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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.

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    $\begingroup$ "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. $\endgroup$
    – JohnHoltz
    Jun 28, 2023 at 16:13

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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.

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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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I hated the bullies at school who would beat the answers to the homework out of me. So I'd give them solutions which were wrong in an interesting way, so they had to explain "their" error to the whole class. Revenge is a dish best served at absolute zero. I'd get another beating, but it was worth it to see them squirm.

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