THE EARTH AS A SPHERE

1. Explain why the Earth is considered a sphere despite being slightly flattened at the poles.
2. If it's 12:00 noon at Greenwich, what is the local time at 90°E?
3. Why is the shortest distance between two points on the Earth a great circle?
4. Calculate the angular distance between 40°N, 20°E and 40°N, 70°E.
5. How many time zones are there in the world and why?
6. What is the significance of the International Date Line?
7. How many degrees does the Earth rotate in 1 hour?
8. Two cities are 60° apart in longitude. How much time difference exists between them?
9. What is the latitude of the North Pole?
10. How does Earth's sphericity cause time differences?
11. If the Earth rotates from west to east, which direction does the Sun appear to rise from?
12. Explain how longitudes help in calculating local time.
13. Why are all places along the same longitude in the same solar time?
14. What is the longitude of a place whose local time is 6 hours ahead of GMT?
15. Why are great circles important in aviation?
16. Which is longer: 1° of longitude at the equator or at 60° latitude?
17. Why are longitudes not equidistant at all latitudes?
18. What is the length of 1° of latitude in kilometers?
19. What causes the change of seasons on Earth?
20. If it’s 6:00 PM in Tokyo (135°E), what is the time in London (0°)?
21. At what longitude is local time exactly the same as GMT?
22. What is the total number of meridians around the Earth?
23. If a plane travels westward across the International Date Line, what happens to the date?
24. What is the distance in km between two longitudes that are 10° apart at the equator?
25. Why do polar regions have six months of day and night?
26. Define the term "small circle" and how it differs from a great circle.
27. What is the significance of the Tropic of Cancer?
28. Why does a ship heading east gain time?
29. How is solar time different from standard time?
30. Calculate the local time at 75°W when it is 12 noon at GMT.
31. How many kilometers are there between 1° of latitude on Earth's surface?
32. What would be the longitude of a place 3 hours behind GMT?
33. How long does Earth take to complete one rotation?
34. Why are polar routes used by long-distance aircrafts?
35. What is the latitude of the Equator?
36. What is the name of the line opposite the Prime Meridian?
37. Why does the sun appear to move from east to west?
38. If a location is at 15°N, 45°E, in which hemisphere is it located?
39. How many degrees does the Earth rotate per minute?
40. Explain the importance of Earth's curvature in determining time zones.
41. What is the shortest distance in km between two points on the equator that are 90° apart in longitude?
42. Calculate the distance along the great circle between two points on the same meridian, 45° apart in latitude.
43. What is the distance between two points at 30°N latitude and 60°E and 90°E longitude?
44. Explain why the equator is a great circle but the Tropic of Cancer is a small circle.
45. How far apart (in km) are two cities on the equator that are 15° apart in longitude?
46. Find the shortest distance between two points on a sphere along a great circle if the angular distance between them is 120°.
47. Why is traveling along a small circle not the shortest path between two locations?
48. Estimate the surface distance between the North Pole and a point at 60°N latitude along the same meridian.
49. If a plane flies along a great circle route from 0° to 60°N on the same longitude, how far does it travel?
50. Two locations lie on latitude 45°N and are 60° apart in longitude. Estimate the arc distance between them using the cosine formula.

Answers

1. Because it is nearly spherical but slightly flattened at the poles due to rotation — an oblate spheroid.
2. 6:00 PM
3. Because great circles represent the shortest path between two points on a sphere.
4. 70°E - 20°E = 50°
5. 24 — one for each hour and 15° of longitude.
6. It separates two consecutive calendar dates.
7. 15° per hour
8. 60° × 4 = 240 minutes = 4 hours
9. 90°N
10. Due to rotation and the curved surface, different longitudes receive sunlight at different times.
11. East
12. By dividing the difference in degrees from the Prime Meridian by 15.
13. Because they face the Sun at the same time.
14. 6 × 15 = 90°E
15. They help minimize fuel consumption and distance.
16. At equator it’s ~111 km, at 60° it’s ~55.8 km
17. Because meridians converge towards the poles.
18. Approximately 111 km
19. Axial tilt and revolution around the sun.
20. 9:00 AM
21. 0°, the Prime Meridian
22. 360
23. The traveler gains a day.
24. ~1110 km (111 × 10)
25. Due to Earth’s tilt and rotation.
26. Small circles don’t pass through the center; great circles do.
27. It marks the northernmost point the sun appears directly overhead (23.5°N).
28. Because you move into later time zones.
29. Solar time is based on sun’s position, standard time is fixed by zones.
30. 75 × 4 = 300 mins = 5 hrs ⇒ 7:00 AM
31. Approximately 111 km
32. 3 × 15 = 45°W
33. 24 hours
34. They are shorter and save fuel/time
35. 0°
36. 180°, International Date Line
37. Because Earth rotates eastward
38. Northern and Eastern Hemispheres
39. 360° ÷ 1440 mins = 0.25° per minute
40. It causes different areas to experience day/night at different times, hence time zones.
41. 90° × 111.32 km = 10,019 km
42. 45° × 111.32 km = 5,009.4 km
43. ΔLongitude = 30°, so distance = 111.32 × cos(30°) × 30 ≈ 2,894 km
44. The equator passes through Earth’s center, making it a great circle. The Tropic of Cancer doesn’t, so it’s a small circle.
45. 15° × 111.32 = 1,669.8 km
46. 120°/360° × 2πR = (120/360) × 40,075 km = 13,358 km
47. Because small circles do not pass through the center of the sphere and hence do not follow the shortest path.
48. ΔLatitude = 60° ⇒ 60 × 111.32 = 6,679.2 km
49. 60 × 111.32 = 6,679.2 km
50. Arc distance ≈ 60° × 111.32 × cos(45°) ≈ 4,722 km