Spherical Geometry Help (1 Viewer)

[Beege]

Can anyone help me with these questions:

1. What is the shortest distance along the equator from (0 degrees, 120 degrees east) to (0 degrees, 50 degrees west)

2. Tunis in northern africa has coordinates (37 degrees north, 10 degrees east). Hamburg also lies on the 10 degrees east meridian of longitude and is 1020 nautical miles north of Tunis. What are hamburg's position coordinates?

3. Nagasaki in Japan (33 degrees north, 130 degrees east) and koonalda in south australia (0 degrees south, 130 degrees east) are 3840 nautical miles apart. Find the value of theta (0).

Help would be greatly appreciated, I don't like this topic.

 

[PC]

Can anyone help me with these questions:

1. What is the shortest distance along the equator from (0 degrees, 120 degrees east) to (0 degrees, 50 degrees west)

2. Tunis in northern africa has coordinates (37 degrees north, 10 degrees east). Hamburg also lies on the 10 degrees east meridian of longitude and is 1020 nautical miles north of Tunis. What are hamburg's position coordinates?

3. Nagasaki in Japan (33 degrees north, 130 degrees east) and koonalda in south australia (0 degrees south, 130 degrees east) are 3840 nautical miles apart. Find the value of theta (0).

Help would be greatly appreciated, I don't like this topic.

1. Angular distance = 120 + 50 = 170°.
Distance = 170/360 x 2π x 6400
= 18989.18226
= 18989 km

For questions 2 and 3, always draw a diagram.

2. The distance between Tunis and Hamburg lies along a great circle.
So distance = 1020 nm.
Angular distance = 1020/60 = 17°
Therefore Hamburg's latitude = 37 + 17 = 54°N
Position co-ordinates (54°N,10°E)

3. Same as 2 really.
Distance = 3840 nm
Angular distance = 3840/60 = 64°
Koonalda's latitude = 33 – 64 = –31° (or 31°S)
Co-ordinates are (31°S,130°E)

 

[Beege]

1. Angular distance = 120 + 50 = 170°.
Distance = 170/360 x 2π x 6400
= 18989.18226
= 18989 km

For questions 2 and 3, always draw a diagram.

2. The distance between Tunis and Hamburg lies along a great circle.
So distance = 1020 nm.
Angular distance = 1020/60 = 17°
Therefore Hamburg's latitude = 37 + 17 = 54°N
Position co-ordinates (54°N,10°E)

3. Same as 2 really.
Distance = 3840 nm
Angular distance = 3840/60 = 64°
Koonalda's latitude = 33 – 64 = –31° (or 31°S)
Co-ordinates are (31°S,130°E)

thank you very much