PURPOSE: to review basic math and analysis skills and common astronomical quantities

MATERIALS: calculator, ruler, penny, meter stick, graph paper (2 sheets)

INSTRUCTIONS: print out these pages and complete the activities below

2.1. (5 pts) Answer the following questions about metric prefixes:

a) Is a millimeter smaller or larger than a centimeter?

b) Is a kilogram smaller or larger than a gram?

c) Is a microsecond smaller or larger than second?

d) Is a kilometer smaller or larger than a meter?

e) Is a Gigayear smaller or larger than a year?

2.2. (10 pts) Use Table 1 of metric prefixes in your lab text to complete the following:

a) 44 cm = ____________________ m

b) 5,000 g = ____________________ kg

c) 656.3 nm = ____________________ m

d) 10 Gyr = ____________________yr

e) 72.5 km = ____________________ m

f) 2,000,000 ms = ____________________ s

g) 80 kg = ____________________ g

h) 0.19 cm = ____________________ mm

i) 3 x 10⁶ ton = ____________________ Mton

j) 50,000 yr = ____________________ Gyr

2.3.   Use your calculator to solve the following problems, limiting your answer to the correct number of
significant digits. Also, don't forget to record units, as they are part of the answer as well.

a) (2 pts) 345.2 yr + 8858.45 yr = _______________________

b) (2 pts) 32005.7 m / 23.46 s = _______________________

c) (2 pts) 4.991 mm x 2.1 mm = _______________________

d) (2 pts) 6.0036 kg - 2.0015 kg = _______________________

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**EXPERIMENT**
First, we will practice taking measurements and finding errors.

2.4. (3 pts) Locate a ruler and a penny.

a) Is a centimeter smaller or larger than an inch?

b) Measure the width of the penny in millimeters : __________ mm

c) Now measure the width of the penny in centimeters to nearest tenth (e.g., 16.2) : __________ cm

2.5.   Locate a meter stick.

a) (1 pt) Is a foot smaller or larger than a meter?

b) (1 pt) Measure your height to the nearest tenth (e.g., 165.5): ____________ cm

c) (2 pts) Now let two classmates measure you : _________________cm _________________cm

d) (2 pts) Was your first measurement precise? Give one reason to support your answer.




e) (3 pts) List at least three possible sources of systematic error in these measurements .

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**EXPERIMENT**
Now we will practice plotting and analyzing graphs.

2.6.   Look at Graph 1, a 2-d graph of Height vs. Weight. The heights and weights of 20 random people
were measured and recorded to create this graph.

a) (2 pts) What are the minimum and maximum heights represented on this graph?

b) (2 pts) What is the range (i.e., minimum and maximum) of the weight data?

c) (2 pts) Does this graph indicate there is a relationship between height and weight? If so, is it a direct
(i.e., both increase or both decrease) or inverse (i.e., one increases while one decreases) relationship?


d) (2 pts) This graph indicates that there is some kind of relationship between height and weight. But,
we know nothing about the sample of people used to obtain the data. List at least 2 factors about the
sample data that could drastically change the height/weight relationship we deduced from the graph.

2.7.   Look at the sample class height data in the table below.

HEIGHT (cm)	HEIGHT (cm)	HEIGHT (cm)
149.9	165	177.6
152.4	165.2	177.8
157.5	167.6	177.8
158	168	177.9
160	170.1	179.9
160.5	172.7	180.3
162.5	175	183
162.5	175.2	187.9
162.6	175.3	193

a) (10 pts) Using the graph paper provided, make a histogram of the number of people in each 10 cm
height range (i.e., 140-150 cm, 150-160 cm, ..., 190-200 cm). Do not forget to label the graph and use
evenly spaced tick marks. In astrononomy, this type of graph is often called a frequency plot.

b) (1 pt) Which 10 cm height range has the most amount of people?

c) (1 pt) Based on your graph, give one general conclusion about the heights of students in that class.




d) (3 pts) Calculate the average height of the students in the sample class. Show your work.

2.8.   Look at the data table below of temperatures at different heights in the Earth's atmosphere.

a) (10 pts) Use the graph paper provided to make a 2-d graph of temperature vs. height in the Earth's
atmosphere. Place height on the y-axis and temperature on the x-axis, connecting the data points. Be
sure to select evenly spaced tick marks and put labels on your graph.

HEIGHT (km)	TEMP (K)
0	287
10	218
20	218
30	230
45	270
55	270
60	252
80	180
90	180
100	210

b) (1 pt) Does this graph show a relationship (direct or inverse) between temperature and height?

c) (1 pt) In astronomy, this type of 2-d graph is called an atmospheric profile. We define a new layer of
atmosphere every time the data changes direction suddenly. Look at your graph. How many atmospheric
layers could you define from this profile?




SECTION 3 ACTIVITIES :

3.1. (12 pts) Write the following numbers in scientific or regular notation. Do NOT use a calculator!

a) 300000   _________________________   g) 9.22465 x 10^-5   _________________________

b) 7 x 10⁰   _________________________   h) 149600000   _________________________

c) 1 x 10¹²  _________________________   i) 0.52143  _________________________

d) 0.005070  ________________________   j) 18   _________________________

e) 2.86 x 10⁷  ________________________   k) 3.9989 x 10^-3   _________________________

f) 324.4  ___________________________   l) 6.6 x 10⁴   _________________________

3.2. (10 pts) Use your calculator to solve the following problems. Write answers in scientific notation.

a) 1 / 60 =   _________________________            f) Ö 1156 =   _________________________

b) 1 / (4.87 x 10²⁴) =   _____________________    g) (1156)^1/2 =   _________________________

c) 25³ =   ____________________________        h) (3.9 x 10²⁶)^1/4 =   _________________________

d) (2.063 x 10⁵) ² =   _______________________   i) (92 ⁴)^1/4 =   _________________________

e) (1 - 0.55)^-1/2 =   ____________________     j) 1/2 (9.4 x 10^-3) (2.4)² =   _________________________

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**EXPERIMENT**
Let's better understand scientific notation using the "Powers of 10" applet, © M. W. Davidson.

Go ahead and open this webpage. The applet itself is a big box in the center of the page. Once the page
is loaded, the applet will automatically load and begin running. Be patient. The applet begins at a distance
of 10⁺²³ meters away from us and provides an image of what we might see. Each subsequent frame is
one less power of 10, going all the way down to the subatomic level at a distance of 10^-16. Watch the
movie to begin to understand just how big the distances in astronomy really are and how useful the
system of scientific notation is. If you would like to watch it again, press the 'AUTO' button and it will
play in reverse. To control each frame yourself, just click on the 'Increase' and/or 'Decrease' buttons.

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3.3. (10 pts) Now calculate the following functions. Ensure your calculator is set to 'DEGREES' mode.

a) log 0.7 =

b) ln (1/8) =

c) 5 log (0.25) + 10 =

d) ln [1 / (1 + 8.2)] =

e) cos(45°) =

f) sin(8.77°) =

g) 1 / sin (42.3°) =

h) tan^-1 (0.2217) =

i) If tan x = 0.5, what is the angle x?

j) If sin a = 0.29, what is the angle a?

3.4.   Use your calculator to solve the following problems, limiting your answer to the correct number of
significant digits. Also, don't forget to record units, as they are part of the answer as well.

a) (2 pts) (1.5 cm)³ = _______________________

b) (2 pts) 1 / 43.47 s = _______________________

c) (2 pts) log (29 km / 8 km)= _______________________

d) (2 pts) sin^-1 (0.866) = _______________________

Complete the following algebraic and unit conversion problems, showing all your work:

3.5. (3 pts) Many celestial objects are assumed to be spherical. Solve the surface area equation for a
sphere, A = 4pR², for the object radius R. Show your work.

3.6. (3 pts) A basic formula, L =4p s R²T⁴, relates the luminosity, radius, and temperature of a star.
Solve this equation for temperature T. Show your work.

3.7. (3 pts) Astronomy often uses the Doppler equation, D l / l₀ = v/c. Solve this equation for velocity v.

3.8. (3 pts) There is an equation which relates the wavelength of light to its energy as follows: E = hc / l.
The constant, h, has units of kg · m²/s. The constant speed of light, c, has units of m/s. The wavelength,
l, has units of m. Find the units for E, the energy.

3.9. (3 pts) The equation for how fast a rocket must travel to escape Earth's gravity is v = Ö (2GM / R).
The constant, G, has units of m³ / kg · s². The mass, M, has units of kg. The planet's radius, R, has units
of m. Find the units for the escape velocity, v.

3.10. (3 pts) You are trying to buy drinks for a party you are throwing. You buy 576 oz. of a beverage.
The typical size of 1 can is 12 oz. How many cans did you buy?

3.11. (3 pts) If you drive your car 275 miles (1 mile = 1.609 km), then how many km did you travel?

3.12. (6 pts) Calculate how many seconds are in 1 year. (Note: you will need to multiple conversions)

SECTION 4 ACTIVITIES :

4.1 (4 pts) Answer the following questions about astronomical units:

a) Is an Astronomical Unit smaller or larger than a kilometer?

b) Is a arcsecond smaller or larger than a degree?

c) Is a nanometer smaller or larger than an Ångstrom?

d) Is a year smaller or larger than a Gigayear?

4.2. (12 pts) Put these units in order, small to large:   m, pc, mm, AU, Mpc, ly, nm, Å, km, mm, kpc, cm

4.3. (3 pts) The Earth has a mass of 5.97 x 10²⁴ kg (1 kg = 1000 g). How massive is the Earth in grams?

4.4. (3 pts) Jupiter is located at 5.2 AU from the Sun. How far is Jupiter from the Sun in meters?

4.5. (3 pts) You measure the size of a crater on an image of the Moon to be 2.23 inches across. The
image scale is such that 0.5 inches on the image = 20 meters in real life. How big is the crater in real life?

4.6. (3 pts) Light can be thought of as a wave and is described by its wavelength (i.e., distance from crest
to crest). If we observe light of wavelength l = 656.3 nm, how many Ångstroms is this?

4.7. (3 pts) The Earth's diameter is 1.25 x 10⁴ km. The Sun's diameter is 1.392 x 10⁶ km. Calculate how
many times larger the Sun is than Earth.

4.8. (3 pts) A galaxy's angular diameter is 4.84 arcminutes on an image. How many degrees is this?

4.9. (3 pts) The planet Venus has been measured to be near 800°F. How many degrees Kelvin is this?

4.10. (3 pts) Pulsars (rotating stars) spin on an axis. The rotation periods (in milliseconds) for several
pulsars were found: 1.557, 1.100 x 10³, 0.33200, 89.234, 59, 5.362, 2.84 x 10³. Find the average
pulsar period based on this data.

4.11. (3 pts) The closest galaxy to our own is M31 the Andromeda Galaxy. It is 8.9 x 10⁵ pc from here.
Our galaxy, the Milky Way, is 5 x 10⁴ pc across. How many Milky Way's fit between here and M31?

4.12.   The Sun's lifespan is estimated to be another 4.5 billion years or so. It has an angular diameter on
the sky of 0.5 degrees. Using F = (9/5)( K - 273.15 ) + 32, it has a temperature (T) of about 5800 K.
It is located at a distance of R = 8.5 kpc from the Galactic center. It has an orbital speed of v = 2.2 x 10⁵
m/s, as found from the equation v = 2pR / P, where P is period. Show your work to find the following:

a) (2 pts) lifespan of Sun (in scientific notation)

b) (3 pts) angular diameter in arcseconds

c) (3 pts) temperature in Fahrenheit

d) (3 pts) distance from Galactic center in parsecs

e) (3 pts) distance from Galactic center in meters

f) (6 pts) orbital period in seconds (Hint: solve the equation for P first)

* TURN IN THESE ACTIVITIES PAGES TO YOUR TA*  

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