# Astronomical Size and Time Scales: The Vastness of It All...

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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

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

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., 102 = 10 x 10 = 100 e.g., 104 = 10 x 10 x 10 x 10 = 10,000 2. Negative powers of 10: reciprocal of positive power e.g., 10-2 = 1/102 = 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.

Multiplying & Dividing Powers of 10
104 x 102 = 10,000 x 100 = 1,000,000 = 106 105 x 10-1 = 100,000 x 0.1 = 10,000 = 104 Rule of thumb: Multiplication: 10n x 10m = 10n+m Division: 10n  10m = 10n-m THERE ARE NO SIMPLE RULES FOR ADDING OR SUBTRACTING POWERS OF 10.

Scientific Notation: expressing large numbers with powers of 10
EVERY NUMBER CAN BE EXPRESSED AS A NUMBER BETWEEN 1 AND 10 x POWER OF 10 6,000,000,000.0 = 6.0 x 109 237,112 = x 105 = 4.0 x 10-8 Two steps: 1. Move the decimal to appear after the first non-zero digit 2. 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 103) x (2 x 104) = (6 x 2) x (103 x 104) = 12 x 107 Division: (6 x 103)  (2 x 102) = (6  2) x (103  102) = 3 x 101

Scientific notation rules of thumb

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

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.

A light year is a unit of distance, not time!
“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!

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

Start by writing down what you know.
There are 100 cm in a meter: so 100cm = 1m 100cm 1m = 1 and = 1 1m 100cm There are 1000 m in a kilometer: so 1000m = 1km 1000m 1km = 1 and = 1 1km 1000m Now we multiply by 1 until we get our desired units. 1000m 100cm 3km = 3km x x = 3 x 1000 x 100 cm 1km 1m = 3 x 105cm

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

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 60 seconds 60 minutes second minute hour = 6.7 x 108 mph! Speed = Distance Time Distance = Speed x Time

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 year = 3.15 x 107 seconds Speed of light (in metric units) = 3.0 x 105 km/s 1 light year = (3.0 x 105 km/s) x (3.15 x 107 seconds) 1 light year = 9 x 1012 km

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.

Finding the Orion Nebula

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!

The size of things in astronomy
Terrestrial planets Gas giants Gas giants

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!!

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

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)

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.

The funkiest bit of all: the expansion of the Universe!
Raisin Number Distance before baking Distance after baking Speed cm cm 2 cm/hr cm cm 4 cm/hr cm cm cm/hr 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.

How can we sleep when the earth is turning
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

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

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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