Eccentricity of Eliptical Orbit, Scilab calculation and plot, #space
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The eccentricity of an elliptical
The eccentricity of an elliptical orbit is a measure of the amount by which the orbit deviates from a circular orbit. It is found by dividing the distance between the focal points of the ellipse by the length of the major axis.
Ra is the radius at apogee. It is the farthest distance of the orbit to the center of mass of the system, which is the prime focus of the ellipse.
Rp is the radius at periapsis the closest distance of the orbit to the prime focus of the ellipse.
Here are 6 examples of elliptical orbits for 6 different eccentricities. Note that all orbits are calculated for the same orbital period. Practically it means that the length of the major axis is the same for all the plotted ellipses.
The calculation is made in freeware software Scilab. Here is the simple source code.
Eccentricity e or epsilon, semi-major axis a and semi-minor axis b are linked via formula in blue rectangle.
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#Scilab code:
a = 1.0 //semi-major axis length
e = [0, 0.2, 0.4, 0.6, 0.8, 0.9] //eccentricity
b = [sqrt((1-e(1)^2)*a^2), sqrt((1-e(2)^2)*a^2),..
sqrt((1-e(3)^2)*a^2), sqrt((1-e(4)^2)*a^2),..
sqrt((1-e(5)^2)*a^2), sqrt((1-e(6)^2)*a^2)] //semi-minor axis length
plot2d(0,0,-1,"031"," ",[-1,-1,1,1])
arcs=[e(1)-1. e(2)-1 e(3)-1 e(4)-1 e(5)-1 e(6)-1; // upper left x
b(1) b(2) b(3) b(4) b(5) b(6); // upper left y
2*a 2*a 2*a 2*a 2*a 2.0*a; // width of ellipse
2*b(1) 2*b(2) 2*b(3) 2.0*b(4) 2.0*b(5) 2.0*b(6); // height of ellipse
0.0 0.0 0.0 0.0 0.0 0.0; // angle 1
360*64 360*64 4*90*64 4*90*64 4*90*64 4*90*64]; // angle 2
xarcs(arcs,[1,2,3,4,5,6])
e=gce();
e.children(1).thickness=3;
e.children(2).thickness=3;
e.children(3).thickness=3;
e.children(4).thickness=3;
e.children(5).thickness=3;
e.children(6).thickness=3;
----------#---------------------------------
#space
#tutorial
#Scilab
#code
Ra is the radius at apogee. It is the farthest distance of the orbit to the center of mass of the system, which is the prime focus of the ellipse.
Rp is the radius at periapsis the closest distance of the orbit to the prime focus of the ellipse.
Here are 6 examples of elliptical orbits for 6 different eccentricities. Note that all orbits are calculated for the same orbital period. Practically it means that the length of the major axis is the same for all the plotted ellipses.
The calculation is made in freeware software Scilab. Here is the simple source code.
Eccentricity e or epsilon, semi-major axis a and semi-minor axis b are linked via formula in blue rectangle.
If you like my video,please click the like button, and also subscribe to my channel.
#Scilab code:
a = 1.0 //semi-major axis length
e = [0, 0.2, 0.4, 0.6, 0.8, 0.9] //eccentricity
b = [sqrt((1-e(1)^2)*a^2), sqrt((1-e(2)^2)*a^2),..
sqrt((1-e(3)^2)*a^2), sqrt((1-e(4)^2)*a^2),..
sqrt((1-e(5)^2)*a^2), sqrt((1-e(6)^2)*a^2)] //semi-minor axis length
plot2d(0,0,-1,"031"," ",[-1,-1,1,1])
arcs=[e(1)-1. e(2)-1 e(3)-1 e(4)-1 e(5)-1 e(6)-1; // upper left x
b(1) b(2) b(3) b(4) b(5) b(6); // upper left y
2*a 2*a 2*a 2*a 2*a 2.0*a; // width of ellipse
2*b(1) 2*b(2) 2*b(3) 2.0*b(4) 2.0*b(5) 2.0*b(6); // height of ellipse
0.0 0.0 0.0 0.0 0.0 0.0; // angle 1
360*64 360*64 4*90*64 4*90*64 4*90*64 4*90*64]; // angle 2
xarcs(arcs,[1,2,3,4,5,6])
e=gce();
e.children(1).thickness=3;
e.children(2).thickness=3;
e.children(3).thickness=3;
e.children(4).thickness=3;
e.children(5).thickness=3;
e.children(6).thickness=3;
#space
#tutorial
#Scilab
#code
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