URGENT: Co-ordinates Calculation?

Question

I have a coordinate (614486.180E, 2148998.500N). Now I have to define another point which is 5000m east and 5000m north of this reference point.

Can I simply add the 5000m to the Easting coordinate and 5000m to the Northing coordinate?

If not, please kindly advise me how? Many thanks.

Answer 1

At that latitude (about 19 N) you can get by with it, but not to millimeter accuracy.  Going 5,000 m E and then 5,000 m N will land you at a different point than going 5,000 m N and then 5,000 m E.  (Going 7,070 m NE will land you at still a third different point.)

For simplicity, assume that the Earth is a perfect sphere with a circumference of 40,007,860 m.  2,148,998.500 m N is about 19.33718674° N.  2,153,998.500 m N is about 19.38217790° N.

614486.180 m E is about

5.529289115° E at the Equator and about 5.859866208° E at 19.33718674° N.  This is not necessary to the problem, but is illustrates the difference caused by different order of measuring on a sphere.

The latitudinal circumference is about 37,750,866.136 m at 19.33718674° N, and about 37,740,451.841 m at 19.38217790° N.

5,000 m E is about

0.04768103° E at 19.33718674° N, and about 0.04769418° E at 19.38217790° N.

This is a difference of 0.00001316° longitude which, at 19.38217790° N, translates back to 1.379 m difference in location between going East first or going North first.  The farther North you are, the more pronounced this difference becomes.