# How to get parallels of tilted Equator?

I have a Great Circle on Earth, which is not an Equator nor Meridian, and it's not parallel to these. I have four geographical coordinate pairs for it, separated by 90 degrees, so I can use these in KML files and display the circle in Google Earth.

From these coordinates I need to calculate the Longitude and Latitude pairs for a Small Circle that is parallel to that Great Circle and x degrees away from it.

I know how to draw small circles parallel to Equator, which means just adding some degrees of latitude to Equator (or subtracting), but how you do it when you have a Great Circle that is not an Equator or Meridian?

Can it be done like Equatorial coordinates conversion into Ecliptical coordinates in Astronomy?

I have been trying to use this formula but with no success.

http://neoprogrammics.com/php_level-0/Equ_To_Ecl_Coords.txt

• Are you drawing on a spherical globe, or on a flat projection of the globe? If it's the latter, which projection are you using? – Vectornaut Oct 25 '15 at 4:32
• I have it in Google Earth as a kml file. So, it's spherical. – Abhi Oct 25 '15 at 4:57
• When you're drawing on a physical sphere, drawing circles parallel to the equator is just as hard as drawing circles parallel to some other great circle. From the way your question is phrased, and my impression of the way KML files work, it sounds like your difficulty is that you need to describe your circle in latitude/longitude coordinates with respect to the equator. Is that right? – Vectornaut Oct 25 '15 at 6:56
• Yes. I need the lon, lat coordinates for this circle. Or rather the formulas to calculate these. :) I have four coordinate pairs of mentioned great circle that is tilted version of equator. I need to get lat, long for a circle parallel to it, say 17 degress to the north. Other way to put it is, how to convert geographical coordinates from current equator and greenwich meridian based system to other, imaginary one if I know the coordinates of imaginary north pole in current system? – Abhi Oct 25 '15 at 8:03