Arcseconds

[KvickFlygarn87]

How would one go through to calculate the length of 1 degree/arcminute/arcsecond at a given latitude and radius/circumference/diameter of a sphere?

I am aware that it has to do with cosine, which I'm not that great with, so please, PLEASE! Make your explanation clear.

[maltesh]

An arcsecond of latitude on a particular spherical body is always the same size: 2*À*r/(360*60*60). A good rule of thumb is: Divide the radius of the body by 200km, the resulting answer will be very close to the length along the surface of an arcsecond of longitude in meters.

An arcsecond of longitude at a particular latitude is based on the circumference of that parallel of latitude, which in turn is based on the radius of that parallel of latitude. To find the radius of the latitude parallel, if r is the radius of the world in question, and θ is the latitude

r_θ = r*cos θ

The length of an arcsecond of longitude at latitude θ can then be found by using a variant of the previous equation: L = 2*À*r_θ/(360*60*60) , or for the quick-and-dirty option, divide r_θ's value in kilometers by 200 km to get the approximate length of a second of arc longitude on that body at that latitude in meters.

[KvickFlygarn87]

Ooh, shiny math! I think I get it now, I'll post back if I don't!