One city is at a longitude of 78^∘ E while a second on is at 95^∘ W How many hours will pass bet

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One city is at a longitude of 78^∘ E while a second on is at...

One city is at a longitude of $78^{\circ} \mathrm{E}$ while a second on is at $95^{\circ} \mathrm{W}$ How many hours will pass between a star crossing the meridian in the first city and in the second? If the time zone of each city is based on the closest longitude that is a multiple of $15^{\circ}$ and the star passes overhead in the first city exactly at midnight, what time (by the clock) will it pass over the second city?

Key Concepts

Earth Rotation Rate

The Earth rotates 360° in 24 hours, which means it rotates at a rate of approximately 15° per hour. This basic relation allows one to convert differences in longitude directly into time differences, making it a key concept when calculating how much local time shifts between different locations on the globe.

Longitude and Local Solar Time

Longitude determines the position of a location on Earth relative to a prime meridian, and it directly affects the local solar time. As the Earth rotates, a difference in longitude corresponds to a difference in the time a celestial object, such as a star, crosses the local meridian. Each degree of longitude translates roughly to 4 minutes of time difference.

Time Zones and Standard Time

Time zones are defined based on standardized longitudinal divisions, typically in 15° increments, to simplify the synchronization of clocks within a region. While actual solar time varies continuously with longitude, time zones round each location to the nearest standard meridian, which can introduce a minor offset between local solar time and the clock time.

Meridian Transit

Meridian transit refers to the moment when a celestial object crosses the local meridian, reaching its highest point in the sky. This event marks local midnight for a fixed star when it is directly overhead at the observer’s location, and by comparing the times of transit at different longitudes, one can determine the time difference between locations.

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