# How can I know the time difference between two cities almost at the same latitude?

Well I know that's the earth rotation speed is:

$v=1669.756481\frac{km}{h}$

I have two cities New York, Madrid almost at the same latitude and the distance between them is:

$d=5774.39$ $km$

I know that's :

$\Delta t=\frac{d}{v}=3.4582$ $hours$ --> +3:27

But after I calculated it I found it wrong (according to http://www.timeanddate.com/worldclock/) and (http://www.happyzebra.com/timezones-worldclock/difference-between-New%20York-and-Madrid.php) time difference = +6:00 ???!!!

• What Jorge mentioned in his answer is correct. If you calculate this you will get $4.5$ h and I think you need to consider the summer timing. As you know some countries add i hour in the summer. – Mhenni Benghorbal Jun 27 '13 at 11:58
• The distance you give is by the great circle route, not around the circle of latitude. This is the first error. If you had the distance around the circle of latitude, you would have to consider the latitude correction that Jorge Fernández gives, which is correct. Between them, you get to five hours. Red's approach is a simpler route to the same. Although Madrid is at almost $0^\circ$ longitude, it uses Central European Time, which is one hour ahead of UT in winter, two in summer. It is one hour ahead of where "it should be". New York does summer time, too, so this cancels out. – Ross Millikan Jun 27 '13 at 13:02
• @Mohammad Fakhrey: You should know the difference between the great circle and the circle of latitude. – Mhenni Benghorbal Jun 27 '13 at 13:38
• @RossMillikan The only error is that I wasn't know that the speed of earth change by changing latitude .. thank you. – Mohammad Fakhrey Jun 27 '13 at 15:05

Speed of the earth at equator is equal to $1669.756481$ km/h. Speed of the earth at latitude of $40.400$ degrees equals

$$1669.756481 \cos\left(40.400\right )\,km/h$$

• @MohammadFakhrey Think of a fan blade spinning (which undergoes the same phenomenon). The part of the fan blade farther out from the center has to move through more space in a given time than does the part nearer the center. By definition, it must move faster. – user714630 Jun 27 '13 at 12:49

I think that you have to take not the real distance between the two cities but the projected distance on the equator. That is the distance between the points of intersection of the meridian of New York and the equator and of the meridian of Madrid and the equator. This because the velocity of rotation of earth of 1669 km/h is taken at equator.

In more details:

Longitudes of New York and Madrid are 78°51' W and 3°41' W so the difference is approximately of 75° (see here).

The Earth's circumference at the equator is 40075.017 km, so the distance between two principal meridians is of

$\frac{40075.017\ \text{km}}{360} = 111.32\ \text{km}$

If you multiply this quantity for 75° that is the difference in longitude between New York and Madrid you get the distance of these two cities projected at the equator:

$111.32\ \text{km} \cdot 75 = 8348.96\ \text{km}$

so

$\Delta t = \frac{8348.96\ \text{km}}{1669.756481\ \text{km}/\text{h}} = 5\ \text{h}$

But Madrid is not in the time zone corresponding to its position but in the Europe Central one so this add an hour giving exactly 6 hours.

• Although Madrid is at almost $0^\circ$ longitude, it uses Central European Time, which is one hour ahead of UT in winter, two in summer. It is one hour ahead of where "it should be". New York does summer time, too, so this cancels out (except a couple weeks a year). – Ross Millikan Jun 27 '13 at 12:56
• @RossMillikan Sorry, I am not an expert of time zones but if I understand correctly my last line is wrong. You are saying that the difference is of 6h instead of 5h because Madrid uses Central European Time, do you? Beside that I think that the calculation until last line is correct. – Red Jun 27 '13 at 13:03
• Your calculation is correct. You have shown that the difference should be 5h. But civil time is whatever the authorities want it to be. New York does summer time, too, on almost the same schedule as Madrid, so this cancels out. I think there is a week or two difference in the transition dates. – Ross Millikan Jun 27 '13 at 13:05