1. There are 360º of longitude and the Earth rotates once every 24 hours. How many degrees does it rotate in one hour?

360º / 24 = 15º per hour.  That is why you often see longitude lines drawn every 15º

2.. How many degrees does the Earth rotate in one minute?

15º / 60 = 0.25º or 1/4º
If we use the minute notation (one minute = 1/60º) then 1/4º = 15 minutes (written 15'

3. If you sailed to the mid Atlantic on the 45º meridian how man hours behind Greenwich time would you be? Let's say it took you six days to sail that far.

Your local time would be 3 hours behind Greenwich time. Noon where you are is three hours later than noon in Greenwich.
Think about how long it would take for your ship on the 45º meridian to move in space to where the 0º Greenwich meridian was. It would take 3 hours because your ship and the ocean and indeed the whole surface of the planet are moving east at about 580 miles per hour.

So what's the problem? All you have to do is compare Greenwich time with local time. If you are three hours behind, then you are at longitude 45º West.

Today it is not a problem! However, in 1714 nobody could build a clock that would keep accurate time on a ship for long enough to sail from England to the West Indies. That was the challenge.

4. My smartphone knows where it is. What latitude and longitude is it at?

The phone gives its position using degrees, minutes (1/60 of a degree) and seconds (1/60 of a minute)
The latitude is 53º35'3'' North. The Longitude is 1º42'37'' West (just a little west of Greenwich).

This technology depends on being able to tell the time, accurate to billionths of a second.

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