outline

1. Course Format, Philosophy and Requirements

## 1. Course Format, Philosophy, and Requirements

• Motivation and Goals
• WWW Pages
• Homework
• 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?

 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