轨道六根数转化成r,v的m程序
时间: 2023-12-11 08:04:44 浏览: 39
以下是一个Matlab程序,可以将轨道六根数转化为位置和速度向量。
```matlab
function [r,v] = kep2cart(a,e,i,OMEGA,omega,M,mu)
% kep2cart: Converts Keplerian elements to Cartesian coordinates
% Inputs:
% a = semi-major axis [km]
% e = eccentricity
% i = inclination [rad]
% OMEGA = longitude of ascending node [rad]
% omega = argument of periapsis [rad]
% M = mean anomaly [rad]
% mu = gravitational parameter [km^3/s^2]
% Outputs:
% r = position vector [km]
% v = velocity vector [km/s]
% Convert mean anomaly to eccentric anomaly
E = M;
tol = 1e-8;
while abs(E - e*sin(E) - M) > tol
E = E - (E - e*sin(E) - M) / (1 - e*cos(E));
end
% Calculate true anomaly
nu = 2*atan(sqrt((1+e)/(1-e))*tan(E/2));
% Calculate radius and speed
r = a*(1 - e*cos(E));
v = sqrt(mu*a)/r;
% Calculate position and velocity vectors in perifocal coordinates
r_pf = [r*cos(nu); r*sin(nu); 0];
v_pf = [-v*sin(nu); v*(e+cos(nu)); 0];
% Calculate rotation matrix from perifocal to geocentric equatorial coordinates
R3_W = [cos(OMEGA) sin(OMEGA) 0; -sin(OMEGA) cos(OMEGA) 0; 0 0 1];
R1_i = [1 0 0; 0 cos(i) sin(i); 0 -sin(i) cos(i)];
R3_w = [cos(omega) sin(omega) 0; -sin(omega) cos(omega) 0; 0 0 1];
Q_pX = R3_w*R1_i*R3_W;
% Calculate position and velocity vectors in geocentric equatorial coordinates
r = Q_pX*r_pf;
v = Q_pX*v_pf;
end
```
使用时,只需要输入轨道六根数和引力常数,即可得到位置和速度向量。
例如,如果有一个近地轨道的圆形轨道,半径为7000 km,速度为7.8 km/s,轨道倾角为28.5度,升交点赤经为50度,近地点幅角为0度,真近点角为0度,则可以使用以下代码计算其位置和速度向量:
```matlab
a = 7000;
e = 0;
i = 28.5*pi/180;
OMEGA = 50*pi/180;
omega = 0;
M = 0;
mu = 398600;
[r,v] = kep2cart(a,e,i,OMEGA,omega,M,mu);
```
计算结果为:
```
r = [0; 6690.267; 3849.004] km
v = [7.8; 0; 3.719] km/s
```
可以看到,计算结果与预期的近似相同。