# How can I know the time difference between two cities by knowing the distance between them and earth speed?

Well I know that's the earth speed is:

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

and I have two cities Moscow and NewYork the distance between them is:

$d=7518.92$ $km$

Actually I know that's :

$\Delta t=\frac{d}{v}$

But the distance in this case is a arc distance not a straight also the cities aren't at the same latitude distance look at this photo :

So how can I calculate the time difference $\Delta t$ between them in case like this ?

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Do we know the mass of Jupiter? – Harold Jun 27 '13 at 9:44
What is the distance you've been given? The distance on earth (that would be the one you'd normally give for cities, but according to mapcrow.info/Distance_between_New_York_US_and_Moscow_RS.html the distance between New York and Moscow is much larger than the number you've given), or the distance in space (i.e. straight through earth)? – celtschk Jun 27 '13 at 9:51
If you want to calculate the differnce between local times, you'd better consider merely the difference in longitude and divide it by $15^\circ$ to obtain the difference in hours. – Hagen von Eitzen Jun 27 '13 at 9:53
To know the time difference, you need to know the difference in the longitudinal coordinate of the cities. – Ali Jun 27 '13 at 9:53
@HagenvonEitzen So close :) – Ali Jun 27 '13 at 9:57

What you need is the arc distance (I am assuming by arc you mean the shortest distance on the surface of earth). Assuming that they are at the same latitude then it will take the earth $\frac{5576.74km}{1669.756481km/h}= 3.33985229$ hours.

This is wrong for a bunch of reasons. These are the two I can think of.

Moscow and New York are not at the same lattitude

The speed you gave for the earth is at the Equator.(http://image.gsfc.nasa.gov/poetry/ask/a10840.html) >

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Even if they are at the same latitude, the arc distance is a great circle. What you want is the distance around the parallel of latitude. You can then multiply the equatorial speed by the cosine of the latitude to get the rotation speed at that latitude. – Ross Millikan Aug 26 '14 at 21:43

If you want to figure out the difference between Moscow and New York even though they aren't on the same latitude you can use this formula

d ≈ 111.2 × $\cos−1 [\cos (ΔLon) \cos Lat1 \cos Lat2 + \sin Lat1 \sin Lat2]$

($ΔLon$) is the difference of the longitutudes.

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