Given an existing point in lat/long, distance in (in KM) and bearing (in degrees converted to radians), I would like to calculate the new lat/long. This site crops up over and over again, but I just can't get the formula to work for me.
The formulas as taken the above link are:
lat2 = asin(sin(lat1)*cos(d/R) + cos(lat1)*sin(d/R)*cos(θ))
lon2 = lon1 + atan2(sin(θ)*sin(d/R)*cos(lat1), cos(d/R)−sin(lat1)*sin(lat2))
The above formula is for MSExcel where-
asin = arc sin()
d = distance (in any unit)
R = Radius of the earth (in the same unit as above)
and hence d/r = is the angular distance (in radians)
atan2(a,b) = arc tan(b/a)
θ is the bearing (in radians, clockwise from north);
Here's the code I've got in Python.
import math
R = 6378.1 #Radius of the Earth
brng = 1.57 #Bearing is 90 degrees converted to radians.
d = 15 #Distance in km
#lat2 52.20444 - the lat result I'm hoping for
#lon2 0.36056 - the long result I'm hoping for.
lat1 = 52.20472 * (math.pi * 180) #Current lat point converted to radians
lon1 = 0.14056 * (math.pi * 180) #Current long point converted to radians
lat2 = math.asin( math.sin(lat1)*math.cos(d/R) +
math.cos(lat1)*math.sin(d/R)*math.cos(brng))
lon2 = lon1 + math.atan2(math.sin(brng)*math.sin(d/R)*math.cos(lat1),
math.cos(d/R)-math.sin(lat1)*math.sin(lat2))
print(lat2)
print(lon2)
I get
lat2 = 0.472492248844
lon2 = 79.4821662373
Needed to convert answers from radians back to degrees. Working code below:
from math import asin, atan2, cos, degrees, radians, sin
def get_point_at_distance(lat1, lon1, d, bearing, R=6371):
"""
lat: initial latitude, in degrees
lon: initial longitude, in degrees
d: target distance from initial
bearing: (true) heading in degrees
R: optional radius of sphere, defaults to mean radius of earth
Returns new lat/lon coordinate {d}km from initial, in degrees
"""
lat1 = radians(lat1)
lon1 = radians(lon1)
a = radians(bearing)
lat2 = asin(sin(lat1) * cos(d/R) + cos(lat1) * sin(d/R) * cos(a))
lon2 = lon1 + atan2(
sin(a) * sin(d/R) * cos(lat1),
cos(d/R) - sin(lat1) * sin(lat2)
)
return (degrees(lat2), degrees(lon2),)
lat = 52.20472
lon = 0.14056
distance = 15
bearing = 90
lat2, lon2 = get_point_at_distance(lat, lon, distance, bearing)
# lat2 52.20444 - the lat result I'm hoping for
# lon2 0.36056 - the long result I'm hoping for.
print(lat2, lon2)
# prints "52.20451523755824 0.36067845713550956"