Answer to Question #202914 in Astronomy | Astrophysics for Prachi

Question

The latitude and longitude (in degrees) of Mumbai and Shillong are as follows:

Mumbai: latitude 19 N longitude 73 E

Shillong: latitude 26 N longitude 92 E.

When it is 12:00 O’clock local time at Shillong, what is the local time in Mumbai?

Answer 1

Solution. If we talk about the local mean time, then we use the formulas

$$T_{lmt1}=T_0+\lambda_1$$ $$T_{lmt2}=T_0+\lambda_2$$

where T₀ -is the local mean time for the longitude 0E, T_lmt1 - is the local mean time Mumbai; T_lmt2 - is the local mean time Shillong; λ₁ - is the longitude Mumbai; λ₂ - is the longitude Shillong.

Therefore

$$T_{lmt2}-T_{lmt1}=\lambda_2-\lambda_1.$$

To transform longitude from degrees into hours (1hour is 15 degrees; 1degree is 4minutes)

Hence

$$T_{lmt1}=T_{lmt2}-\lambda_2+\lambda_1=12^h-6^h8^m+4^h52^m=10^h46^m$$

If we talk about the local apparent time, that these places are situated in one time zone, so times of time zone will be the same.

Answer. these places are situated in one time zone, so times of time zone will be the same; the local mean time in the Mumbai is equal to

$$T_{lmt1}=10^h46^m$$