# How to calculate latitude and longitude based on relative distance

The coordinates of A on Mars are 125°E and 25°N. The distance of point B is x meters due east from A and y meters due north from A. How to calculate the latitude and longitude of B. Please try to use Matlan language; the coordinate point is located on Mars.

• "Due East" means point B is at the same latitude as point A, and "Due North" means point B is at the same longitude as point A. Point B cannot be both Due East and Due North at the same time! You probably mean than point B is x meters east and y meters north. Commented Jun 28, 2023 at 16:13

This question is more complicated than you might think.

Are you assuming that Mars is a perfect sphere, an oblate spheroid or another type of spheroid shape.

Also, even on a perfect sphere, a change of position of 1 m east or west will translate to a different change in longitude co-ordinates than a similar change of position more poleward or equatorward.

On Earth 1 minute of (great circle) arc is equivalent to 1 nautical mile, which is 1.852 km, which works for latitude here. Because Mars is smaller than Earth 1 minute of arc on Mars will be a smaller distance.

It's clearly a homework question, so I'm going to answer it in the style of a "marking scheme".

The answer needs to state somewhere "The radius of Mars is " and give a value, with units of metres. Units must be stated explicitly.

The answer needs to calculate the length in degrees of arc (or minutes, or seconds, or radians, but STATE UNITS) of 1 m on the ground on the N-S great circle. It needs to be stated as being a GREAT circle.

The answer needs to calculate the length in degrees of arc (etc) of 1 m on the ground along a SMALL circle 25 degrees from the equator (which is a GREAT circle). That it's a small circle must be stated.

Given those factors, develop by simple arithmetic an expression for the Lat/Long of the new point in terms of the lengths X and Y of the ground displacements, and the Lat/Long of the original point.

I think that covers it. I reckon there should be about 12 points for a perfect answer, with 4 of them being for the final expression.

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