Hi All,
This is probably nothing, but for the last 3 days I've been struggling to find a way to accurately determine Lat/Long co-ords on a sphere of known radius (1,122km for the Ruins planet) from a starting point and a bearing - because I had a theory... It also ties into the discussions above nicely, but my thought was this...
The monoliths and triangles lead me to believe the builders of the ruins (not confirmed as the Guardians yet) really like the number 3 - and it suddenly dawned on me that on a sphere you can easily have a triangle where all the internal angles are 90 degrees!
Think of our own dear planet - slice a globe through the equator. Take another slice perpendicular to that (e.g. through the Greenwich meridian, or 0 degrees longtitude), then another slice perpendicular again. You end up with something like a quarter slice of one hemisphere - and the internal angles are all 90 degrees!.
Now, what if the ruins are on one corner, it should be easy to calculate where the other two corners are... except it wasn't that easy. In the past two days I've learnt more about the HAversine formula, and Arctangents / radians and everything else I forgot many years ago!
Anyway - I calculated the coordinates, given the bearing of 65 degrees using the most prominent ridge in the ruins (surely a pointer of some sort) and worked out the four possible points exactly one quarter of the circumference away from the ruins aligned to 65 degrees (and 155, 245, 335) and came up with the following co-ordinates:
+21.07 / -52.66
-50.45 / +09.51
-21.07 / -232.66
+50.45 / -170.48
Thinking I only need to check 3 of these, I've checked the first two, but couldn't find anything there, and its currently dark (really dark) in the last one.
However, I'm not so sure my calculations are correct - that third longtitude looks wrong to me (surely max of -180??)
Can someone check my working?
Radius of 1122 gives a Circumference of 7049.73, so one quarter circumference is 1762.43
Known Lat1 and Lon1 cords, and using this formula to find Lat2 and Lon2:
Lat2=ASIN(SIN(LAT1)*COS(distance/Radius)+COS(Lat1)*SIN(distance/Radius)*COS(Bearing))
Lon2 =Lon1+ATAN2(COS(distance/Radius)-SIN(Lat1)*SIN(Lat2),SIN(Bearing1)*SIN(distance/Radius)*COS(Bearing))
(Note: all angles entered and shown in Radians = 57.296 degrees)
Pretty please?
Thoron