Transcript 1 light year = 9 x 10 12 km

Astronomical Size and Time Scales:
The Vastness of It All...
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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.
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 = 2.37112 x 105
0.00000004 = 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
( x 10 )  ( y 10 )  ( x  y) 10
a
b
x
a b
( x 10 )  ( y 10 )    10
 y
a
b
a b
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.
“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
1m
100cm = 1
There are 1000 m in a kilometer: so 1000m = 1km
1000m
1km = 1
and
1km
1000m = 1
Now we multiply by 1 until we get our desired units.
1000m x 100cm
x
3km = 3km
1km
1m
= 3 x 1000 x 100 cm
= 3 x 105cm
What about light years? Sounds
like a unit of time...
is
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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
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 astronomy
Terrestrial planets
Gas
giants
Gas
giants
The Solar System, scaled to the size of the
Massachusetts Turnpike
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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(Figure
were1.12)
1 calendar year, then 1 month would
be equivalent to roughly 1 billion
years
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
The
of the
1 funkiest bit1 of
cm all: the expansion
3 cm
2 cm/hr
2
2 cm
6 cm
4 cm/hr
Universe!
3
3 cm
9 cm
6 cm/hr
• 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? 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