Download Laboratory A

Laboratory A
Question Reservoir
With Answers
Mathematical Voyage
The Dimensions Program
Optical Interferometer Project
Telescope
Figure 1 Milky Way Galaxy Artist Concept
Courtesy of planetquest.jpl.nasa.gov
Project Grant Team
Prof. Kathryn Kozak
Project Designer
Patricia L. Hirschy
Principal Investigator
John S. Pazdar
Program Director
Prof. Mary Beth Orrange
Project Tester
Dennis C. Ebersole
Principal Investigator
Geometry
I.
Dimensional
A. The Sun is the largest object in our solar system. Some interesting facts about the
solar system:
The Sun has a diameter of 1,400,000 km.
The distance from the Earth to the Sun is 149,600,000 km.
The mass of the Sun is 330,000 times that of the Earth.
1. What is the circumference of the Sun in kilometers?
≈ 4,398,000,000 km
2. What is the circumference of the Sun in miles?
≈ 2,732,933.241 mi
3. What is the surface area of the Sun in square kilometers?
4. What is the surface area of the Sun in square miles?
5. What is the volume of the Sun in cubic kilometers?
6. What is the volume of the Sun in cubic miles?
Optical Interferometer QR – Lab A - 2
≈ 6.158 X 1012 sq km
≈ 2.38 X 1012 sq mi
≈ 1.437 X 1018 cu km
≈ 8.928 X 1023 cu mi
B. Technically, the orbit that a planet follows around the Sun is actually an ellipse.
However, most of the orbits are close to a circle. Interestingly, the one planet that
had an orbit that was the most elliptical was Pluto, and that was one of the reasons
that it was reclassified to a dwarf planet. So the eight planets all have orbits that are
mostly circular.
1. Find the area of the orbit that a planet sweeps out in one period (the time it takes
to go all the way around the sun) in square kilometers.
2. Find the area of the orbit that a planet sweeps out in one period (the time it takes
to go all the way around the sun) in square miles.
(All answers are approximates)
Planet
Area of orbit
(in square kilometers
- scientific notation)
Area of orbit
(in square miles scientific notation)
Mercury
2.63 X 1015
1.07 X 1015
Venus
9.19 X 1015
3.55 X 1015
Earth
1.76 X 1016
6.79 X 1015
Mars
4.08 X 1016
1.58 X 1016
Jupiter
4.76 X 1017
1.84 X 1017
Saturn
1.60 X 1018
6.17 X 1017
Uranus
6.47 X 1018
2.50 X 1018
Optical Interferometer QR – Lab A - 3
C. Find the following for one or more of the planets.
1. What is the diameter of the planet in meters?
2. What is the diameter of the planet in miles?
Planet
Mercury
Diameter
(in meters)
Diameter
(in miles)
4,878,000
3,031.05
Venus
12,104,000
7,521.08
Earth
12,756,000
7,926.21
Mars
6,794,000
4,221.60
Jupiter
142,984,000
88,846.1
Saturn
120,536,000
74,987.6
Uranus
51,118,000
31,763.3
Neptune
49,528,000
30,775.3
Optical Interferometer QR – Lab A - 4
3. What is the circumference of the planet in kilometers?
4. What is the circumference of the planet in miles?
(All answers are approximates)
Planet
Circumference
(in kilometers)
Circumference
(in miles)
Mercury
15,324.69
9,522.32
Venus
38,025.84
23,628.17
Earth
40,074.16
24,900.92
Mars
21,343.98
13,262.55
Jupiter
449,197.48
279,118.26
Saturn
378,675.01
235,580.49
Uranus
160,591.93
99,787.35
Neptune
155,596.80
96,683.46
Optical Interferometer QR – Lab A - 5
5. What is the surface area of the planet in square kilometers?
6. What is the surface area of the planet in square miles?
(All answers are approximates)
Planet
Surface area
(in square kilometers
- scientific notation)
Surface area
(in square miles scientific notation)
Mercury
7.47 X 107
2.89 X 107
Venus
4.60 X 108
1.78 X 108
Earth
5.11 X 108
1.97 X 108
Mars
1.45 X 108
5.60 X 107
Jupiter
6.42 X 1010
2.48 X 1010
Saturn
4.56 X 1010
1.77 X 1010
Uranus
8.21 X 109
3.17 X 109
Neptune
7.71 X 109
2.98 X 109
Optical Interferometer QR – Lab A - 6
7. What is the volume of the planet in cubic kilometers?
8. What is the volume of the planet in cubic miles?
(All answers are approximates)
Planet
Volume
(in cubic kilometers scientific notation)
Volume
(in cubic miles scientific notation)
Mercury
6.08 X 1010
1.46 X 1010
Venus
9.29 X 1011
2.23 X 1011
Earth
1.09 X 1012
2.61 X 1011
Mars
1.64 X 1011
3.94 X 1010
Jupiter
1.53 X 1015
3.67 X 1014
Saturn
9.17 X 1014
2.21 X 1014
Uranus
6.99 X 1013
1.68 X 1013
Neptune
6.36 X 1013
1.53 X 1013
Optical Interferometer QR – Lab A - 7
Arithmetic
I.
Conversions
A. The Sun is the largest object in our solar system. Some interesting facts about the
solar system:
The Sun has a diameter of 1,400,000 km.
The distance from the Earth to the Sun is 149,600,000 km.
The mass of the Sun is 330,000 times that of the Earth.
1. What is the diameter of the Sun in meters?
1,40,000,000 m
2. What is the diameter of the Sun in miles?
≈ 869,919.669 mi
3. What is the distance from the Earth to the Sun in meters?
149,600,000,000 m
4. What is the distance from the Earth to the Sun in miles?
≈ 92,955,819.23 m
5. What is the mass of the Sun in kilograms?
6. What is the mass of the Sun in metric tons?
Optical Interferometer QR – Lab A - 8
≈ 1.97 X 1030 kg
≈ 1.97 X 1027 metric tons
B. Find the following for one or more of the planets.
1. What is the distance from the planet to the Sun in meters?
2. What is the distance from the planet to the Sun in kilometers?
Planet
Distance from Sun
(in meters - scientific
notation)
Distance from Sun
(in miles - scientific
notation)
Mercury
5.791 X 1010
3.59836 X 107
Venus
1.082 X 1011
6.72324 X 107
Earth
1.496 X 1011
9.29571 X 107
Mars
2.2794 X 1011
1.41635 X 108
Jupiter
7.7833 X 1011
4.83632 X 108
Saturn
1.42694 X 1012
8.86659 X 108
Uranus
2.87099 X 1012
1.78396 X 109
Neptune
4.49707 X 1012
2.79435 X 109
Optical Interferometer QR – Lab A - 9
3. If you were to build a scale model of the solar system and the Sun is 0.4 inches in
diameter, what would be the distance from the Sun to the planet in feet?
4. If you were to build a scale model of the solar system and the Sun is 0.4 inches in
diameter, what would be the diameter of the planet in inches?
(Interesting: if you build the solar system at this scale, you can fit the entire solar
system on a roll of paper towels.)
(All answers are approximates)
Planet
Scaled diameter (in
inches)
Scaled distance from
Sun (in feet)
Mercury
0.001
1.38
Venus
0.003
2.57
Earth
0.004
3.56
Mars
0.002
5.42
Jupiter
0.041
18.50
Saturn
0.034
33.92
Uranus
0.015
68.26
Neptune
0.014
106.91
Optical Interferometer QR – Lab A - 10
5. If you were to build a scale model of the solar system to a scale of 1 : 64,000,000,
how far would the planet be from the Sun in meters?
6. If you were to build a scale model of the solar system to a scale of 1 : 64,000,000,
how far would the planet be from the Sun in meters?
(All answers are approximates)
Planet
Mercury
Scaled diameter
(in centimeters)
Scaled distance from
Sun
(in meters)
7.62
904.844
Venus
18.91
1,696.03
Earth
19.93
2,337.50
Mars
10.616
3,561.56
Jupiter
223.41
12,161.40
Saturn
188.34
22,295.90
Uranus
78.97
44,859.20
Neptune
773.88
70,266.70
Optical Interferometer QR – Lab A - 11
II.
Ratios & Proportions
A. The Sun is the largest object in our solar system. Some interesting facts about the
solar system:
The Sun has a diameter of 1,400,000 km.
The distance from the Earth to the Sun is 149,600,000 km.
The mass of the Sun is 330,000 times that of the Earth.
1. What is the ratio of the diameter of the Sun to the Earth?
≈ 109.873
2. If you were to build a scale model of the solar system and the Sun is 0.4 inches in
diameter, at what scale factor would you be building?
≈ 1 : 1.38 X 1011
3. For the scale factor found in #2, what would be the distance from the Sun to the
Earth in inches?
≈ 42.68 in
4. If you were to build a scale model of the solar system to a scale of 1 : 64,000,000,
what would be the diameter of the Sun in centimeters?
≈ 2,187.50 cm
5. If you were to build a scale model of the solar system to a scale of 1 : 64,000,000,
how far would the Earth be from the Sun in meters?
≈ 2,337.50 m
Optical Interferometer QR – Lab A - 12
B. Find the following for one or more of the planets.
1. What is the volume of the planet in cubic kilometers?
2. What is the volume of the planet in cubic miles?
(All answers are approximates)
Planet
Volume
(in cubic kilometers scientific notation)
Volume
(in cubic miles scientific notation)
Mercury
6.08 X 1010
1.46 X 1010
Venus
9.29 X 1011
2.23 X 1011
Earth
1.09 X 1012
2.61 X 1011
Mars
1.64 X 1011
3.94 X 1010
Jupiter
1.53 X 1015
3.67 X 1014
Saturn
9.17 X 1014
2.21 X 1014
Uranus
6.99 X 1013
1.68 X 1013
Neptune
6.36 X 1013
1.53 X 1013
Optical Interferometer QR – Lab A - 13
3. What is the ratio of the diameter of the Sun to the diameter of the planet?
4. What is the ratio of the distance of this planet to the Sun versus the distance from
the Earth to the Sun?
5. What is the ratio of the mass of the Sun to the mass of the planet?
(All answers are approximates)
Planet
Ratio of Sun diameter
to planet diameter
Ratio of planet
distance from Sun to
Earth distance from
Sun
Ratio of Sun mass to
planet mass
Mercury
287.00 : 1
0.39 : 1
5,969,696.97 : 1
Venus
115.66 : 1
0.72 : 1
404,517.45 : 1
Earth
109.75 : 1
1:1
329,431.44 : 1
Mars
206.06 : 1
1.52 : 1
3,063,763.61 : 1
Jupiter
9.79 : 1
5.20 : 1
1,036.84 : 1
Saturn
11.61 : 1
9.54 : 1
3,462.21 : 1
Uranus
27.39 : 1
19.19 : 1
22,669.74 : 1
Neptune
28.27 : 1
30.06 : 1
19,313.73 : 1
Optical Interferometer QR – Lab A - 14
6. If you were to build a scale model of the solar system and the Sun is 0.4 inches in
diameter, what would be the diameter of the planet in inches?
7. If you were to build a scale model of the solar system and the Sun is 0.4 inches in
diameter, what would be the diameter of the planet in feet?
(Interesting: if you build the solar system at this scale, you can fit the entire solar
system on a roll of paper towels.)
(All answers are approximates)
Planet
Scaled diameter
(in inches)
Scaled distance from
Sun
(in feet)
Mercury
0.001
1.38
Venus
0.003
2.57
Earth
0.004
3.56
Mars
0.002
5.42
Jupiter
0.041
18.50
Saturn
0.034
33.92
Uranus
0.015
68.26
Optical Interferometer QR – Lab A - 15
8. If you were to build a scale model of the solar system to a scale of
1 : 64,000,000, what would be the diameter of the planet in centimeters?
9. If you were to build a scale model of the solar system to a scale of
1 : 64,000,000, what would be the diameter of the planet in meters?
(All answers are approximates)
Planet
Mercury
Scaled diameter
(in centimeters)
Scaled distance from
Sun
(in meters)
7.62
904.844
Venus
18.91
1,696.03
Earth
19.93
2,337.50
Mars
10.616
3,561.56
Jupiter
223.41
12,161.40
Saturn
188.34
22,295.90
Uranus
78.97
44,859.20
Neptune
773.88
70,266.70
Optical Interferometer QR – Lab A - 16
C. Technically, the orbit that a planet follows around the Sun is actually an ellipse.
However, most of the orbits are close to a circle. Interestingly, the one planet that
had an orbit that was the most elliptical was Pluto, and that was one of the reasons
that it was reclassified to a dwarf planet. So the eight planets all have orbits that are
mostly circular.
1. Find the ration of the area of the orbit that a planet sweeps out in one period to the
area of the orbit that the Earth sweeps out in one period.
(All answers are approximates)
Planet
Ratio of planet orbit
area to Earth orbit
area
Mercury
0.15 : 1
Venus
0.52 : 1
Earth
1:1
Mars
2.32 : 1
Jupiter
27.05 : 1
Saturn
90.91 : 1
Uranus
367.61 : 1
Neptune
903.41 : 1
Optical Interferometer QR – Lab A - 17
III.
Percents
Planet
Mercury
Diameter
(in meters)
Diameter
(in miles)
4,878,000
3,031.05
Venus
12,104,000
7,521.08
Earth
12,756,000
7,926.21
Mars
6,794,000
4,221.60
Jupiter
142,984,000
88,846.1
Saturn
120,536,000
74,987.6
Uranus
51,118,000
31,763.3
Neptune
49,528,000
30,775.3
A. By what percent is the diameter of Earth bigger than Mercury?
61.8%
B. By what percent is the diameter of Earth bigger than Venus?
5.1%
C. By what percent is the diameter of Earth smaller than Jupiter?
1020.9%
D. By what percent is the diameter of Sun bigger than Jupiter?
879.1%
Optical Interferometer QR – Lab A - 18
Laboratory B
Question Reservoir
With Answers
Mathematical Voyage
The Dimensions Program
Optical Interferometer Project
Site
Figure 1 State of Arizona
Courtesy of myonlinemaps.com
Project Grant Team
Prof. Kathryn Kozak
Project Designer
Patricia L. Hirschy
Principal Investigator
John S. Pazdar
Program Director
Prof. Mary Beth Orrange
Project Tester
Dennis C. Ebersole
Principal Investigator
Geometry
I.
Dimensional
A. The Naval Prototype Optical Interferometer (NPOI) is located on a piece of property
that is roughly a square that is 375 m by 375 m.
1. What is the perimeter of the property in meters?
1,500 m
2. What is the perimeter of the property in feet?
4,921 33/127 ft,
625,000/127 ft,
≈ 4,921.260 ft
3. What is the area of the property in square meters?
140,625 sq m
4. What is the area of the property in square feet?
≈ 1,513,675.901 sq ft
5. What is the area of the property in acres?
≈ 34.749 acres
Optical Interferometer QR – Lab B - 2
B. The NPOI is located on a piece of property that is roughly a square that is 375 m by
375 m. It could also be on a piece of property that is a triangle with the length of the
base being 375 m, and the height also being 375 m.
1. What is the perimeter of the property as a triangle in meters?
1,125 m
2. What is the perimeter of the property as a triangle in feet?
3,690 120/127 ft,
468,750/127 ft,
≈ 3,690.945 ft
3. What is the area of the property as a triangle in square meters?
70,312.5 sq m,
140,625/2 sq m,
70,312.5 sq m
4. What is the area of the property as a triangle in square feet?
≈ 756,837.454 sq ft
5. What is the area of the property as a triangle in acres?
≈ 17.375 acres
Optical Interferometer QR – Lab B - 3
C. The Beam Combining Building for the NPOI is 13.5 m in length, by 6.75 m in width,
and 4 m in height.
1. What is the perimeter of the Beam Combining Building in meters?
40.5 m
2. What is the perimeter of the Beam Combining Building in feet?
132 111/254 ft,
16,875/254 ft,
≈ 132.874 ft
3. What is the surface area of the Beam Combining Building, excluding the bottom,
in square meters?
162 sq m
4. What is the surface area of the Beam Combining Building, excluding the bottom
in square feet?
≈ 1,743.753 sq ft
5. What is the area of the floor of the Beam Combining Building in square meters?
91 1/8 sq m,
729/8 sq m,
91.125 sq m
6. What is the area of the floor of the Beam Combining Building in square feet?
≈ 980.861 sq ft
7. What is the volume of the Beam Combining Building in cubic meters?
364.5 cu m,
729/2 cu m,
364.5 cu m
8. What is the volume of the Beam Combining Building in cubic feet?
≈ 12,872.196 cu ft
Optical Interferometer QR – Lab B - 4
D. The Control Building for the NPOI is 16.5 m in length, by 6.5 m in width, and 4 m in
height.
1. What is the perimeter of the Control Building in meters?
46 m
2. What is the perimeter of the Control Building in feet?
150 350/381 ft,
57,500/381 ft,
≈ 150.919 ft
3. What is the surface area of the Control Building, excluding the bottom, in square
meters?
184 sq m
4. What is the surface area of the Control Building, excluding the bottom, in square
feet?
≈ 1,980.560 sq ft
5. What is the area of the floor of the Control Building in square meters?
107.25 sq m,
429/4 sq m,
107.25 sq m
6. What is the area of the floor of the Control Building in square feet?
1,154 1,420/3,307 sq ft,
3,817,698/3,307 sq ft,
≈ 1,154.429 sq ft
7. What is the volume of the Control Building in cubic meters?
429 cu m
8. What is the volume of the Control Building in cubic feet?
≈ 174,224.908 cu ft
Optical Interferometer QR – Lab B - 5
Arithmetic
I.
Conversions
A. The Naval Prototype Optical Interferometer (NPOI) is located on a piece of property
that is roughly a square that is 375 m by 375 m.
1. What is the length of property in kilometers?
0.375 km
2. What is the length of the property in centimeters?
.00375 cm
3. What is the length of the property in feet?
1,230 40/127 ft,
156,250/127 ft,
≈ 1,230.315 ft
4. What is the length of the property in miles?
≈ 0.233 mi
Optical Interferometer QR – Lab B - 6
B. The Beam Combining Building for the NPOI is 13.5 m in length, by 6.75 m in width,
and 4 m in height.
1. What is the length of the Beam Combining Building in kilometers?
0.135 km
2. What is the length of the Beam Combining Building in centimeters?
1,350 cm
3. What is the length of the Beam Combining Building in feet?
44 37/127 ft,
5,625/127 ft,
≈ 44.391 ft
4. What is the width of the Beam Combining Building in kilometers?
0.00675 km
5. What is the width of the Beam Combining Building in centimeters?
675 cm
6. What is the width of the Beam Combining Building in feet?
22 37/254 ft,
5,625/254 ft,
≈ 22.146 ft
7. What is the height of the Beam Combining Building in kilometers?
0.004 km
8. What is the height of the Beam Combining Building in centimeters?
400 cm
9. What is the length of the Beam Combining Building in feet?
13 47/381 ft,
5,000/381 ft,
≈ 13.123 ft
Optical Interferometer QR – Lab B - 7
10. On the scale drawing of the NPOI site, 1 in is 140 ft. What is this in centimeters
to meters?
2.54 cm to 42.672 m,
or 1 cm to 16.8 m
11. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Beam Combing Building on the drawing in inches?
length = 1,125/3,556 in,
≈ 0.316 in
width = 1,125/7,112 in,
≈ 0.158 in
height = 250/2,667 in,
≈ 0.094 in
12. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Beam Combing Building on the drawing in centimeters?
length = 45/56 cm,
≈ 0.804 cm
width = 45/112 cm,
≈ 0.402 cm
height = 5/21 cm,
≈ 0.238 cm
Optical Interferometer QR – Lab B - 8
D. The Control Building for the NPOI is 16.5 m in length, by 6.5 m in width, and 4 m in
height.
1. What is the length of the Control Building in kilometers?
0.0165 km
2. What is the length of the Control Building in centimeters?
1,650 cm
3. What is the length of the Control Building in feet?
54 17/127 ft,
6875/127 ft,
≈ 54.134 ft
4. What is the width of the Control Building in kilometers?
0.0065 km
5. What is the width of the Control Building in centimeters?
650 cm
6. What is the width of the Control Building in feet?
21 124/381 ft,
8,125/381 ft,
≈ 21.325 ft
7. What is the height of the Control Building in kilometers?
0.004 km
8. What is the height of the Control Building in centimeters?
400 cm
9. What is the length of the Control Building in feet?
13 47/381 ft,
5,000/381 ft,
≈ 13.123 ft
10. On the scale drawing of the NPOI site, 1 in is 140 ft. What is this in centimeters
to meters?
2.54 cm to 42.672 m,
or 1 cm to 16.8 m
Optical Interferometer QR – Lab B - 9
11. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Control Building on the drawing in inches?
length = 1,375/3,556 in,
≈ 0.387 in
width = 1,625/10,668 in,
≈ 0.152 in
height = 250/2,667 in,
≈ 0.094 in
12. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Control Building on the drawing in centimeters?
length = 55/56 cm,
≈ 0.982 cm
width = 65/168 cm,
≈ 0.387 cm
height = 5/21 cm,
≈ 0.238 cm
Optical Interferometer QR – Lab B - 10
II.
Ratios & Proportions
A. The NPOI is located on a piece of property that is roughly a square that is 375 m by
375 m. It could also be on a piece of property that is a triangle with the length of the
base being 375 m, and the height also being 375 m.
1. What is the ratio of the perimeter of the property as a square to that of the
perimeter of the property as a triangle?
4:3
III.
2. What is the ratio of the area of the property as a square to that of the area of the
property as a triangle?
2:1
Ratios & Proportions
A. On a scale drawing of the NPOI site, the Beam Combining Building is 8 centimeters
in length. By what percent is the scale drawing length from the actual length?
59.3%
B. On a scale drawing of the NPOI site, the Control Building is 4 centimeters in length.
By what percent is the scale drawing length from the actual length?
24.2%
Optical Interferometer QR – Lab B - 11
Laboratory C
Question Reservoir
With Answers
Mathematical Voyage
The Dimensions Program
Optical Interferometer Project
Optical Interferometer
Figure 1 Site Map of the NPOI, Flagstaff, AZ
Courtesy of Lowell Observatory
Project Grant Team
Prof. Kathryn Kozak
Project Designer
Patricia L. Hirschy
Principal Investigator
John S. Pazdar
Program Director
Prof. Mary Beth Orrange
Project Tester
Dennis C. Ebersole
Principal Investigator
Geometry
I.
Dimensions
A. Each arm of the NPOI consists of tubes that are 6 inches in diameter. The longest
tube on each arm spans the entire length of 250 m.
1. What is the cross-sectional area of the tube in square inches?
≈ 0.349 sq in
2. What is the cross-sectional area of the tube in square centimeters?
≈ 182.415 sq cm
3. What is the cross-sectional area of the tube in square meters?
≈ 0.182 sq m
4. What is the cross-sectional area of the tube in square feet?
≈ 0.196 sq ft
5. What is the surface area of the tube in square feet?
≈ 1,288.886 sq ft
6. What is the surface area of the tube in square meters?
≈ 119.731 sq m
7. What is the volume of the tube in cubic feet?
≈ 161.048 cu ft
8. What is the volume of the tube in cubic meters?
≈ 4.560 cu m
Optical Interferometer QR – Lab C - 2
B. To connect the tubes to the mirrors, piers were created every so often to put the
imaging Siderostat Station on. The piers were placed on pads that are 1 ft thick, 10 ft
wide, and 20 ft long. Each pier is 6 ft in diameter.
1. What is the surface area of the pad in square feet?
460 sq ft
2. What is the surface area of the pad in square meters?
≈ 42.735 sq m
3. What is the cross-sectional area of the pad in square feet?
200 sq ft
4. What is the cross-sectional area of the pad in square meters?
≈ 18.581 sq m
5. What is the volume of the pad in cubic feet?
200 cu ft
6. What is the volume of the pad in cubic meters?
≈ 5.663 cu m
7. What is the cross-sectional area of the pier in square feet?
≈ 28.274 sq ft
8. What is the cross-sectional area of the pier in square meters?
≈ 2.627 sq m
Optical Interferometer QR – Lab C - 3
C. The Astrometric Array Siderostat Stations are located inside Astrometric Huts that
are 10 m in length, 4.5 m in width, and 2.5 m in height.
1. What is the surface area of the Astrometric Huts, excluding the bottom, in square
meters?
72.5 sq m,
145/2 sq m
2. What is the surface area of the Astrometric Huts, excluding the bottom, in square
feet?
≈ 780.384 sq ft
3. What is the volume of the Astrometric Huts in cubic meters?
112.5 cu m,
225/2 cu m
4. What is the volume of the Astrometric Huts in cubic feet?
≈ 3,972.900 cu ft
Optical Interferometer QR – Lab C - 4
D. The Long Fixed Path Optical Delay Lines on the NPOI are 20 inches in diameter and
110 m long.
1. What is the cross-sectional area of the Long Delay Lines in square inches?
≈ 314.159 sq in
2. What is the cross-sectional area of the Long Delay Lines in square centimeters?
≈ 2,026.830 sq cm
3. What is the cross-sectional area of the Long Delay Lines in square feet?
≈ 2.182 sq ft
4. What is the cross-sectional area of the Long Delay Lines in square meters?
≈ 0.203 sq m
5. What is the surface area of the Long Delay Lines, excluding one end, in square
inches?
≈ 272,420.610 sq in
6. What is the surface area of the Long Delay Lines, excluding one end, in square
feet?
≈ 1,891.810 sq ft
7. What is the surface area of the Long Delay Lines, excluding one end, in square
meters?
≈ 175.755 sq m
8. What is the surface area of the Long Delay Lines, excluding one end, in square
centimeters?
≈ 1,757,548.805 sq cm
9. What is the volume of the Long Delay Lines in cubic inches?
1,360,532.252 cu in
10. What is the volume of the Long Delay Lines in cubic feet?
≈ 787.345 cu ft
11. What is the volume of the Long Delay Lines in cubic meters?
≈ 22.295 cu m
12. What is the volume of the Long Delay Lines in cubic centimeters?
≈ 22,295,129.080 cu cm
Optical Interferometer QR – Lab C - 5
E. The fast delay lines inside the Beam Combining Building on the NPOI are 20 inches
in diameter and 18 meters long.
1. What is the cross-sectional area of the Fast Delay Lines in square inches?
≈ 314.159 sq in
2. What is the cross-sectional area of the Fast Delay Lines in square centimeters?
≈ 2,026.830 sq cm
3. What is the cross-sectional area of the Fast Delay Lines in square feet?
≈ 2.182 sq ft
4. What is the cross-sectional area of the Fast Delay Lines in square meters?
≈ 0.203 sq m
5. What is the surface area of the Fast Delay Lines, excluding one end, in square
inches?
≈ 44,840.669 sq in
6. What is the surface area of the Fast Delay Lines, excluding one end, in square
feet?
≈ 311.394 sq ft
7. What is the surface area of the Fast Delay Lines, excluding one end, in square
meters?
≈ 28.929 sq m
8. What is the surface area of the Fast Delay Lines, excluding one end, in square
centimeters?
≈ 289,294.062 sq cm
9. What is the volume of the Fast Delay Lines in cubic inches?
≈ 222,632.550 cu in
10. What is the volume of the Fast Delay Lines in cubic feet?
≈ 128.838 cu ft
11. What is the volume of the Fast Delay Lines in cubic meters?
≈ 3.648 cu m
12. What is the volume of the Fast Delay Lines in cubic centimeters?
≈ 3,648,293.850 cu cm
Optical Interferometer QR – Lab C - 6
Arithmetic
I.
Conversions
A. Each arm of the Naval Prototype Optical Interferometer (NPOI) is 250 m long.
1. What is the length of each arm in kilometers?
0.250 km
2. What is the length of each arm in centimeters?
25,000 cm
3. What is the length of each arm in feet?
820 80/381 ft,
312500/381 ft,
≈ 820.210 ft
4. What is the length of each arm in mi?
≈ 0.155 mi
5. On the scale drawing of the NPOI site, 1 in is 140 ft. What is this in centimeters
to meters?
2.54 cm to 42.672 m,
or 1 cm to 16.8 m
6. On the scale drawing of the NPOI site, 1 in is 140 ft. What is the length of each
arm on the drawing in inches?
5 2,290/2,667 in,
15,625/2,667 in,
≈ 5.859 in
7. On the scale drawing of the NPOI site, 1 in is 140 ft. What is the length of each
arm on the drawing in centimeters?
14 37/42 cm,
625/42 cm
≈ 14.881 cm
Optical Interferometer QR – Lab C - 7
8. If you were going to make a scaled drawing that was 1 cm is 3 m, what would be
the length of each arm on the drawing in centimeters?
83 1/3 cm,
250/3 cm,
≈ 83.333 cm
9. If you were going to make a scaled drawing that was 1 cm is 3 m, what would be
the length of each arm on the drawing in inches?
32 308/381 in,
12,500/381 in,
≈ 32.808 in
Optical Interferometer QR – Lab C - 8
B. Each arm of the NPOI consists of tubes that are 6 inches in diameter. The longest
tube on each arm spans the entire length of 250 m.
1. What is the diameter in centimeters?
15 6/25 cm,
381/25 cm,
15.24 cm
2. What is the diameter in meters?
381/2,500 m,
0.1524 m
3. What is the diameter in feet?
1/2 ft,
.5 ft
C. To connect the tubes to the mirrors, piers were created every so often to put the
Imaging Siderostat Station on. The piers were placed on pads that are 1 ft thick, 10 ft
wide, and 20 ft long. Each pier is 6 ft in diameter.
1. What are the dimensions of the pad in meters?
length: 6 12/125 m,
762/125 m,
6.096 m
width: 3 6/125 m,
381/125 m,
3.048 m
height: 381/1,250 m,
0.3048 m
2. What are the dimensions of the pad in inches?
length: 240 in
width: 120 in
height: 12 in
3. What are the dimensions of the pad in centimeters?
length: 0.0609 cm
width: 0.03048 cm
height: 0.003048 cm
Optical Interferometer QR – Lab C - 9
D. The Astrometric Array Siderostat Stations are located inside Astrometric Huts that
are 10 m in length, 4.5 m in width, and 2.5 m in height.
1. What are the dimensions of the Astrometric Huts in feet?
length: 32 308/381 ft,
12,500/381 ft,
≈ 32.808 ft
width: 14 97/127 ft,
1,875/127 ft,
≈ 14.764 ft
height: 8 77/381 ft,
3,125/381 ft,
≈ 8.202 ft
2. What are the dimensions of the Astrometric Huts in centimeters?
length: 1/10 m,
0.1 m
width: 9/200 m,
0.045 m
height: 1/40 m,
0.025 m
3. What are the dimensions of the Astrometric Huts in inches?
length: ≈ 328 32/381 in,
125,000/381 in,
328.084 in
width: 177 21/127 in,
225,00/172 in,
≈ 177.165 in
height: 462 26/27 in,
125,00/27 in,
≈ 462.963 in
Optical Interferometer QR – Lab C - 10
4. On the scale drawing of the NPOI site, 1 in is 140 ft. What is this in centimeters
to meters?
length: 25/42 cm,
≈ 0.595 cm
width: 15/56 cm,
≈ 0.268 cm
height: 25/168 cm,
≈ 0.149 cm
5. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Astrometric Huts on the drawing in inches?
length: 625/2667 in,
≈ 0.234 in
width: 375/355 in,
≈ 0.105 in
height: 3,125/53,340 in,
≈ 0.059 in
6. On the scale drawing of the NPOI site, 1 in is 140 ft. What are the dimensions of
the Astrometric Huts on the drawing in centimeters?
length: 25/42 cm,
≈ 0.595 cm
width: 15/56 cm,
≈ 0.268 cm
height: 25/168 cm,
≈ 0.149 cm
Optical Interferometer QR – Lab C - 11
7. If you were going to make a scaled drawing that was 1 centimeter is 3 meter, what
would be the dimensions of the Astrometric huts on the drawing in centimeters?
length: 3 1/3 cm,
10/3 cm,
≈ 3.333 cm
width: 1 1/2 cm,
3/2 cm,
≈ 1.5 cm
height: 5/6 cm,
≈ 0.833 cm
8. If you were going to make a scaled drawing that was 1 cm is 3 m, what would be
the dimensions of the Astrometric Huts on the drawing in inches?
length: 1 119/381 cm,
500/381 cm,
≈ 1.312 cm
width: 75/127 cm,
≈ 0.591 cm
height: 125/127 cm,
≈ 0.984 cm
Optical Interferometer QR – Lab C - 12
E. The long fixed path optical delay lines on the NPOI are 20 inches in diameter and 110
m long.
1. What is the diameter of the Long Delay Lines in feet?
1 2/3 ft,
5/3 ft,
≈ 1.667 ft
2. What is the diameter of the Long Delay Lines in meters?
127/250 m,
0.508 m
3. What is the diameter of the Long Delay Lines in centimeters?
50 4/5 cm,
254/5 cm,
50.8 cm
4. What is the length of the Long Delay Lines in feet?
360 340/381 ft,
137,500/381 ft,
≈ 360.892 ft
5. What is the length of the Long Delay Lines in inches?
4,330 90/127 in,
550,000/127 in,
4,330.709 in
6. What is the diameter of the Long Delay Lines in centimeters?
11,000 cm
7. On the scale drawing of the NPOI site, 1 in is 140 ft. What is this in centimeters
to meters?
2.54 cm to 42.672 m,
or 1 cm to 16.8 m
8. On the scale drawing of the NPOI site, 1 in is 140 ft. What is the length of the
Long Delay Lines on the drawing in inches?
2 1541/267 in,
6,875/2,667 in,
≈ 2.578 in
9. On the scale drawing of the NPOI site, 1 in is 140 ft. What is the length of the
Long Delay Lines on the drawing in centimeters?
2 1,541/267 in,
6,875/2,667 in,
≈ 2.578 in
Optical Interferometer QR – Lab C - 13
10. If you were going to make a scaled drawing that was 1 cm is 3 m, what would be
the length of the Long Delay Lines on the drawing in centimeters?
36 2/3 cm,
110/3 cm,
≈ 36.667 cm
11. If you were going to make a scaled drawing that was 1 cm is 3 m, what would be
the length of the Long Delay Lines on the drawing in inches?
14 166/381 in,
5,500/381in,
≈ 14.436 in
F. The Fast Delay Lines inside the Beam Combining Building on the NPOI are 20
inches in diameter and 18 meters long.
1. What is the diameter of the Fast Delay Lines in feet?
1 2/3 ft,
5/3 ft,
≈ 1.667 ft
2. What is the diameter of the Fast Delay Lines in meters?
127/250 m,
0.508 m
3. What is the diameter of the Fast Delay Lines in centimeters?
50 4/5 cm,
254/5 cm,
50.8 cm
4. What is the length of the Fast Delay Lines in feet?
59 7/127 ft,
7,500/127 ft,
≈ 59.055 ft
5. What is the length of the Fast Delay Lines in inches?
708 84/127 in,
90,000/127 in,
≈ 708.661 in
6. What is the diameter of the Fast Delay Lines in centimeters?
1,800 cm
Optical Interferometer QR – Lab C - 14
II.
Ratios and Proportions
A. What is the ratio of the cross-sectional area to the surface area of the tube?
0.00152
B. What is the ratio of the cross-sectional area to the surface area of the pier?
2.30
III.
Percents
A. On a scale drawing of the NPOI site, an arm is 15 centimeters long. By what percent
is the scale drawing length from the actual length?
0.06%
B. On a scale drawing of the NPOI site, a tube is 3 centimeters in diameter. By what
percent is the scale drawing diameter from the actual diameter?
19.7%
D. On a scale drawing of the NPOI site, an Astrometric Hut is 3 centimeters high. By
what percent is the scale drawing height from the actual height?
1.2%
Optical Interferometer QR – Lab C - 15
Laboratory D
Question Reservoir
With Answers
Mathematical Voyage
The Dimensions Program
Optical Interferometer Project
Light-Years
Figure 1 Milky Way Galaxy Artist Concept
Courtesy of NASA/JPL-Caltech/R Hurt (SSC)
Project Grant Team
Prof. Kathryn Kozak
Project Designer
Patricia L. Hirschy
Principal Investigator
John S. Pazdar
Program Director
Prof. Mary Beth Orrange
Project Tester
Dennis C. Ebersole
Principal Investigator
Geometry
I.
Dimensions
A. The Binary Star IM Pegasi is 300 light-years from Earth. The primary star is about
13 times the size of the Sun and is know as a red giant. The Sun has a diameter of
1,400,000 km.
1. What is the surface area of the primary star in IM Pegasi in square meters?
≈ 1.041 X 1021 sq m
2. What is the surface area of the primary star in IM Pegasi in square miles?
≈ 4.018 X 1014 sq mi
3. What is the surface area of the primary star in IM Pegasi in square kilometers?
≈ 1.041 X 1015 sq km
4. What is the cross-sectional are of the primary star in IM Pegasi in square meters?
≈ 2.602 X 1020\ sq m
5. What is the cross-sectional are of the primary star in IM Pegasi in square miles?
≈ 1.005 X 1014 sq mi
6. What is the cross-sectional are of the primary star in IM Pegasi in square
kilometers?
≈ 2.602 X 1020\ sq m
7. What is the volume of the primary star in IM Pegasi in cubic meters?
≈ 3.157 X 1030 cu m
8. What is the volume of the primary star in IM Pegasi in cubic miles?
≈ 6.060 X 1021 cu mi
9. What is the volume of the primary star in IM Pegasi in cubic kilometers?
≈ 3.157 X 1021 cu km
Optical Interferometer QR – Lab D - 2
B. Zeta Orionis is the left most star in Orion’s belt in the constellation Orion and was
imaged by the NPOI in 1998. At that time, it was determined to be a binary star
system. It is approximately 800 light-years from the Earth. The primary star has a
diameter that is 20 times the sun. The Sun has a diameter of 1,400,000 km.
1. What is the surface area of the primary star in Zeta Orionis in square meters?
≈ 2.463 X 1021 sq m
2. What is the surface area of the primary star in Zeta Orionis in square miles?
≈ 9.511 X 1014 sq mi
3. What is the surface area of the primary star in Zeta Orionis in square kilometers?
≈ 2.463 X 1015 sq km
4. What is the cross-sectional are of the primary star in Zeta Orionis in square
meters?
≈ 6.158 X 1020 sq m
5. What is the cross-sectional are of the primary star in Zeta Orionis in square miles?
≈ 2.38 X 1014 sq mi
6. What is the cross-sectional are of the primary star in Zeta Orionis in square
kilometers?
≈ 6.158 X 1014 sq km
7. What is the volume of the primary star in Zeta Orionis in cubic meters?
≈ 1.149 X 1031 cu m
8. What is the volume of the primary star in Zeta Orionis in cubic miles?
≈ 2.758 X 1021 cu mi
9. What is the volume of the primary star in Zeta Orionis in cubic kilometers?
≈ 1.149 X 1022 cu km
Optical Interferometer QR – Lab D - 3
C. The Mizar system in the Big Dipper consists of Mizar A and Mizar B, which are two
stars that rotate around each other every thousands of years or so. It has been known
that Mizar A is itself a binary system, and was imaged for the first time by the NPOI
in 1996. The period of this system is 20 years. The whole system is 78 light-years
from Earth. The diameter of Mizar A’s primary star is 4.12 times the diameter of the
Sun. The Sun has a diameter of 1,400,000 km.
1. What is the surface area of the primary star in Mizar A in square meters?
≈ 1.045 X 1020 sq m
2. What is the surface area of the primary star in Mizar A in square miles?
≈ 4.035 X 1013 sq mi
3. What is the surface area of the primary star in Mizar A in square kilometers?
≈ 1.045 X 1014 sq km
4. What is the cross-sectional are of the primary star in Mizar A in square meters?
≈ 2.613 X 1019 sq m
5. What is the cross-sectional are of the primary star in Mizar A in square miles?
≈ 1.009 X 1013 sq mi
6. What is the cross-sectional are of the primary star in Mizar A in square
kilometers?
≈ 2.613 X 1013 sq km
7. What is the volume of the primary star in Mizar A in cubic meters?
≈ 1.005 X 1029 cu m
8. What is the volume of the primary star in Mizar A in cubic miles?
≈ 2.410 X 1019 cu mi
9. What is the volume of the primary star in Mizar A in cubic kilometers?
≈ 1.005 X 1020 cu km
Optical Interferometer QR – Lab D - 4
Arithmetic
I.
Conversions
A. The speed of light is 3 x 108 meters per second. A light year is defined to be how far
light travels in one year.
1. What is the speed of light in feet per second?
≈ 984,251,968.504 ft/sec
2. What is the speed of light in miles per hour?
≈ 671,080,887.616 mi/hr
3. What is the speed of light in kilometers per hour?
≈ 1,080,000,000 km/hr
4. How many meters can light travel in one year?
5. How many miles can light travel in one year?
6. How many kilometers can light travel in one year?
Optical Interferometer QR – Lab D - 5
≈ 9.4608 X 1015 m
≈ 5.879 X 1012 mi
≈ 9.4608 X 1012 km
B. The Binary Star IM Pegasi is 300 light-years from Earth. The primary star is about
13 times the size of the Sun and is know as a red giant. The Sun has a diameter of
1,400,000 km.
1. What is the distance that IM Pegasi is from the Earth in meters?
2. What is the distance that IM Pegasi is from the Earth in miles?
≈ 2.838 X 1018 m
≈ 1.764 X 1015 m
3. What is the distance that IM Pegasi is from the Earth in kilometers?
≈ 2.838 X 1015 km
4. What is the diameter of the primary star in IM Pegasi in meters?
1,820,000,000,000 m
5. What is the diameter of the primary star in IM Pegasi in miles?
≈ 1.131 X 107 mi
6. What is the diameter of the primary star in IM Pegasi in kilometers?
18,200,000 km
Optical Interferometer QR – Lab D - 6
C. Zeta Orionis is the left most star in Orion’s belt in the constellation Orion and was
imaged by the NPOI in 1998. At that time, it was determined to be a binary star
system. It is approximately 800 light-years from the Earth. The primary star has a
diameter that is 20 times the sun. The Sun has a diameter of 1,400,000 km.
1. What is the distance that Zeta Orionis is from the Earth in meters?
≈ 7.569 X 1018 m
2. What is the distance that Zeta Orionis is from the Earth in miles?
≈ 4.703 X 1015 m
3. What is the distance that Zeta Orionis is from the Earth in kilometers?
≈ 7.569 X 1015 km
4. What is the diameter of the primary star in Zeta Orionis in meters?
28,000,000,000 m
5. What is the diameter of the primary star in Zeta Orionis in miles?
≈ 1.740 X 107 mi
6. What is the diameter of the primary star in Zeta Orionis in kilometers?
28,000,000 km
Optical Interferometer QR – Lab D - 7
D. The Mizar system in the Big Dipper consists of Mizar A and Mizar B, which are two
stars that rotate around each other every thousands of years or so. It has been known
that Mizar A is itself a binary system, and was imaged for the first time by the NPOI
in 1996. The period of this system is 20 years. The whole system is 78 light-years
from Earth. The diameter of Mizar A’s primary star is 4.12 times the diameter of the
Sun. The Sun has a diameter of 1,400,000 km.
1. What is the distance that Mizar is from the Earth in meters?
2. What is the distance that Mizar is from the Earth in miles?
3. What is the distance that Mizar is from the Earth in kilometers?
≈ 7.379 X 1017 m
≈ 5.586 X 1014 mi
≈ 7.379 X 1014 km
4. What is the diameter of the primary star in Mizar A in meters?
5,768,000,000 m
5. What is the diameter of the primary star in Mizar A in miles?
≈ 3.584 X 106 mi
6. What is the diameter of the primary star in Mizar A in kilometers?
5,768,000 km
Optical Interferometer QR – Lab D - 8
II.
Ratios & Proportions
A. The Binary Star IM Pegasi is 300 light-years from Earth. The primary star is about
13 times the size of the Sun and is know as a red giant. The Sun has a diameter of
1,400,000 km.
1. What is the ratio of the surface area of the primary star in IM Pegasi to the surface
area of the Sun?
169 : 1
2. What is the ratio of the cross-sectional area of the primary star in IM Pegasi to the
surface area of the Sun?
169 : 1
3. What is the ratio of the volume of the primary star in IM Pegasi to the surface
area of the Sun?
2,197 : 1
B. Zeta Orionis is the left most star in Orion’s belt in the constellation Orion and was
imaged by the NPOI in 1998. At that time, it was determined to be a binary star
system. It is approximately 800 light-years from the Earth. The primary star has a
diameter that is 20 times the sun. The Sun has a diameter of 1,400,000 km.
1. What is the ratio of the surface area of the primary star in Zeta Orionis to the
surface area of the Sun?
400 : 1
2. What is the ratio of the cross-sectional area of the primary star in Zeta Orionis to
the surface area of the Sun?
400 : 1
3. What is the ratio of the volume of the primary star in Zeta Orionis to the surface
area of the Sun?
8,000 : 1
Optical Interferometer QR – Lab D - 9
C. The Mizar system in the Big Dipper consists of Mizar A and Mizar B, which are two
stars that rotate around each other every thousands of years or so. It has been known
that Mizar A is itself a binary system, and was imaged for the first time by the NPOI
in 1996. The period of this system is 20 years. The whole system is 78 light-years
from Earth. The diameter of Mizar A’s primary star is 4.12 times the diameter of the
Sun. The Sun has a diameter of 1,400,000 km.
1. What is the ratio of the surface area of the primary star in Mizar A to the surface
area of the Sun?
16.9744 : 1
2. What is the ratio of the cross-sectional area of the primary star in Mizar A to the
surface area of the Sun?
16.9744 : 1
3. What is the ratio of the volume of the primary star in Mizar A to the surface area
of the Sun?
69.934528 : 1
Optical Interferometer QR – Lab D - 10
III.Percents
A. By what percent is the surface area of the primary star of IM Pegasi bigger than the
Sun?
16,900%
B. By what percent is the cross-sectional area of the primary star of IM Pegasi that of
the Sun?
16,900%
C. By what percent is the volume of the primary star of IM Pegasi that of the Sun?
219,700%
D. By what percent is the surface area of the primary star of Zeta Orionis that of the
Sun?
40,000%
E. By what percent is the cross-sectional area of the primary star of Zeta Orionis that of
the Sun?
40,000%
F. By what percent is the volume of the primary star of Zeta Orionis that of the Sun?
800,000%
G. By what percent is the surface area of Mizar A that of the Sun?
1,697%
H. By what percent is the cross-sectional area of Mizar A that of the Sun?
1,697%
I. By what percent is the volume of Mizar A that of the Sun?
6,993%
Optical Interferometer QR – Lab D - 11