Distance Measurement in Astronomy
Name: _______________________
On a cosmic scale, our ‘Earthly’ distance measurements like miles & kilometers fail us
miserably! Imagine using millimeters to measure from here to Hong Kong, China …
that’d be insane! We would have to apply very large numbers which would be like
expressing the distance between Adelaide, Australia and St Petersburg, Russia in
centimeters (2,168,225,200) instead of the more usual units of kilometers (21,682).
Soooo …what units do astronomer USE???
Your job: Find out as much as you can, starting with some of the links below! Complete
the chart below with appropriate info on the 3 Units of Distance Measurement in
Astronomy … then be ready to write all about it tomorrow during class! You may also
write notes on the back of this sheet as well, including anything I’ve said in class during
our ‘Intro’. You may use search engines like Google & Bing, or whatever you like!
http://janus.astro.umd.edu/astro/distance/
http://www.sky-watch.com/articles/howfar.html
places in Space … input different speeds & time units.
3 Units of Distance Measurement in Astronomy
*AU’s (Astronomical Units)
*Light Years
*Parsecs (Parallax –Second)
Interactive website on “How Far” to other
Name: ____________________________________ Period: _______________
Questions on Distance Measurement in Astronomy
Directions: First, read through the packet of information on ‘Distance Measurement in
Astronomy’ & then answer these ?’s below. ALL ANSWERS SHOULD BE IN COMPLETE
SENTENCES, PROPER PUNCTUATION, ETC.!!!
1) What is the largest dimension you have personal knowledge of?
(Example: Have you run a mile? Hiked 10 miles? Run a marathon?)
2) What is an ‘A.U.’?
- Definition:
- Equivalent distance in miles:
- Example of a real distance measured in A.U.’s:
3) Give an example of Where an ‘A.U.’ would be the most useful unit of distance
measurement? (cite a real example from your packet!).
4) What is a ‘Light-year’?
- Definition:
- Equivalent distance in miles:
- Example of a real distance measured in ‘Light-years’:
5) Give an example of Where a ‘Light-year’ would be the most useful unit of distance
measurement (cite a real example from your packet!).
6) What is a ‘Par-sec’?
- Definition:
- Equivalent distance in miles:
- Example of a real distance measured in ‘Par-secs’:
7) Give an example of Where a ‘Par-sec’ would be the most useful unit of distance
measurement (cite a real example from your information packet!).
8) Why do stars look so small to us?
9) When we look into the night sky at the stars, we are actually looking back in time and into
the past. The Hubble telescope was designed to help astronomers see deep into the universe and
possibly far enough back in time to collect information about the beginning of the universe.
How is it possible that a telescope (… or even ‘Us’!) can see “back into time” just by looking at
distant objects in space? (Explain!)
10) Explain WHY we needed to come up with specialized units for measuring distances in
space rather than just sticking with our familiar units of miles or kilometers??
11) Explain what ‘Parallax’ means (from the unit ‘Par-sec’).
12) How is ‘Parallax’ measured?
Discovery Streaming: Video Clip: Measuring the Universe [04:24]
Some Common Distance Units:
 Light Year: the distance that light travels in one year (9.46 x 10^17 cm).
 Parsec (pc): 3.26 light years (or 3.086 x 10^18 cm).; also kiloparsec (kpc) = 1000
parsecs and megaparsec (Mpc) = 1,000,000 parsecs.
 Astronomical Unit (AU): the average separation of the earth and the sun (1.496 x
10^13 cm).
Units for
Stellar Distances
Because the distances to stars are so large, it is useful to introduce some large units of
distance measure. The most common are the light year and the parsec.
The Light Year Distance Unit
In popular discussions, large distances (such as the ones between stars) are often give in
units of light years (which we shall abbreviate LY). A light year (which is a unit of
distance, NOT time!) is the distance that light travels in a single year. Since light is very
fast, the light year is a very large distance. From the knowledge that light travels at a
speed of 3 x 1010 cm/s in a vacuum, we can determine the length of a light year in
centimeters simply by multiplying by the number of seconds in a year (a tropical year has
3.156 x 107 seconds in it). The result is that a light year is equal to 9.46 x 1017 centimeters,
or 9.46 x 1012 kilometers. (Since distances in astronomy often involve large numbers, you
may wish to review scientific notation, which is the most useful way to write either very
large or very small numbers.)
A light year is often a convenient unit in discussing distances between stars, because the
average separation between stars in a galaxy is typically of that order of magnitude. For
example, the nearest star to the Sun is Proxima Centauri, which is about 4.4 light years
away. Here is a summary of some important distances expressed in light years:
 Light Year: the distance that light travels (through a vacuum) in one year (9.46 x
1017 cm).
 The nearest star (other than the Sun) is 4.4 light years away.
 Our galaxy (the Milky Way) is about 100,000 light years in diameter.
 The distance to the galaxy M87 in the Virgo cluster is 50 million light years.
 The distance to most distant object seen in the universe is about 18 billion light
years (18 x 109 light years).
The Parsec Distance Unit
The method of parallax gives rise to a natural distance unit that astronomers call the
parsec (which we shall abbreviate as pc). The parsec is defined to be the distance at which
a star would have a parallax angle p equal to one second of arc. From basic trigonometry
we find that this distance is equal to 206,265 astronomical units (where the astronomical
unit is the average separation of the Earth and the Sun) or 3.26 light years. One also
commonly uses the kiloparsec (kpc) and the megaparsec (Mpc) as a distance unit, which
correspond to 1000 and 1,000,000 parsecs, respectively. Although the light year is often
found in popular level discussions, professional astronomers probably use the parsec,
kiloparsec, and megaparsec more commonly as units of large distance. It is useful to
remember the following average distance scales:
 The average separation between stars in a galaxy like our own is of order parsecs.
 The diameter of a galaxy like our own is typically of order 100 kpc.
 The separation between galaxies in a cluster of galaxies like our own local cluster is
typically several Mpc.
 The separation between clusters of galaxies is typically of order 10 Mpc.
 The most distant galaxies observed are thousands of Mpc away from us.
Here is a concise summary of some distance scales commonly used in astronomy.
Units of Stellar Distance
The distance to stars are so great that the ordinary units - miles - are no longer practicable.
The nearest star is 25 trillion miles (25,000,000,000,000 miles) away - a number too awkward
to write, to remember, or to use.
Three units are commonly used in Astronomy: (1) the Astronomical Unit; (2) the Light
Year; and (3) the Parsec.
(1.) The Astronomical Unit is, by definition, equal in length to the distance from the earth to
the sun - 93 million miles (93,000,000 miles)
This unit, astronomically speaking, is a fairly small one, and it is used primarily in stating
distances within the Solar System. Thus, the distance of Pluto is 40 Astronomical Units, or 40
X 93,000,000 miles = 3,720,000,000 miles
(A.U. is the proper abbreviation for Astronomical Unit.)
(2) Another unit of astronomical distance is the Light Year, defined simply as the distance
traveled by a ray of light in a year. Knowing that the speed of light is 186,000 miles in one
second, it is easy to compute that distance. 186,000 is multiplied by the number of seconds in a
year:
186,000 X 60 (seconds per minute) X 60 (min's per hour) X 24 (hours per day) X 365� (days
per year) = 5,880,000,000,000 miles (5.88 trillion miles) or ( 5.88 X 1012 miles)
Using this unit of distance, Alpha-Centauri is at a distance of 4.2 light years; or, the light by
which we see the star has been traveling 4.2 years.
(3) The definition of the Parsec is based on a triangle as follows:
If (a), in a triangle, one of the angles is 90�; and if (b), one of the legs at the right angle is
93 million miles long; and if (c), the angle opposite it is one second;
then, the length of the other 90� leg is equal to one Parsec. Thus, if angle B is the 90�
angle, AB is 1 A.U. long, and angle D is 1 second of angle in size, then BD will have a length
of 1 Parsec.
If (a), the angle B is 90�; (b), the side of AB is 1 A.U. (93,000,000 miles) long; (c), the angle
D is 1 second, then: the side BD is equal to one Parsec.
Distance Measure
In astronomy, the most commonly used measures of distance are the light year, parsec and
astronomical unit.
Astronomical Unit (A.U.)
An astronomical unit (A.U.) is the average distance between the Earth and the Sun, which
is about 93 million miles or 150 million kilometers. Astronomical units are usually used to
measure distances within our solar system. For example, the planet Mercury is about 1/3
of an A.U. from the Sun, while the farthest planet, Pluto, is about 40 A.U. from the Sun
(thats 40 times as far away from the Sun as the Earth is).
Light-Year (ly)
Most objects in space are so far away, that using a relatively small unit of distance, such as
an astronomical unit, is not practical. Instead, astronomers measure distances to objects
which are outside our solar system in light-years. A light-year (ly) is the distance that light
can travel in one year in a vacuum (empty space). The speed of light is about 186,000 miles
or 300,000 kilometers per second. So, in one year light travels a distance of about
5,880,000,000,000 miles or 9,460,000,000,000 kilometers or 63,240 A.U.. This distance is 1
light-year. For example, the nearest star to us is about 4.3 light-years away. Our galaxy,
the Milky Way, is about 150,000 light-years across, and the nearest large galaxy,
Andromeda, is 2.3 million light-years away.
Parsec (pc)
Astronomers use another unit of distance called a parsec (pc), which is equal to 3.26 lightyears. The definition of the parsec is based on a triangle. A parsec is the length of the long
leg of a right triangle, whose short leg is one astronomical unit when the angle between the
Sun and the Earth, as seen from an object in space (a star for example), is one arcsecond
The word parsec stands for "parallax of one arc second" One kiloparsec (kpc), is one
thousand parsecs. One megaparsec (Mpc) is one million parsecs.
SUMMARY
1 Astronomical Unit (A.U.) is the average distance between the Sun and the Earth.
1 A.U. = 93 million miles = 150 million kilometers
1 light-year (ly) is the distance that light travels in one year in a vacuum.
1 ly = 5,880,000,000,000 miles = 9,460,000,000,000 kilometers = 63,240 A.U
1 parsec (pc) = 3.26 light-years
The Question
(Submitted February 26, 1998)
I have searched everywhere, and cannot find the
measurement of distance in space. What is it? Light years,
kilometers, what?
The Answer
The common distance measures we use depend on what
we are measuring.
1. For distances within our solar system, or other solar systems, the common unit is the
'Astronomical Unit' (A.U.)
1 A.U. = the average distance between the Earth and the Sun
2. For most everything else, stars, galaxies etc..., the distance unit is the parsec (pc). This is a
convenient unit when measuring distances to stars by triangulation (what astronomers call
parallax).
1 pc = 3.26 light years = about the distance to the nearest star
1 pc = 60 x 60 x 180/pi A.U. = 206265 A.U. --- by definition.
for distances within our galaxy or other galaxies it is kiloparsecs (kpc):
1 kpc = 1,000 pc
for distances between galaxies, and cosmology it is Megaparsecs (Mpc):
1 Mpc = 1,000,000 pc 3. The exception to these is when one is studying smaller object, such as
a star or a planet. Then we might use kilometers. For dust grains, we might use microns
(1/1,000,000 of a meter).
4. It is also common to compare objects. For example, if one is studying a star one might say
"its radius is 5 solar radii", meaning it is 5 times the size of our sun. Similarly with galaxies, is it
bigger or smaller than the Milky Way.
So, all in all, we use many units is astronomy. But, all in all, the parsec is the most common.
Note, astronomers only use light-years when talking to the general public or teaching classes.
Distance in space
All our lives we have grown up with the familiar units of distance used on Earth, namely
centimetres, metres, and kilometres. We tend to think perhaps of a centimetre as a small unit
and a kilometre as a long way indeed.
We find, however, that when we venture to think of the distances in space that earthly units are
completely inadequate to express most distances. To use the same units as employed on Earth
we would have to apply very large numbers which would be like expressing the distance
between Adelaide and St Petersburg in centimetres (2,168,225,200) instead of the more usual
units of kilometres (21,682).
Astronomers therefore use quite different measurement units. The best known is the LIGHT
YEAR, which is the distance light travels in one year. Lights travels at a finite speed of
299,792,500 metres per second which is about 9,460,000,000,000 kilometres per year.
This means that light travels the distance from the Moon to the Earth, 384,400km in 1.28
seconds, and it travels from the Sun to the Earth, 149,597,870km in 8.3 minutes. So instead of
saying that the sun is nearly 150 million km away we say that the Sun is 8.3 minutes light time
away. Now when we come to the nearest star, Alpha Centauri (Rigil Kentaurus), we say it
takes light 4 years 4 months to reach us. So Alpha Centauri is 4.3 light years away from Earth.
In kilometres this is the unwieldy number of about 40,681,156,000,000 km. The brightest star
in the night sky is Sirius which is twice as far away at 8.7 light years.
If we were able to fly a commercial airplane (at a constant speed of 800km/h) to Alpha Centauri
(4.3 light years distant) it would take about 5.8 million years to reach Alpha Centauri from
Earth. Consider that our galaxy, the Milky Way is about 100,000 light years in diameter then
this gives us some idea of the vastness of space.
http://www.sky-watch.com/articles/howfar.html
How Far Away?
“How far can you see with it?” is a typical question asked by those who are
unfamiliar with telescopes. People who ask this question are not aware of the
enormous distances one can see with just the naked eye. We’ll discuss just how far at the end of
this article. Astronomers, both amateur and professional, routinely deal with enormous
distances. This article won’t explain how to make precise calculations of the distances to the
planets, stars and beyond, but will give you a better understanding and appreciation of
astronomical distances.
Our Solar System
Let’s start with the Earth. The distance from the center of the Earth to its surface is 3820 miles
or 6371 kilometers and its circumference at the equator is about 24,000 miles or 40,000
kilomters. It’s no coincidence that the Earth circumference is a round number in kilometers
because the kilometer was originally defined as 1/10,000 of the distance from the pole to the
equator. The next distance is the 240,000 miles (400,000 kilometers) from the Earth to its Moon
and then the average distance from the Sun to the Earth: 94 million miles (150 million
kilometers).
It’s difficult enough dealing with hundreds of thousands of miles; how can you handle over a
hundred million? The answer is: you don’t – at least not directly. The average distance between
the Earth and the Sun (it has to be an average because the Earth’s orbit is not a circle and
constantly varies) has been defined as one “astronomical unit” or A.U. Distances such as those
between the various planets and the Sun are usually expressed in astronomical units. For
instance, Mars whose orbit’s radius is a little over one and a half times that of the Earth has an
average distance from the Sun of 1.52 A.U. Venus whose orbit is within that of the Earth
averages only 0.723 A.U. from the Sun.
The following is a list of the planets and their average distance from the Sun in Astronomical
Units:
Mercury 0.387
Venus 0.723
Earth 1 (of course)
Mars
1.52
Jupiter 5.20
Saturn 9.54
Uranus 19.2
Neptune 30.1
Pluto
39.4
By expressing these vast distances in Astronomical Units, even far away Pluto – billions of
miles away – can be easily compared to the other planets. But tables like the one above create
an illusion of a crowded Solar System especially when they display the planets with both
correct orbits and relative sizes but not using the same scale. To get a more accurate picture, let
us imagine shrinking the Earth down to the size of a pea. At the same time, let the rest of the
Solar System be proportionally reduced in size.
The Sun will be the size of a beach ball. The first planet Mercury be 200 feet from the Sun and
will be the size of a pinhead. Then, 300 feet away from the Sun will be Venus, represented by a
pea only slight smaller than that representing the Earth. In this scheme of things, the Earth is
500 feet from the Sun. About 20 inches from our pea revolves the Moon. Mars is the size of a
grape pit and is 700 feet away from the Sun. Skipping over the asteroids, at a distance of over
2,000 feet from the Sun we come to Jupiter, the largest planet. A tennis ball represents Jupiter,
while Saturn, which is over 4,000 feet away from the center, is only slightly smaller than a
baseball. The next planet Uranus is over one and a half miles from the Sun and is the size of a
ping pong ball. Neptune also is a ping pong ball, but one that is over two and a half miles from
the Sun. Finally, Pluto is over three miles away from the Sun and the size of a sesame seed.
The general idea is that we have within a radius of over three miles a space filled by only an
occasional golf ball and a few widely separated peas. Most of the Solar System is empty space.
By the way, on this scale, the nearest star is 25,000 miles away.
And Beyond...
As you can see although an Astronomical Unit is very useful for dealing with distances within
our Solar System, it’s not going to help us much when we go out to the stars – even the nearest
ones. For these distances we need a much larger unit of distance: a light year. A light year is the
distance that light travels within a single year: 5 trillion 869 billion miles and change (about 9
trillion kilometers). The nearest star – alpha Centauri – which can only be seen from the
Southern hemisphere is 4.3 light years away. Most of the brighter stars than can be seen from
the Earth are no more than a few hundred light years away. A light year is not only a way of
conveniently expressing large numbers but is related to a fundamental fact about the stars. Let’s
take a look at the star Rigel from the constellation of Orion which is over 500 light years from
us. The light that is entering our eyes while observing it left at least 500 years ago. When we
gaze into the sky we are not only look across great distances, but also look into the past. By
using light years, we are reminded that the farther the star is away from us, the longer we are
looking into the past.
The question was posed at the beginning of this article: “how far can one see?” If you take a
look at the constellation of Andromeda during a particularly dark night, you might see a small
patch of light that is designated M31 (see skytour - andromeda). This is the Andromeda galaxy
which is similar to our own and is the most distant object (2.9 million light years away) that can
be seen with the naked eye.
Postscript
Many Americans are unfortunately not yet comfortable with kilometers. A kilometer is about
six tenths of a mile. A better way to picture it is as ten American football fields lined up one
after the other.