Download Introduction to Astronomy

Lecture 2
The Scale of the Cosmos
POWERS OF 10 & SCIENTIFIC NOTATION
•
In science and especially in astronomy, you have to deal
with very large numbers and very small numbers.
•
For example, the number of kilometers in a light year is
approximately 9,500,000,000,000 (9.5 trillion).
•
The diameter of the hydrogen atom is 0.000000013
centimeters (13 billionths).
To manage large numbers and small numbers, professionals
make use of powers of 10 and scientific notation.
10,000,000,000 (10 billion) years is the approximate age of the
Milky Way Galaxy (MWG). Instead of writing out the large
number in expanded form (i.e., 10,000,000,000) it is written as
as a power of 10…1010).
10
9
8
7
6
5
4
3
2
1
10,000,000,000.
1010
The number of place values to move
the decimal behind the 1.
The diameter of the MWG is approximately 100,000
(100 thousand) light years.
5
4
3
2
1
100,000.
105
The number of stars in the MWG is approximately
100,000,000,000 (100 billion).
11
10
9
8
7
6
5
4
3
2
1
100,000,000,000.
1011
Large numbers have a positive exponent when written as a
power of 10. Small numbers have a negative exponent when
written as a power of 10.
Consider the small number 0.000000001 (1 billionth):
1
2
3
4
5
6
7
8
9
0.000000001
10-9
The number of place values to move
the decimal behind the 1.
Positive Exponents
Negative Exponents
100 = One
101 = Ten
102 = One Hundred
103 = One Thousand
104 = Ten Thousand
105 = One Hundred Thousand
106 = One Million
107 = Ten Million
108 = One Hundred Million
109 = One Billion
1010 = Ten Billion
1011 = One Hundred Billion
1012 = One Trillion
100 = One
10-1 = One Tenth
10-2 = One Hundredth
10-3 = One Thousandth
10-4 = Ten Thousandth
10-5 = One Hundred Thousandth
10-6 = One Millionth
10-7 = Ten Millionth
10-8 = One Hundred Millionth
10-9 = One Billionth
10-10 = Ten Billionth
10-11 = One Hundred Billionth
10-12 = One Trillionth
SCIENTIFIC NOTATION
A number is put into scientific notation if it is in the form
d x 10n (large number) or d x 10-n (small number) where d is a
decimal between 1 and 10 (i.e., 1 ≤ d < 10).
The distance to the Sun is about 150,000,000 km
150,000,000 = 1.5 x 108
8
7
6
5
4
3
2
1
150,000,000.
1.5 x 108
10
9
8
7
6
5
4
3
2
1
38,000,000,000.
3.8 x 1010
1
2
3
4
5
6
7
0.000000478
4.78 x 10-7
1
2
3
4
5
0.000031
3.1 x 10-5
To multiply or divide powers of ten you:
Add the exponents when you multiply
Subtract the exponents when you divide
105 * 107 = 105+7 = 1012
103 * 104 = 103+4 = 107
108 = 108-5 = 103
105
1012 = 1012-3 = 109
103
ARITHMETIC OF NUMBERS IN
SCIENTIFIC NOTATION
(2.1 x 103) . (1.5 x 106) = (2.1 . 1.5) x (103 . 106) = 3.15 x 109
Multiply the Decimals
Add the Exponents
7.2 x 1017 = 7.2 x 1017 = 2.4 x 107
3 x 1010
3
1010
Divide the Decimals
Subtract the Exponents
When it comes to the arithmetic of numbers in
scientific notation, let your fingers do the
walking…USE YOUR CALCULATOR.
Your calculator will handle all of the decimal
calculations and the addition/subtraction of the
exponents.
All you have to do is to set your calculator to scientific
notation mode then key in the numbers in the
arithmetic problem.
Note – DO NOT enter a number as “3” “x” “10” “^4”, it
will treat the “3” and the “10^4” as separate numbers.
Use the “exp” or “EE” button (for “exponent”) as in “3”
“EE” “4”. (Often written in shorthand form as 3e4).
SAMPLE PROBLEMS
Light travels at the speed of c = 300,000 km/s. The distance
from Earth to the Sun is 150,000,000 km. How long does it
take light travel from the Sun to Earth?
Distance = Speed . Time
Speed = Distance
Time
Time = Distance
Speed
Time = Distance = 150,000,000 km
Speed
300,000 km/s
Time = 500 seconds
500 s . 1 min/60 s = 8.3 minutes
The Earth is 8.3 light-minutes from the Sun.
The metric system as opposed to the British system of units
is used in science. There are two versions of the metric
system:
MKS = Meters (m) Kilograms (kg) Seconds (s)
CGS = Centimeters (cm) Grams (g) Seconds (s)
It is customary to use CGS in stellar astronomy and MKS in
the other branches of astronomy. We will be using the MKS
system of units.
The meter is the unit of distance in the MKS system. It is
approximately one yard in length (39.3 inches).
The kilogram is the unit of mass (weight). It is approximately two
pounds of weight at Earth’s surface.
Scales of Size and Time
Astronomy deals with objects on a vast
range of size scales and time scales.
Most of these size and time scales are way
beyond our every-day experience.
Humans, the Earth, and even the solar
system are tiny and unimportant on cosmic
scales.
A Campus Scene
16 x 16 m
(52 x 52 ft)
A City View
1.6 x 1.6 km
(1 x 1 mile)
The Landscape of Pennsylvania
160 x 160 km
(100 x 100 miles)
The Earth
Diameter of the Earth: 12,756 km
Earth and Moon
Distance Earth – Moon: 384,000 km
No atmosphere.
Maria – Younger Surface
3 billion years old
Diameter:
3500 km
Sidereal Period: 27.3 days
Synodic Period: 29.5 days
Distance from Earth:
385,000 km
Highlands – Older Surface
4.5 billion years old
EARTH’S MOON
Earth Orbiting Around the Sun
Distance Sun – Earth = 150,000,000 km
Earth Orbiting Around the Sun
In order to avoid large numbers beyond our
imagination, we introduce new units:
1 Astronomical Unit (AU)
= Distance Sun – Earth =
150 million km
(93 million miles)
SUN
Sunspots (Magnetic Storms)
Solar Flares & Prominences
Boiling Earth-Sized
Convection Cells
Diameter:
1,400,000 km
Rotation Period:
25 days
Surface Temperature:
5,800 K
Core Temperature:
15,000,000 K
The Solar System
Approx. 100 AU
MERCURY
With no atmosphere, Mercury is heavily cratered by
4.5 billion years of meteoritic impacts.
Nearest the Sun of all the planets.
60,000,000 km (0.4 AU)
Diameter:
5000 km
Orbital Period:
88 days
Rotational Period: 58 days
Although not much bigger than Earth’s Moon it is much
denser, 5.5 times that of water compared to the Moon’s
3.5 times.
Thick atmosphere of
carbon dioxide and sulfuric acid.
VENUS
Venus has a hot thick atmosphere. It is so thick that optical-based
telescopes cannot penetrate to the surface. Closer to the Sun than
Earth, the temperature at the surface is a blistering 800o F.
Diameter:
12,100 km (almost a match for Earth)
Orbital Period:
225 days
Rotational Period:
243 days (retrograde)
Distance from Sun: 110,000,000 km (0.7 AU)
Soviet Venra Spacecraft photograph of the surface of Venus.
MARS
Diameter:
6800 km
Orbital Period:
1.88 years
Rotational Period: 24h
Distance from Sun:
225,000,000 km (1.5 AU)
Gigantic gorge in the surface of Mars (Valles Marinaris)
stretching 3000 km across. It would reach across the
entire continental United States.
Thin atmosphere of carbon dioxide and water.
Polar Cap
Dry Ice & Water Ice
ASTEROID BELT
The Asteroid Belt is located between
2 and 4 AU from the Sun. It contains
billions of rock boulders. The two at
the right are 20-60 km in size.
Gaspra
Ida
Dactyl
JUPITER
Atmospheric cloud bands due to
high winds.
Extensive atmosphere of
methane and ammonia.
Diameter:
143,000 km
Orbital Period:
12 years
Rotational Period:
10h
Distance from Sun: 680,000,000 km (5 AU)
Great Red Spot
Jupiter is the largest of the planets in the solar system. It is large enough to fit all of the other planets
inside of it…twice! It can easily engulf over 1000 Earths.
It has an extensive atmosphere tens of thousands of kilometers thick. It is believe to have been the
first planet to form in the solar system, 100 million years after the Sun formed from a large cloud of
gas and dust in the rotational plane of the Milky Way Galaxy.
Moon-wide ocean encrusted in ice
Most volcanically-active object
In the solar system
THE GALILEAN SATELLITES
This composite includes the four largest moons of Jupiter which are known as the
Galilean satellites. From left to right, the moons shown are Ganymede, Callisto,
Io, and Europa.
The Galilean satellites were first seen by the Italian astronomer Galileo Galilei in
1610. In order of increasing distance from Jupiter, Io is closest, followed by
Europa, Ganymede, and Callisto.
SATURN
Extensive system of rings
Diameter:
121,000 km
Orbital Period:
29 years
Rotational Period:
10h 30m
Distance from Sun:
1,400,000,000 km (9.5 AU)
Atmospheric clouds
URANUS
NEPTUNE
Diameter:
51,000 km
Diameter:
50,000 km
Orbital Period:
84 years
Orbital Period:
164 years
Rotational Period:
15h
Rotational Period:
15h
Distance from Sun: 2,900,000,000 km (19 AU)
Distance from Sun: 4,500,000,000 km (30 AU)
OORT
CLOUD
&
KUIPER
BELT
(a) Diagram of the Oort cloud, showing a few cometary orbits. Most Oort cloud
comets never come close to the Sun. Of all the orbits shown, only the most
elongated ellipse represents a comet that will actually enter the solar system
(which is smaller than the dot at the center of the figure on this scale) and
possibly become visible from Earth.
(b)The Kuiper belt, the source of the short-period comets, whose orbits hug the
ecliptic plane.
PLUTO
Pluto
Charon
Diameter:
2,200 km
Orbital Period:
248 years
Rotational Period:
6 days
Distance from Sun: 5,900,000,000 km (40 AU)
Discovered in the 1930’s by Clyde
Tombaugh, Pluto was long
considered the 9th planet in the
solar system. Although it built up
in the same way as the planets, it
is now better classified as a
Kuiper Belt Object (KBO).
Along with newly-discovered KBO
Eris and the asteroid Ceres, it is
now also classified as a dwarf
planet.
The Kuiper Belt is a region
outside Neptune’s orbit where
billions of ice boulders (the
building blocks of the planets) are
located. The second KBO after
Pluto was discovered in 1992,
although their presence was
predicted circa 1950 by Gerard
Kuiper.
(Almost) Empty Space Around Our
Solar System
Approx. 10,000 AU
The Solar Neighborhood
Approx. 17 light years
The Solar Neighborhood
New distance scale:
1 light year (ly) =
Distance traveled by light
in 1 year
= 63,000 AU = 1013 km
= 10,000,000,000,000 km
(= 1 + 13 zeros)
= 10 trillion km
Approx. 17 light years
Nearest star to the Sun:
Proxima Centauri, at a
distance of 4.2 light years
The Extended Solar Neighborhood
Approx. 1,700 light years
The Milky Way Galaxy
Diameter of the Milky Way: ~ 75,000 ly
The Local Group of Galaxies
Distance to the nearest large galaxies:
several million light years
The Universe on Very Large Scales
Clusters of galaxies are grouped into superclusters.
Superclusters form filaments and walls around voids.
For next time
Read Units 5 and 6
Remember that the homework is due on
Monday