Answer to Question #173606 in Astronomy | Astrophysics for ANJU JAYACHANDRAN

Question

1d) 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

We don't know does the question concern the local apparent time or the local mean time. Nevertheless, the difference between these times will be the same for two places. We also know that these places are situated in one time zone, so times of time zone will be the same. But local mean times will be different.

$T_2-T_1 = \lambda_2 - \lambda_1,$ where $\lambda$ is the longitude measured in hours. To transform longitude from degrees into hours, we should divide h by 15.

$T_S-T_M = \lambda_S - \lambda_M = \dfrac{92}{15} - \dfrac{73}{15} = \dfrac{19}{15} = 1\dfrac{4}{15}$ h, or 1 hour 16 minutes. Therefore, the time at Mumbai will be $12^h - 1^h16^m = 10^h44^m.$