How to find latitude and longitude

Question

I have latitude and longitude of a point.I have to find out the latitude and longitude of another point from a relative distance from the known point.For example point A has some location with latitude and longitude.What is the latitude and longitude after moving 1000m south and 500m west from point A.Is there any direct equation to find this? Thanks in advance

Answer 1

Instead of looking up an equation you can calculate as follows. Let R be the radius of the Earth. Let a be the current latitude and b be the current longitude. Then if you move δx metres east (negative for west) then δy metres south, calculating the new longitude can be done as follows.

Intersecting a horizontal plane with the Earth at the current latitude will give you a circle of radius R*cos(a). So to convert δx to the change in longitude, you get something like

δlong = δx * 2π / (2π * R * cos(a)) = δx / (R * cos (a))

The change in latitude is easier, since it doesn't depend on the current position. You're always moving around a great circle through the two poles. Then δlat = δy / R. (Of course you need to mod out by 2 π at some point).

Answer 2

Note the accepted answer is basically the flat earth projection equations:

x = δlon * EarthRadius * cos( lat )
y = δlat * EarthRadius 

For better accuracy over larger distances, you should compute the final lat/lon from a typical bearing/range calculation. See the section Destination point given distance and bearing from start point at this website: http://www.movable-type.co.uk/scripts/latlong.html