用matlab写一段将春分点轨道根数转为地理经纬度的程序
时间: 2023-09-06 13:07:33 浏览: 47
以下是一个将春分点轨道根数转化为地理经纬度的 Matlab 程序:
```matlab
function [lat, lon] = root2geo(root1, root2, root3, root4, root5, root6)
% 输入:春分点轨道根数 root1-root6
% 输出:地理经度 lon 和纬度 lat
mu = 3.986004418e14; % 地球引力常数
a = root1^2 / mu^(1/3); % 半长轴
e = sqrt(root2^2 + root3^2 + root4^2); % 偏心率
i = acos(root5); % 轨道倾角
OMEGA = atan2(root6, root5); % 升交点赤经
omega = atan2(root3, root2); % 近地点幅角
M = 0; % 平近点角
E = M; % 偏近点角
while abs(E - e*sin(E) - M) > 1e-8
E = E - (E - e*sin(E) - M) / (1 - e*cos(E));
end
nu = 2*atan(sqrt((1+e)/(1-e))*tan(E/2)); % 真近点角
r = a * (1 - e^2) / (1 + e*cos(nu)); % 距离
x = r * cos(nu);
y = r * sin(nu);
z = 0;
P = [cos(OMEGA)*cos(omega)-sin(OMEGA)*sin(omega)*cos(i), -cos(OMEGA)*sin(omega)-sin(OMEGA)*cos(omega)*cos(i), sin(OMEGA)*sin(i); ...
sin(OMEGA)*cos(omega)+cos(OMEGA)*sin(omega)*cos(i), -sin(OMEGA)*sin(omega)+cos(OMEGA)*cos(omega)*cos(i), -cos(OMEGA)*sin(i); ...
sin(omega)*sin(i), cos(omega)*sin(i), cos(i)]; % 旋转矩阵
P = P';
pos = P * [x; y; z]; % 地心惯性系下位置坐标
lon = atan2(pos(2), pos(1)); % 地理经度
lat = atan2(pos(3), sqrt(pos(1)^2 + pos(2)^2)); % 地理纬度
lon = lon * 180 / pi; % 转为角度制
lat = lat * 180 / pi;
end
```
输入春分点轨道根数 `root1`-`root6`,即可输出地理经度 `lon` 和纬度 `lat`。