Longitude & Time

Recall:

→   The Earth rotates about its axis to make complete rotation in 24hours a whole day.

→  This implies that 1-hour interval is equivalent to 15° interval between two meridians

e.g. Ghana and Cameroon

→   That is 4 minutes is equivalent 1° interval.

→   Places to the East gain time, while places to the West loses time.

Example 1

X(0^o, 35^oE) and Y(0^o, x^oE) are two places on the surface of the Earth such that Y is due  East of X. If the difference in the local times at X and Y is 2 hours 40 minutes, find x^o.

Solution:

Recall 2hours 40minutes = 160 minutes

i.e. 160 minutes ≡y°

4 minutes ≡1°

y° = 1 × \( \frac{160}{4} \) 

y° = 40°

Since Y is due East of x, i.e. Y gains time rather x.

i.e. Longitude of Y = 35 + 40 =75^oE

i.e. x^o = 75^oE

Example 2

Points A and B are two places on Latitude 57^oN. The distance between them is 6,671Km. If B is due East of A, find the:

(i) Local time at A, if the local time at B is 6:30am

(ii) Local time at B if the local time at A is 10:45pm.

Solution

(i) Distance \( \scriptsize AB = 6671 = \normalsize \frac{θ}{360} \scriptsize \; \times \; 2 \; \times \; \normalsize \frac{22}{7} \scriptsize \; \times \; 6400 \)

= θ × 60.8612

i.e.    θ = 109.609

θ = 109.6°

109.6^o ≡ \( \frac{109.6}{15} \)hours

i.e. 109.6 ≡ 7.3 hours

If local time is 6:30am at B, then A will lose time for 7 hours 18 minutes.

i.e. at A = 11:12pm of previous day.

(ii)  Local time at A = 10:45pm, then B will gain time for 7hours 18minutes.

i.e. local time at B = 6:03am of the next day.