已知起点经纬度及两点间距离、方位角如何求出终点经纬度？（附C#与python代码）

Get lat/long given current point, distance and bearing.

1、计算公式：
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))
其中，

• 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);

2、C#代码：

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;namespace ConsoleApplication1
{class Program{static void Main(string[] args){    const double radiusEarthKilometres = 6371.01f; //地球半径，以km为单位double lat0 = -42.3993; //起点的纬度double lon0 = 172.7393; //起点的经度double kmDistance =76; //两点间的距离double angleRadHeading = 248.352;  //方位角：以正北为起始方向顺时针angleRadHeading =angleRadHeading/180 * Math.PI;double newLat = 0;double newLong = 0;var distRatio = kmDistance / radiusEarthKilometres;var distRatioSine = Math.Sin(distRatio);var distRatioCosine = Math.Cos(distRatio);var startLatRad = lat0/180*Math.PI;var startLonRad = lon0 / 180 * Math.PI;var startLatCos = Math.Cos(startLatRad);var startLatSin = Math.Sin(startLatRad);var endLatRads = Math.Asin((startLatSin * distRatioCosine) + (startLatCos * distRatioSine * Math.Cos(angleRadHeading)));var endLonRads = startLonRad+ Math.Atan2(Math.Sin(angleRadHeading) * distRatioSine * startLatCos,distRatioCosine - startLatSin * Math.Sin(endLatRads));newLat = endLatRads/Math.PI*180;newLong = endLonRads / Math.PI * 180;Console.WriteLine("终点的纬度为：{0}", newLat.ToString());Console.WriteLine("终点的经度为：{0}", newLong.ToString());Console.ReadLine();}}
}

3、python代码：

import mathR = 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 = math.radians(52.20472) #Current lat point converted to radians
lon1 = math.radians(0.14056) #Current long point converted to radianslat2 = 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))lat2 = math.degrees(lat2)
lon2 = math.degrees(lon2)print(lat2)
print(lon2)

4、参考：

• https://stackoverflow.com/questions/7222382/get-lat-long-given-current-point-distance-and-bearing
• https://cloud.tencent.com/developer/ask/152388

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