24 lines
1.2 KiB
Mathematica
24 lines
1.2 KiB
Mathematica
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function [w,d,b,T,Tau] = OrbitalElements2TransitParams(n,aor,ex,ey,I,Omega,r)
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%OrbitalElements2TransitParams: returns the duration, ingress-egress time and angular velocity as a
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%function of the orbital properties.
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%inputs: n - mean motion, aor - semi-major axis over stellar radius, ex,ey - eccentricity vector components, x
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%pointing at observer, I,Omega - inclination with respect to the planet xy,
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%r - planetary radius in units of stellar radii.
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%where x points at observer. Outputs: T=Duration, Tau=ingress/egress time,
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%w = angular velocity at mid-transit, d = planet-star distance at
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%mid-transit, b = impact parameter
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%Yair Judkovsky, 9.9.2020
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w = n.*(1+ex).^2./(1-ex.^2-ey.^2).^(3/2);
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d = aor.*(1-ex.^2-ey.^2)./(1+ex);
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b = d.*sin(I).*sin(Omega);
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if nargout>3
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asin0 = asin(sqrt(((1+ex).^2./(aor.^2.*(1-ex.^2-ey.^2).^2)-sin(I).^2.*sin(Omega).^2)./(1-sin(I).^2.*sin(Omega).^2)));
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T=1./n*2.*((1-ex.^2-ey.^2).^(3/2))./((1+ex).^2).*asin0;
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asin2 = asin(sqrt(((1+r).^2.*(1+ex).^2./(aor.^2.*(1-ex.^2-ey.^2).^2)-sin(I).^2.*sin(Omega).^2)./(1-sin(I).^2.*sin(Omega).^2)));
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asin1 = asin(sqrt(((1-r).^2.*(1+ex).^2./(aor.^2.*(1-ex.^2-ey.^2).^2)-sin(I).^2.*sin(Omega).^2)./(1-sin(I).^2.*sin(Omega).^2)));
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Tau=1./n.*((1-ex.^2-ey.^2).^(3/2))./((1+ex).^2).*(asin2-asin1);
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end
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