Angle, distance, and
Powers of Ten
Lecture 2
by Inseok Song
 In this class, you will learn
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1-5 How astronomers measure the positions and sizes of celestial objects
1-6 How to express very large or very small numbers in convenient
notation
1-7 Why astronomers use different units to measure distances in space
1-8 What astronomy can tell us about our place in the universe
Before we begin these, let’s first get realized how vacant the space truly is!
Solar System Overview
Put it on a tangible scale
about 1/3 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Mercury = a quarter at the Stegeman Coliseum
So much of empty space…
about a mile away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Earth = an apple at the intramural field
So much of empty space…
~3 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Asteroids = millions of planktons scattered around the Loop 10 (perimeter road)
So much of empty space…
~5 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Jupiter = a classroom desk near the west-end of Athens
So much of empty space…
~10 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Saturn= a classroom desk near Bogart on highway 316
So much of empty space…
~20 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Neptune = a basketball near the Gwinnett county airport (Lawrenceville)
So much of empty space…
~30 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Pluto = a penny at the I-85 / GA-316 intersection
So much of empty space…
~40-60 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
K-B objects = millions of microbes + small insects scattered around northern Georgia
So much of empty space…
~200,000 miles away
If we scale down everything by 100 million times…
Sun = a small truck at the Physics Building at UGA
Nearest Star = another truck at the distance to the Moon
Angles in
astronomy
 circumference = 2π × radius  for a given
radius, the length of an arc will be
proportional to an angle.
Astronomers use angles to denote the
positions and apparent sizes of objects
in sky.
angular distance
angular size
a complete circle = 360°
1° = 60’
1’ = 60”
d=α×R

Small angle formula
 when the angle is small, we can approximate that
the length (A) is equal to the arc length (B)
A
 Linear size of an object (D), α in arcseconds.
D
d
206265
B
Figure 1-11a
Vertical
Moon
90°
1/2°
Horizontal
The angular
diameter of the
full moon in the
sky is about 1/2°.
Complete circle = 360°
(a) Measuring angles in the sky
The angular distance between the
Figure 1-11b,c
two pointer stars at the front of the
Big Dipper is about 5°, roughly 10
times the angular diameter of the
Moon.
5°
6°
The angular distance
between the stars at the top
and bottom of the Southern
Cross is about 6°.
(b) Angular distances in the northern
hemisphere
(c) Angular distances in the southern
hemisphere
Powers of Ten notation
 From atoms to the entire Universe, astronomy is a subject of extremes.
 If we express the size of a Hydrogen atom and the Universe in meters…
Universe = 100,000,000,000,000,000,000,000,000 meters = 1026 meters
atom = 0.0000000001 meter = 10-10 meters
 To efficiently express a wide range of numbers, astronomers use the power-of-ten
notation
 1 giga bytes = 1 billion bytes
 Study box 1-2 : arithmetic with powers-of-ten
Astronomical distances
 Although we could express all sizes and distances in astronomy using one unit (e.g.,
meter), it is oftentimes more convenient to use different units
 scale of planetary systems  A.U.
 average distance between stars  parsec or light-year
 AU = astronomical unit = average distance between Earth and the Sun
1 AU = 1.496×108 km
 light-year = the distance that light travels in one year
1 ly = speed of light × (365 days × 24 hours × 60 minutes × 60 seconds)
= 300,000 km/sec × (3.156×107 seconds)
= 9.46 × 1012 km
Yet, another distance unit
1 AU
The parsec (pc), a unit of length most commonly
used by astronomers, is defined by the
apparent size of the Earth orbit.
Sun
At 1pc away from the solar system, the angle
between the Sun and Earth is 1 arcsec.
Earth’s
orbit
1 kiloparsec = 1 kpc = 103 pc
1 megaparsec = 1Mpc = 106 pc
Distance:
1 parsec
(3.26 light-years)
Angle:
1 arcsec" = 1
At a distance of 1 parsec,
a length of 1 AU subtends
an angle of 1 arcsec.
Observer
Sizes in the Universe
Cosmic connection (SWF animation)
In summary…
Important Concepts
Important Terms
 Angular Measure: Astronomers use
angles to denote the positions and
sizes of objects in the sky. The size of
an angle is measured in degrees,
arcminutes, and arcseconds.
 Powers-of-Ten Notation is a
convenient shorthand system for
writing numbers. It allows very large
and very small numbers to be
expressed in a compact form.
 Units of Distance: Astronomers use
a variety of distance units. These
include the astronomical unit (the
average distance from Earth to the
Sun), the light-year (the distance
that light travels in one year), and
the parsec.
 arcsec = arc seconds = second of
arc
 armin = arc minutes
 Astronomical Unit (AU)
 Parsec (pc)
Chapter/sections covered in this lecture : sections 1.5-1.8