Chapter 17 Longitudes & Latitudes 8/22/2018 FYHS-Kulai, Chtan

N longitudes latitude S 8/22/2018 FYHS-Kulai, Chtan

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East North West South 子午线 N The prime Meridian Equator 赤道 S 8/22/2018 FYHS-Kulai, Chtan

latitudes 纬线 8/22/2018 FYHS-Kulai, Chtan

N (0 degree Equator) S Center of the circle 8/22/2018 FYHS-Kulai, Chtan

we said that the position of P is . N If , we said that the position of P is . N P O Q The side view is shown on next slide S 8/22/2018 FYHS-Kulai, Chtan

N 北纬 P Q O Equator S 8/22/2018 FYHS-Kulai, Chtan

The side view of the earth : N R:radius of the earth=6370km O E r1 r1, r2, r3 are radius of each small circle r2 r3 S 8/22/2018 FYHS-Kulai, Chtan

R=6370 km R 8/22/2018 FYHS-Kulai, Chtan

r How to calculate the radius of small circles? N P Q O S 8/22/2018 FYHS-Kulai, Chtan

Find the difference between the latitudes: (a) (b) e.g. 1 Find the difference between the latitudes: (a) (b) 8/22/2018 FYHS-Kulai, Chtan

Soln : Difference between latitudes (b) Difference between latitudes 8/22/2018 FYHS-Kulai, Chtan

Find the difference between the latitudes: (a) (b) e.g. 2 Find the difference between the latitudes: (a) (b) 8/22/2018 FYHS-Kulai, Chtan

Soln : Difference between latitudes (b) Difference between latitudes 8/22/2018 FYHS-Kulai, Chtan

longitudes 经线 8/22/2018 FYHS-Kulai, Chtan

N B C O A D S Greenwich Meridian 8/22/2018 FYHS-Kulai, Chtan

Longitude of A and B are Longitude of C and D are 8/22/2018 FYHS-Kulai, Chtan

What is the position of R ? Q S Greenwich Meridian 8/22/2018 FYHS-Kulai, Chtan

Viewing from the top of N So, R is O P R Q Greenwich Meridian 8/22/2018 FYHS-Kulai, Chtan

e.g. 2 Given that and , find the difference between P and Q. 8/22/2018 FYHS-Kulai, Chtan

Soln : Latitude O P E Q G So, angle POQ is 8/22/2018 FYHS-Kulai, Chtan

Some important facts : Radius of the Earth = 6370km 1 nautical mile = 1.853 km Arc length of a circle = , where is in radians Radius of small circle , 8/22/2018 FYHS-Kulai, Chtan

5. 1’ = 1 nautical mile 海里 1 hour = 8/22/2018 FYHS-Kulai, Chtan

e.g. 3 Find the distance between P and Q in (a) nautical miles , (b) in km of e.g. 2 8/22/2018 FYHS-Kulai, Chtan

Soln : Latitude PO=r O P Q G 8/22/2018 FYHS-Kulai, Chtan

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e.g. 4 8/22/2018 FYHS-Kulai, Chtan

Soln : N P E O Q S Distance between PQ=6300x1.853 km =11,673.9 km =6300 n.m. E O Q S Distance between PQ=6300x1.853 km =11,673.9 km 8/22/2018 FYHS-Kulai, Chtan

e.g. 5 If the standard time (标准时) of London is 9am (0900), find the local time of Tokyo . 8/22/2018 FYHS-Kulai, Chtan

Soln : L has the same logitude as Greenwich i.e. zero degree. O The time difference between L and T : L T 8/22/2018 FYHS-Kulai, Chtan

i.e. It is 06:20 pm Tokyo is on the East side of London. 8/22/2018 FYHS-Kulai, Chtan

e.g. 6 8/22/2018 FYHS-Kulai, Chtan

Soln : Sydne NY G i.e. afternoon 4 o’clock. Longitude difference between 2 cities : NY G Time difference Local time of Sydne is i.e. afternoon 4 o’clock. 8/22/2018 FYHS-Kulai, Chtan

e.g. 7 8/22/2018 FYHS-Kulai, Chtan

Soln : A and B are both on the same longitude : 110 degree East A Distance between A and B = 2000 km B O E 8/22/2018 FYHS-Kulai, Chtan

A B O E So, the latitude of A is : Hence, the location of A is 8/22/2018 FYHS-Kulai, Chtan

e.g. 8 8/22/2018 FYHS-Kulai, Chtan

Soln : N P/Q r O O E Q P S 8/22/2018 FYHS-Kulai, Chtan

= 6065.98 km = 6065.98 / 1.853 n.m. = 3273.60 n.m. 8/22/2018 FYHS-Kulai, Chtan