Astronomy Assignment – Measurement and Calculation

Objectives/HW

The student will be able to:		HW:
1	Utilize and convert SI units and other appropriate units in order to solve problems.	1
2	Utilize the concept of orders of magnitude to compare amounts or sizes.	2 – 3
3	Solve problems involving rate, amount, and time.	4 – 7
4	Solve problems involving “skinny triangles.”	8 – 13
5	Solve problems relating the radius of a circle to diameter, circumference, arc length, and area.	14 – 15
6	Define and utilize the concepts of latitude, longitude, equator, North Pole and South Pole in order to solve related problems.	16 – 21
7	Define and utilize the concepts of altitude, azimuth, zenith, and nadir in order to solve related problems.	22 – 24

The following problems must be worked on separate paper. In order to receive full credit for problems 1 – 15, 19, and 24 you must show work on the paper, showing the method by which the answer was obtained or some written support for the answer given. Anyone reading your paper should be able to tell both your answer to the problem or question and the way that you arrived at that answer. Place each answer in a box or circle to distinguish it from the work or explanation for that problem.

1.     Do the following conversions using the factor label method. Show work – calculations using metric prefixes and one or more of these conversion factors: 1 inch = 2.54 cm, 12 in = 1 ft, 3 ft = 1 yd, 1 min = 60 s, 60 min = 1 h, 1 mile = 5280 ft, 1 L = 1000 cm³, 1 kg ≈ 2.205 lbs
a. 100.0 yds = ? m                                   (The length of a football field)
b. 5.00 km = ? mi                                    (Length of a cross-country race)
c. 6.00 ft = ? cm                                       (Height of a person)
d. 3.00 × 10⁸ m/s = ? mph                      (The speed of light!)
e. 3.00 × 10⁸ m/s = ? miles per second    (Often quoted in these units…)
f. 55 mph = ? km/h                                 (The speed of Milligan)
g. 43560 ft² = ? m²                                   (This is 1.000 acre or 0.4047 hectare.)
h. 1.00 g/mL = ? lbs/ft³                            (The density of water)

2. Use information found in your book or on the internet to determine the following ratios and state the order of magnitude: (a) The mass of Jupiter compared to the mass of Earth. (b) The mass of the Sun compared to the mass of Earth. (c) Given that a person is about 100 kg, what are some common objects that would have the same order of magnitude ratios as found in parts (a) and (b)?

3. The volume of a sphere is (4πr³)/3. The mean radius of Earth is 6370 km. The mean radius of Jupiter is 71,400 km. Use this information to compare the size of these two planets. (a) Calculate the ratio of the diameters and state as an order of magnitude. (b) Calculate the ratio of the volumes and state as an order of magnitude.

4. The typical driver has a speed of around 30 m/s (65 mph). (a) At this speed what distance does a car travel in 1.00 minute? (b) At the same speed how much time will it take to travel 1.00 km?

5. Driving from Knoxville to Yellowstone Mr. M traveled about 1800 miles. Over the course of three days he was at the wheel about 34 hours. Determine the average speed of his 1974 Volkswagen bus as it traveled over the road.

6. Traveling at a speed of 3.00 × 10⁸ m/s light travels a certain distance in one year of time. This distance is known as a light-year. (a) Determine the distance equal to one light-year in units of kilometers and in units of miles. (b) It takes about one second for light to travel the distance from the Earth to the Moon. Determine the distance equal to one “light-second” in units of kilometers and in units of miles. (c) Determine the time required to travel one “light-second” at a speed of 30 m/s (driving speed).

7. The distance from the Sun to the Earth is about 149.6 Gm. (a) Determine the amount of time in minutes for light to travel from the Sun to the Earth. (P.S. This means when we look at the Sun we are seeing it as it was this many minutes in the past – i.e. we are looking “into the past.”) (b) What distance is 149.6 Gm, measured in “light-minutes”? (c) Determine the time required to go from Earth to Sun at a speed of 30 m/s (driving speed).

8. A certain telescope has a field of view of 1.0°. What is the actual width, in meters, of the view seen through the telescope from a distance of 1600 m?

9. Suppose you view a 6.0 foot tall person from a distance of 100 yards. What is the angular size of the person?

10. At its closest to Earth, Jupiter is 5.9 × 10¹¹ m away. Given the diameter of Jupiter is 1.4 × 10⁸ m, determine the apparent angular diameter of Jupiter as seen from Earth. Give your answer in units of arc seconds.

11. The angular diameter of the Moon (as it appears from Earth) varies from about 33 arc minutes when it is closest to the Earth to about 29 arc minutes when it is farthest from the Earth. Given that the actual diameter of the Moon is 3480 km determine the closest and farthest distance from the Earth to the Moon.

12. The diameter of the Sun is about 1.39 × 10⁹ m. As seen from Earth at the distance given above what is the apparent angular diameter of the Sun in arc minutes?

13. At a certain point in time Mercury appears half lit as seen from Earth. This indicates that the Sun, Earth, and Mercury form a (somewhat skinny) right triangle. Suppose the angular separation between the Sun and Mercury is 19° from our perspective on Earth (this angular value is known as the elongation of a planet). The distance from the Sun to the Earth (the hypotenuse of this triangle) is 150 Gm. Use this information to determine: (a) the distance from the Sun to Mercury and (b) the distance from the Earth to Mercury. A diagram should help tremendously!

14. The radius of the Earth is 6378 km at its equator. A person standing on the equator moves in a huge circle as the Earth rotates about its own axis once every 24 hours. (a) Determine the circumference of the equator. (b) Determine the distance the person moves in 1.0 hour (this is an arc length). (c) Determine the speed of the person moving in the circular path and covert to mph.

15. At a certain point in time the sun of an alien world is directly overhead that world’s equator. At the exact same time, alien inhabitants 1000 km due north of the equator observe the sun’s rays strike the surface at an angle of 5.0° from vertical (meaning they are at latitude 5.0° north of the equator). (a) Determine the circumference of this alien world. (b) Determine the diameter of this alien world.

16. The following coordinates of latitude on the Earth specify locations that are known by other names. For each degree of latitude given state its significance. Or in other words if you were at this latitude, where would you be? (a) Latitude +90°. (b) Latitude −90°. (c) Latitude 0°.

17. Consider the location of the United States on the Earth. (a) Does it lie in a region of positive (N) or negative (S) values of latitude? (b) Does it lie in a region of positive (E) or negative (W) values of longitude?

18. State the values of longitude for (a) the Prime Meridian, and (b) the International Date Line.

19. Time zones such as the Eastern, Central, Mountain, and Pacific Time Zones are defined in terms of longitude. Given that there are 24 equally spaced time zones around the world, calculate how “wide”, in degrees of longitude, each time zone should be. Show work!

20. Use your map of the globe to determine the approximate coordinates of the following: (a) Los Angeles, (b) the southern tip of Africa, (c) London, (d) the Galapagos Islands (off the coast of Ecuador), (e) Sydney.

21. Use your map of the globe to name the location specified by the following coordinates: (a) 90° W, 30° N; (b) 158° W, 21° N; (c) 2°, 49° N; (d) 140° E, 36° N; (e) 145° E, 42° S.

22. Describe the following sightings from a ship at sea by using compass points and a description in words of “how far up” in the sky: (a) a ship is spotted at altitude 0°, azimuth 315°; (b) a seagull is spotted at the zenith; (c) an airplane is spotted at altitude 45°, azimuth 180°; (d) an octopus is spotted at the nadir; (e) the star Polaris is spotted at altitude 20°, azimuth 0°.

23. Suppose you live on the equator. On the day of the equinox the sun will rise exactly due east at 6 AM, pass directly overhead at 12 noon, and set exactly due west at 6 PM. (This will never happen in Knoxville on any day!) For this location and date determine the Sun’s position in the altazimuth coordinate system for the following times: (a) 6 AM, (b) 9 AM, (c) noon, (d) 2 PM, (e) 8 PM. (Hint: assume the Sun moves equal increments across the sky in equal amounts of time. Make a diagram!)

24. Suppose you sight a radio tower and determine the coordinates of its base to be altitude 5.0°, azimuth 135° and of its top to be altitude 6.1°, azimuth 135°. Assume the tower to be 5.0 miles away. (a) In what direction (compass point) is the tower located? (b) Calculate the apparent angular height of the tower. (c) Determine the approximate actual height of the tower measured in feet. (1 mile = 5280 ft) Show your work for parts (b) and (c).

Objectives/HW

Answers