1 | % Orbit eccentric anomaly, Kepler's equation keplers equation
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2 | % Richard Rieber
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3 | % 1/23/2005
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4 | % rrieber@gmail.com
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5 | %
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6 | % Revision 8/21/07: Fixed typo in line 38 if statement
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7 | % Added H1 line for lookfor functionality
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8 | %
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9 | % function E = CalcEA(M,ecc,tol)
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10 | %
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11 | % Purpose: Solves for eccentric anomaly, E, from a given mean anomaly, M,
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12 | % and eccentricty, ecc. Performs a simple Newton-Raphson iteration
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13 | %
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14 | % Inputs: o M - Mean anomaly in radians.
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15 | % o ecc - Eccentricity of the orbit.
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16 | % o tol - a tolerance at which to terminate iterations; Default
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17 | % is 10^-8 radians. [OPTIONAL]
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18 | %
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19 | % Outputs: o E - The eccentric anomaly in radians.
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20 | %
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21 | % E = CalcEA(M,ecc) uses default tolerances
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22 | %
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23 | % E = CalcEA(M,ecc,tol) will use a user specified tolerance, tol
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24 | %
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25 |
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26 | function E = CalcEA(M,ecc,tol)
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27 |
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28 | %Checking for user inputed tolerance
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29 | if nargin == 2
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30 | %using default value
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31 | tol = 10^-8;
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32 | elseif nargin > 3
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33 | error('Too many inputs. See help CalcEA')
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34 | elseif nargin < 2
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35 | error('Too few inputs. See help CalcEA')
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36 | end
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37 |
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38 | if (M > -pi && M < 0) || M > pi
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39 | E = M - ecc;
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40 | else
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41 | E = M + ecc;
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42 | end
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43 |
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44 | Etemp = E + (M - E + ecc*sin(E))/(1-ecc*cos(E));
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45 | Etemp2 = E;
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46 |
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47 | while abs(Etemp - Etemp2) > tol
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48 | Etemp = Etemp2;
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49 | Etemp2 = Etemp + (M - Etemp + ecc*sin(Etemp))/(1-ecc*cos(Etemp));
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50 | end
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51 |
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52 | E = Etemp2; |
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