# Math Help - geodesic calculation.

1. ## geodesic calculation.

I have a formula I will post below that I have posted to numerous GIS forums and received no response to my question. The lack of response in those forums has prompted me to post my question here. The question is in what units are 'd'? What would I enter if I wanted 'd' to represent 0.25 miles? I am also assuming that bearing 'tc' is in decimal units between zero and 360. I would like to verify that as well.

Code:
Lat/lon given radial and distance

A point {lat,lon} is a distance d out on the tc radial from point 1 if:

lat=asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
IF (cos(lat)=0)
lon=lon1      // endpoint a pole
ELSE
lon=mod(lon1-asin(sin(tc)*sin(d)/cos(lat))+pi,2*pi)-pi
ENDIF

This algorithm is limited to distances such that dlon <pi/2, i.e those that extend around less than one quarter of the circumference of the earth in longitude. A completely general, but more complicated algorithm is necessary if greater distances are allowed:

lat =asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))
dlon=atan2(sin(tc)*sin(d)*cos(lat1),cos(d)-sin(lat1)*sin(lat))
lon=mod( lon1-dlon +pi,2*pi )-pi

2. Assuming that tc is measured in degrees, then so is d. The actual "distance" would then be given by $d\left(\frac{\pi}{180}\right)R$ where R is the radius of the earth and is in whatever units R is measured in.