Measurements And Powers-of-Ten
Objectives: After completing this exercise the student should be able to:
1. make measurements using cm and mm to the nearest tenth of a mm.
2. use a protractor to measure angles to the nearest degree.
3. use a compass to draw circles.
4. average a set of numbers.
5. multiply and divide large numbers using power-of-ten notation.
Materials Needed: a pencil, compass (to draw circles), protractor, ruler (mm), and
calculator
Introduction: In Astronomy, labs you will be asked to measure lengths in cm and mm,
use a protractor to measure and construct angles and draw circles with a simple compass.
You will also be expected to do simple arithmetic such as finding the average of a data
set or working with powers-of-ten. This exercise is designed to help you remember these
skills. Please be sure you can perform all the objectives of this exercise by the next lab.
Procedure:
Length and Distance
One of the tools you will use for measuring length is a simple ruler which has a
metric scale along one edge. When using a ruler it is a good idea to place your eye
directly above the ruler and look a straight down in order to reduce parallax errors. To
further reduce errors a measurement should be made at least three times and the average
used as the best value. An average is calculated by adding up the measurements and
dividing the sum by the total number of measurements.
Your ruler should have a metric scale which is divided into cm and mm. The cm
is divided into ten equal parts which are called mm; these are the smallest divisions on
your ruler. You should see that 1.0 cm = 10 mm. With your ruler you can accurately
measure length to the nearest tenth of a cm. However, with the aid of a magnifying lens
you can estimate length to the nearest tenth of a mm. Throughout the Astronomy labs,
you will be asked to make measurements estimating to the nearest tenth of a mm.
Measure the length of a wooden block to the nearest tenth of a cm. Make your
measurement along both edges and in the middle. Record all three measurements in
Table I and compute the average length of the block. Your calculator may give you an
answer with six or seven decimal places. However, since the original measurements are
only good to the tenths, your average will, at best, be good only to the hundredths place.
Do not write down all the meaningless digits your calculator may give you. Repeat the
above measurement, except this time estimate to the nearest tenth of a mm. You will
need a magnifying lens to do this. Record your measurements and their average in Table
I as before.
Angles
The main instrument you will use to measure angles is a protractor. Since each
protractor is somewhat different in design, it is not practical to describe how to use each
one. If you are unfamiliar with how your protractor is to be used, please ask your teacher
for help.
Measure the angles A, B, C, D, indicated by the arrows in Fig. 1. Your
measurements should be to the nearest degree. Record your answers in the spaces
provided along the right margin. In the blank area on Fig. 2, construct angles to within
one degree of 26°129°, 250°, and 311°. Be sure to use an arrow and the letters A, B, C,
D to indicate the angle as was done in Fig. 1.
A Scale Drawing of the Solar System
Drawing planetary orbits is a very important part of this chapter. Most planetary
orbits can be approximated using an off-center circle. In order to practice drawing circles
you will make two scale drawings of the solar system. One drawing will be for the inner
planets and the other one will be for the outer planets.
A compass is used to draw circles. The compass point and the pencil tip should
be separated a distance equal to the radius of the circle you wish to construct. This is best
done by placing the compass point and pencil tip along the edge of a ruler and opening
the compass to the desired amount using the ruler’s scale. Do not use the scale on the
compass itself because these scales are not accurate.
The distance between the Earth and sun is called an astronomical unit (AU). In
Table II and III a list of planers and their distances from the sun in AU’s is given. Note
that two different scales have to be used because the outer planets are significantly father
from the sun than the inner planets. For continuity, Jupiter is repeated in both scales.
Multiply each planet’s distance in AU’s by the scale factor given for each table and
record your results in the last column of Tables II and III. These distances are in cm and
will be used to make your scale drawing.
In the center of Fig. 3 is a dot which will represent the sun. With a compass, draw
circles centered on the sun which have radii equal to the scale distance of Mercury
through Jupiter as listed in the first part of Table II. Label each circle by the name of the
planet whose orbit it represents. You have completes a scale drawing of the inner planers
and one outer planet, Jupiter. Notice that a rather large gap exists between Mars and
Jupiter. It is known to be filled with thousands of small rocks called asteroids. On your
model, label this gap as the asteroid belt.
In the center of Fig. 4 is a dot that represents the sun. With a compass draw
circles centered on the sun which have radii equal to the scale distances of Jupiter
through Neptune, as listed in Table III. Label each circle by name of the planet whosr
orbit it represents. Notice how much smaller Jupiter’s orbit is on this drawing than on the
previous system onto a single page. Pluto’s orbit is so eccentric that its center is basically
near the orbit of Saturn and not near the sun. Therefore place the point of your compass
on Saturn’s orbit (use the side nearest the bottom of your page) and draw Pluto’s orbit
with a radius equal to the scale distance in Table III. Notice that Pluto’s orit actually
comes inside Neptune’s orbit.
Beyond the Solar System
Table IV lists several objects and their distances from the sun in AU’s. By
comparing Table IV to Table II and Table III it can be seen that the objects in Table IV
are outside the solar system. Compute the scale distance in cm for each object in table IV
using the scale of Table II, 2.0 cm = 1 AU. To do this, multiply the AU distances in
Table IV by 2.0 cm and record your results. If you do not understand how to multiply
using scientific notation, please ask for help. So that you can get a better feeling for how
far in miles the scale distances of Table IV are from our classroom, divide them by the
conversion factor 1.6 X 105 cm/mile and record your answers using scientific notation.
You might say these large numbers are astronomical.
Fig. 1: Angles to be measures by students.
Fig. 2: Construction of angles by students.
Fig. 3: Scale Drawing of Inner Solar System
Fig. 4: Scale Drawing of Outer Solar System
Table I – Length of Block
Trial Number
Length to hundredths
of a cm
Length to tenths
of a mm
1
2
3
Average length in cm = ___________________
Average length in mm = _____________________
Table II – Scale of Planets
Scale: 2.0 cm = 1 AU
Planet
Distance
AU
Mercury
0.4
Venus
0.7
Earth
1.0
Mars
1.5
Jupiter
5.2
Scale Distance
cm
Table III – Scale of Planets
Scale: 0.25 cm = 1 AU
Planet
Distance
AU
Jupiter
5.2
Saturn
9.6
Uranus
19.6
Neptune
30.5
Pluto
39.5
Scale Distance
cm
Table IV – Beyond the Solar System
Scale: 2.0 cm = 1 AU
Object
Distance
AU
Alpha Centauri
2.8 X 105
Center of the
Milky Way
1.6 X 109
Andromeda Galaxy
(nearest spiral
galaxy)
1.2 X 1011
Scale Distance
Cm
Scale Distance
Miles