AST1110-lab1-spring2024
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Date
Feb 20, 2024
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AST 1110: Planetary Astronomy
Spring 2024
Lab 1 (30 points) Name: Jenna McCarthy
Intro to Planetary Astronomy
Learning Goals
Solve math problems, including labeling units and using scientific notation when appropriate
Recognize the difference between direct proportionalities and indirect proportionalities
Interpret graphical information
Use percent error to compare collected data with known values
Show your work on all math problems this semester (including today)! 1.
You log in to d2l and see that your grade in AST 101 is 668 out of 800 points. Based on these numbers, what is your current grade in planetary astronomy?
668/800 = .835 or 83.5% or a B
2.
Based on the grade in question 1, if you do not lose any more points for the rest of the semester, what is the highest grade you can earn in the course? The entire
course is worth 1000 points. To get an A, you need at least 900 out of 1000 points. To get a B, 800 out of 1000 points are needed. To get a C, you need at least 700 out of 1000 points. Less than 700 points is a D grade. 800-668 = 132
1000-132 = 868
868/1000 = .868 or 86.8% or a B
3.
Based on the grade in question 1, if you do not gain any more points for the rest of the semester, what is the highest grade you can earn in the course? To get an A, you need at least 900 out of 1000 points. To get a B, 800 out of 1000 points are needed. To get a C, you need at least 700 out of 1000 points. Less than 700 points is a D grade.
668/1000 = .668 or 66.8% or a D
Figure 1 represents the orbital speed of planets in our solar system compared to
their mean distance from the Sun. Orbital speed has units of km/sec (kilometers per second) and mean distance has units of AU (Astronomical Units).
Figure 1
4.
Based on Figure 1, how does orbital speed vary with increased distance away from the Sun? Is this relationship inversely proportional or directly proportional? The higher the orbital speed of a planet, the closer to the sun it is. This is inversely proportional. 5.
On Figure 1, sketch a line that shows planets closest to the Sun moving most slowly and distant planets orbiting faster. Would this relationship be inversely proportional or directly proportional? This is inversely proportional. 6.
Based on Figure 1, what is the orbital speed of Jupiter in km/sec? This answer will be your “data.” An estimate is fine. The graph is not that precise.
14 km/sec
7.
If the known value for the orbital speed of Jupiter is really 13.07 km/sec, what is the percent error that you get from reading the graph? Use the equation below. Note the absolute value sign. Your answer will be a positive number.
%
error
=
|
(
(
14
−
13.07
)
13.07
)
|
×
100
=
¿
.0712 = 7.12%
2
Figure 2 - This graph shows average high (upper line) and average low (lower line) temperatures throughout the year for Colorado Springs, CO.
8.
Based on Figure 2, what is the overall average temperature for the month of January?
43+17 = 60/2 = 30º is the average temperature for January. 9.
What is the actual temperature outside right now? ___
40º F
____
10. What is your source for the current temperature? My cell phone's weather app. 11.If you measured the temperature outside right now with a thermometer, would you get the same answer as the source you used? Explain. No, the temperature would probably not be the same as what shows on my cell phone app because I could be receiving more sunlight or less sunlight which would change the thermometer and more than likely give me a different reading. There will be some math in astronomy labs this semester. Keep the following rules in mind:
Use scientific notation for numbers larger than thousands (1,000 becomes
1
×
10
3
) or smaller than thousandths (0.001 becomes 1
×
10
−
3
)
Always label the units of your final answer
Round numbers of your final answer to three significant figures. Examples of three significant figures (sig figs):
2.08
meters
(the zero is significant because it is in between two significant figures)
3
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0.0411
inches
(zeros are not significant here, just place holders to determine the exponent)
6.67
×
10
−
11
meters
1.51
×
10
8
light
−
years
Pay close attention to the exponents (“powers of ten”) of the numbers you are working with. A.) To enter exponents in scientific notation on your calculator, look for a button marked EE or EXP (these are just examples).
a.
For 2
×
10
30
enter:
2 EE 30
or 2 EXP 30
b.
For 5.67
×
10
−
8
enter:
5.67 EE (-) 8 or 5.67 EXP (-1) 8
B.) If you are multiplying two positive exponents together, the exponent of your answer should be larger
than the exponents you started with. Here are some examples (you don’t need to solve these).
a.
Ex: 10
5
×
10
8
=
10
(
5
+
8
)
=
10
13
b.
Ex: (
2
×
10
5
)
×
(
3
×
10
8
)
=
(
2
×
3
)
×
10
(
5
+
8
)
=
6
×
10
13
c.
Ex: (
9
×
10
5
)
×
(
3
×
10
8
)
=
(
9
×
3
)
×
10
(
5
+
8
)
=
27
×
10
13
=
2.7
×
10
14
Solve the numbered problems below.
12.
(
7
×
10
5
)
×
(
3
×
10
8
)
=
(
7
×
3
)
×
10
(
5
+
8
)
=
21
×
10
13
=
2.1
×
10
14
13.
(
9
×
10
4
)
×
(
3
×
10
7
)
=
(
9
×
3
)
×
10
(
4
+
7
)
=
27
×
10
11
=
2.7
×
10
12
C.) If you are squaring or cubing a positive exponent, the exponent of your answer should be larger than the exponent you started with. a.
Ex. (
2
×
10
6
)
2
=
(
2
2
)
×
10
(
6
×
2
)
=
4
×
10
12
b.
Ex. (
8
×
10
3
)
3
=
(
8
3
)
×
10
(
3
×
3
)
=
512
×
10
9
=
5.12
×
10
11
Solve the numbered problems below. 14.
(
6
×
10
3
)
2
=
¿
(
6
2
)
×
10
(
3
×
2
)
=
36
×
10
6
4
15.
(
7
×
10
4
)
3
=
(
7
3
)
×
10
(
4
×
3
)
=
343
×
10
12
D.) If you are dividing two positive exponents by each other, the exponent of your answer should be smaller
than the numerator that you started with. a. Ex. 10
13
10
8
=
10
(
13
−
8
)
=
10
5
b. Ex. 6
×
10
13
2
×
10
8
=
6
2
×
10
(
13
−
8
)
=
3
×
10
5
c. Ex. 2
×
10
6
5
×
10
3
=
2
5
×
10
(
6
−
3
)
=
0.4
×
10
3
=
4
×
10
2
Solve the numbered problems below.
16.
3
×
10
21
1
×
10
8
=
3
1
×
10
(
21
−
8
)
=
3
×
10
13
17.
1
×
10
15
3
×
10
8
=
1
3
×
10
(
15
−
8
)
=
0.3
×
10
7
=
3
×
10
6
E.) When solving math problems, do the math first and then worry about the units of the final answer. Very often the problem will state what the units should be.
Ex. How long does it take to travel 2 AU if you are traveling at the speed of light, 8.3 minutes per 1 AU? 2
×
8.3
=
16.6
2
AU ×
8.3
minutes
1
AU
=
16.6
minutes
Note that the unit in the example above that shows up twice cancels out. Note that in unit conversions, you are often multiplying or dividing by 1. This does not change the numbers of your answer at all. It only changes the units of your answer. Ex. How many minutes are there in one year? 1
year×
365
days
1
year
×
24
hours
1
day
×
60
minutes
1
hour
=
5.256
×
10
5
minutes
18.How many meters are there in 400,000 centimeters? Solve the following and include the units of the final answer: 5
(
4
×
10
5
cm
)
×
(
1
meter
1
×
10
2
cm
)
= 4000 meters
19.How many meters are there in 90,000,000 kilometers? Solve the following and include the units of the final answer: (
9
×
10
7
km
)
×
(
1
×
10
3
meter
1
km
)
= 9
×
10
10
Meters
20.How many minutes are there in 418 seconds? Solve the following and include the units of the final answer: (
418
seconds
)
×
(
1
minute
60
seconds
)
= 6.97 Minutes
To measure angles on the sky, we use degrees, arcminutes and arcseconds. 1 degree = 60 arcminutes (60
'
)
1 arcminute = 60 arcseconds (60
' '
) Figure 3 – Angular Measurements
6
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Examples: Andromeda galaxy is roughly 2 degrees on the sky. To convert this into arcseconds:
2
°×
60
'
1
°
×
60
' '
1
'
=
7200
' '
21.The full moon measures about ½ a degree on the sky. How many arcseconds is this? 1
2
°×
60
'
1
°
×
60
' '
1
'
=
1800
' '
22.The angular size of Mars at a recent opposition was 20 arcseconds across. How many Mars would fit across the size of the full moon? X ° ×
60
'
1
°
×
60
' '
1
'
=
20
''
X = 0.005556º
23.Which of these symbols represents arcminutes?
a.
°
b.
'
c.
' '
d.
∞
Figure 4 - Homemade Sextant
7
24. If you were to use a sextant like the one in Figure 4 to measure the angle (in degrees) of
an object on the horizon, what value would you get? Angle of Horizon __
90º
__________
25. If you were to use a sextant like the one in Figure 4 to measure the angle (in degrees) of
an object at zenith (straight overhead), what value would you get? Angle of Zenith ______
0º
_____________
8