Measuring what you can't touch from the size of the Earth to the
structure of the solar system, black
holes and the expansion of the
Universe
Middle and High School
investigations in astronomy

Ian Dell'Antonio
› Associate Professor of Physics at Brown (since 1999)
› Research astronomer (focus on the distribution of
matter in the Universe and gravity)
› Instructor of astronomy courses at all level from nonspecialist through graduate courses.
› New to RITES in 2010

Laura Woods
--Woonsocket High School since 1998
› Cohort 1, year 2 resource team
› Biology, Oceanography
What drew you to this class?

First create your student login: go to
› http://rites-investigations.org

Directions for signing in are in your registration
packet.
› For this course, you should register as a student
› At the end of the course you can create a teacher
account, but for now use a student account (make sure
you don’t use your favorite login name, as you’ll want to
save that for your teacher account).

Add this course (course word “astro1”)—you should
see our names and four investigations—we will only
be using the two astronomy investigations.
ESS 2 The earth is part of a solar system, made up of distinct parts
that have temporal Earth & Space and spatial interrelationships.
ESS 3 The origin and evolution of galaxies and the universe
demonstrate fundamental principles of physical science across
vast distances
We have attempted to construct two investigations that address
the GSEs—but do not cover all topics in astronomy.
One of the central ideas of astronomy is that even
in the distant Universe, the same laws of physics
apply. Building the connection between
measurements on Earth and in space can help
make astronomy seem less remote and abstract.
The philosophy behind these investigations is to
build student understanding starting from ideas
that are familiar to them.
GSEs concerning astronomy are overlooked
for a variety of reasons—each investigation
has three activities (each broken down into
multiple sub-activities) that address different
aspects of the ESS GSEs.
 Many of the sub-activities can “stand
alone” in order to target any holes you
have identified
 The activities can be combined in many
different ways to focus on different topics
 We’ll provide you with background
knowledge so that you feel comfortable
using the activities

Distances—important for understanding the
scale of the Universe.
“Depth” of space is not obvious—you can’t
measure distances directly. But you can
measure directions.
Using angles to measure distances and sizes—
connect to measures on Earth and to
geometry.
We will begin with activity 1 of the
investigation (both MS and HS)
One of the fundamental
issues in astronomy is
that space is big.
Inconvenient!
At the same time, when
you look at the night
sky, it looks flat—there is
(almost) no 3-D
information that is
apparent in the sky.
How do you figure out the
scale of the Universe?
We don’t have large
enough rulers…
Angles can be thought as measuring the
difference between two directions
(technically of vectors, but no matter).
If you look in
two directions,
the difference
in directions
defines an
angle.
If you move
but look at the
same object,
the two
directions you
look in also
define an
angle.
We will use both
these ways of
defining angles to
measure distances
and sizes in this
investigation.
Imagine you’re driving on a road, and you see a tree with a mountain
behind it in the distance. As you drive, the direction to the tree changes
quickly—the direction to the mountain does not!
This is the secret to
measuring distances
with angles—for a
fixed distance
between the two
viewpoints, the angle
changes more if the
object you are viewing
is closer.
Trigonometry tells you that the relationship between the angle and the
distances traveled is:
Tangent(angle)= distance traveled/distance to object
If the ratio of the distances is small (the distance traveled is less than
distance to the object)
We can use the “small angle
approximation”—to a good approximation,
Tan(x) ~ x if x<<1 (good to 20% even when
x=1!)
This is only true if the angle is measured in
radians (these are units in which a circle has
2p radians) .
To convert from radians to degrees:
If 360 degrees= 2p radians, then
1 radian = 360/2p = 180/p ~ 57.3 degrees. So,
in degrees: Tan(x) = x/57.3. For small angles,
our relation is:
For small angles, our relation is:
angle/57.3 = dtraveled/dobject
The same relation
works with the relation
between size or height
and distance of an
object (it’s the same
triangle after all).
The apparent size of an object—how big it appears to our eyes— is just a
measure of the angle between one end of the object and the other. We call
this angle the “subtended angle”.
Notice, from the formula above, that the subtended angle is proportional to
1/distance. This is just the mathematical statement of something you all know.
To get a practical feel for measuring
distances with angles, we will build an
instrument to measure angles and explore
the measurements.
 Open the investigation: Measuring what
you can't touch - from the size of the Earth
to the structure of the solar system

(We will start with the middle-school version—the
high school version is very similar but adds one more
sub-activity and uses a little more math).


Teacher Guide
Activity 1, sub activity 1

www.xtranormal.com
› Make your own movies with any text (examples
within teacher introduction and other
investigations)
› Free for educators, but you must request an
account

http://www.forestwatch.sr.unh.edu/
› Tool used to measure heights indirectly
(hypsometer clinometer)
› Students collect data that is used to assess tree
health – white pine trees are “green canaries”

How Far Away is the Moon?
It makes sense to start the
investigation of space with our
nearest neighbor.
(familiar to everybody)
Even though the distance to
the Moon is no longer
measured using angles
(radar is even more accurate)
The Moon is too far away for the direction
to change much if you just move a short
distance
(have you experienced the “Moon seems to
follow you” phenomenon? We are so used
to directions changing as we move that the
fixed direction to the Moon seems odd!)
However, moving a bit further and using a
telescope (why a telescope?), it can be
done
(this is sub-activity 2 of the MS and HS
investigations)

As the distances get bigger, the angles get smaller.
Measuring the angles in degrees no longer works.
Introduce smaller units:
Look familiar? The
sexagesimal system is our
1 degree = 60 arcminutes
inheritance from the
babilonians
1 arcminute = 60 arcseconds.
If we measure the angles in arcseconds, the small
angle formula becomes:
angle/(57.3x60x60) = angle/206,265 = dtraveled/dobject
The naked eye can resolve differences in direction of about 1
arcminute. Telescopes can do much better—even a small
amateur telescope brings this down to around an arcsecond,
where the atmosphere permits it.
To see a shift in the direction to
the Moon, you have to move a
long way – road trip! You also
need a reference point to
compare to (remember the
mountain?)
But, there’s a catch. The Moon
moves, too. It takes about 27.5
days to orbit the Earth– that’s
about ½ an arcsecond every
second. If you wait two hours,
the Moon wll have moved a
degree.
How can you measure from two
places at once?
On October 10, 2006, the Moon passed
right in front of the Pleiades—it happened
to be Brown’s fall break.
Robert Horton, Brown astronomy lab manager was on
vacation in New Hampshire, about 120 miles north of
Providence; the exact distance can be found using the
latitude and longitude of the observing sites.
Using the same telescopes and cameras, we observed the
Moon at the same time (cell phones are useful)
The two images were digitized, and we measured the
position of a crater on the Moon relative to the stars
(The stars are very far away, and their direction doesn’t
change in a measurable way—they are our reference)
Rhode Island image
New Hampshire image
Maia
Merope
Alcyone

Based on the position of three stars, software
programs can calculate the position of any
object in the image
(we will use the aladin java applet developed by the european southern observatory)
Measure the coordinates on the sky (like
latitude and longitude of the same crater in
both images.
How to measure angles?
Once we have the distance to the Moon, we
can use the same relation to measure the
size of the Moon. Measuring the angular
size of the Moon in arcseconds, we use:
(angle/206,265) = size/distance
The angular size of the Moon is about 2000
arcseconds (it varies, why?) How big is the
Moon?
This part of the investigation is only in the
high-school investigation.
In the previous section, we used the stars
as reference—even between here and
New Hampshire doesn’t change their
direction. Need to move further.
But rockets are expensive.
We are sitting on a moving platform! As the Earth
goes around the Sun, we move relative to the
stars! If we observe the same star twice, six
months apart, we will have moved 300 million
kilometers—much more than to NH.
In six months, the star’s
position changes by 2p (p
is the parallax angle, the
angle shift when one
moves a distance equal to
the Earth-Sun distance).
All we have to do is
measure p, and then
D = 206,265 Dsun / p
The figures are misleading, the angles are really small!
(in fact, in ancient times the lack of parallax was cited as proof that the
Earth stood still. Now we know the stars are just very far away!)
First parallax for a star measured in 1838 (by Bessel)–
p=0.38 arcseconds.
The biggest parallax is Proxima Centauri: p=0.61
arcseconds.
Because the values are small, define a new unit: the
parsec:
1 parsec = 206,265 Dsun. Why? Because
D = 206,265 Dsun / p = 1 parsec / p
Only a few hundred stars measured before 1990
Need to escape the blurring of the atmosphere
Named after the greek
astronomer who made very
early charts of stellar positions.
Launched by ESA (European
version of NASA) in 1989, made
very careful measurements of
stars for 5 years—why multiple
yeears? Stars move, too….
Hipparcos has made available online a catalog
of positions of more than 1 million stars—1000x
what was known before (but less than 0.001%
of the stars in the Milky Way!)
Students can search the parallax via the star
names. For example, Maia:
HIP
catalog
number
RA
Dec
Vmag
Parallax
PM (RA)
PM
(Dec)
e_Plx
B-V
distance
Spectral
type
17573
03 45
49.59
+24 22
04.3
3.87
9.06
21.09
-45.03
1.03
-0.063
0.0073
B8III
Brightness
(smaller is
brighter)
Parallax, in milli-arcseconds
Angular motion of the
star itself.