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

Radius(Jupiter) ~ 10x Radius(Earth)

Radius(Sun) ~ 10x Radius(Jupiter)

Radius(Sun) ~ 100x Radius(Earth)

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.

http://www.hep.upenn.edu/slidelib/powersof10.gif

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 ADDINGOR SUBTRACTING POWERS OF 10.

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 109

237,112 = 2.37112 x 105 0.00000004 = 4.0 x 10-8

2. Count the number of places that the decimal point moved;this is the power of 10. The power is negative if the decimalmoved 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

EVERY NUMBER CAN BE EXPRESSED AS A NUMBER BETWEEN 1 AND 10 x POWER OF 10

Scientific notation rules of thumb

baba yxyx +×⋅=××× 10)()10()10(

baba

y

xyx −×⎟⎟

⎠

⎞⎜⎜⎝

⎛=×÷× 10)10()10(

Do not be a perfectionist!Approximations can be a good thing.

Consider Jupiter vs. Sun size comparison:Jupiter radius = 71,492 kmSun radius = 695,000 km, i. e., 9.7x larger

Jupiter radius ≈ 70,000 kmSun 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.

“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

100cm1m = 1

There are 1000 m in a kilometer: so 1000m = 1km

1m100cm = 1and

1000m1km = 1

1km1000m = 1and

Now we multiply by 1 until we get our desired units.

3km = 3km x 1000m1km

x 100cm1m = 3 x 1000 x 100 cm

= 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 milessecond minute60 seconds 60 minutes

hour

= 6.7 x 108 mph!

Speed = DistanceTime

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 light year = (3.0 x 105 km/s) x (3.15 x 107 seconds)

1 year = 3.15 x 107 seconds

Speed of light (in metric units) = 3.0 x 105 km/s

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

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!

The size of things in astronomyTerrestrial planets

Gas giantsGas 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! • 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 Number Distance before baking Distance after baking Speed 1 1 cm 3 cm 2 cm/hr 2 2 cm 6 cm 4 cm/hr 3 3 cm 9 cm 6 cm/hr

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