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3. Time-scale and Distance
(시간 척도와 거리)
SI 단위계에서 사용하는 접두어
Cosmic Calendar
Cosmic Calendar: Scale 12 Billion year History of Universe into one year.
1 month = 1 Billion years.
우주의 달력 : 우주의 탄생에서 현재까지를 1년으로 두었다
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Jan 1: The Big Bang
Feb. : The Milky Way forms
August 13: The Earth Forms
December 13: Invertebrate (무척추) Life Evolves
December 25: Rise of Dinosaurs
December 30: Dinosaurs Extinct
December 31: 9:00 pm Earliest Human Ancestors
December 31: 11:59:47 pm Pyramids are Built
December 31: 11:59:58.4 pm King Sejong was born
Chronology of the Universe
우주의 연표 (연대기)
13.7 Gyr
13.4 Gyr
12 Gyr
4.567 Gyr
4.5 Gyr
4.45 Gyr
4.4 Gyr
4.2 Gyr
4 Gyr
>3.5 Gyr
>3.5 Gyr
2.3 Gyr
0 Gyr
Big bang; formation of the elements H and He
First stars and galaxies; first supernova explosions produce the heavy
elements (C,N,O,Si,Fe,…)
Formation of the milky way
Formation of the solar system; at this point in time the interstellar
medium has been enriched with 1% heavy elements
Formation of the earth and the moon
Layer structure of the earth
Solid earth crust
Early ocean
Plate tectonics
Earth’s magnetic field
Origin of life
Formation of oxygen-rich atmosphere; formation of ozone
Today
원소의 주기율표
Distance and Size of the Moon
달까지의 거리와 달의 크기
• In the 3rd Century B.C., a Greek, Aristarchus of Samos, figured out a
way to measure the relative sizes and distances of the Moon and Sun.
• He noticed that when the Moon was eclipsed by the Earth (월식) we
can see the Earth's shadow creep across the face of the Moon. Earth's
shadow is circular, and if we assume that the Sun's rays are roughly
parallel to one another.
• From the arc of Earth's shadow we can estimate the size of it's full
circle, then you measure the size of the Moon's circle. This tells us the
relative size of the Earth to the Moon. What you are measuring is the
angular size of the Earth's shadow and the Moon.
• Aristarchus measured a ratio of Earth's size to the Moon's size to be 2.9
(real ratio=3.7).
• Using the angular size of the Moon (=0.5 degree) we can estimate its
distance as shown below:
tan = D/d (when <<1,  in radian)
where D and d denote the diameter of the moon and distance between the
Earth and the moon.
• The angular size of the Moon is about 0.5° ( = 0.5°). Thus we have a
distance to the Moon of about 40 Earth Diameters (actually 30).
Distance and Size of the Sun
태양까지의 거리와 크기
• In addition, Aristarchus considered that when the Moon was seen to be
exactly in either 1st or 3rd Quarter Phase (exactly half lit up as seen
from Earth), we can draw a right triangle between Earth, Moon, and
Sun.
• The legs of the right triangle are the distance from the Earth to the
Moon (d1) and the distance between the Moon and the Sun (d2). The
hypotenuse is then the distance between the Earth and Sun (d). We can
measure the angle between d1 and d (A), it's the angular separation
between the Sun and Moon in the sky. We derive the distance d by the
Pythagorean theorem.
d2
d1
d
• Aristarchus measured A= 87°. This corresponds to a distance to the
Sun of d = 573DE. Now, the angular size of the Sun is also about 0.5°
so by the same method as for the Moon Aristarchus estimated that the
Sun was 5.33 times bigger than the Earth.
• This measurement is a difficult one to make, and the real answer is A=
89.9°. This corresponds to a distance to the Sun of d = 11,700DE and
a size of the Sun, DS = 109DE.
• Either way, Aristarchus was able to establish that the Sun was bigger
than Earth.
Aristarchus of Samos, the ancient Copernicus
• Earth radius
6400 km
• Moon-Earth distance
3.8105 km
• Sun-Earth distance 1.5108 km
1 AU (astronomical unit)
Parallax시차 (視差)
• Parallax = angle subtended (i.e., covered) by 1 A.U., the
distance from Earth to the Sun. (1/2 of the diameter of Earth's
orbit).
• As distance increases the parallax angle decreases. Ultimately
limited by the smallest angles measurable (resolved).
• The distance at which 1 A.U. subtends 1" (one arc second) is
called 1 parsec (pc). (parallax arc second).
• dpc = 1/p(")
• 1 pc = 3.26 Light-years. Distance to nearest star,  Centauri
p = 0.762" ---> d = 1.31 pc = 4.27 light-years
1 parsec = 3.26 light year