Error Ellipses

From February 1999, the errors for the position and the proper
motions are expressed as * error ellipses*, made of three
numbers: the

The units in which the
major/minor axises are expressed are * mas* for the position,
and

If we designate by * (a,b,p)* the 3 values of major axis, minor axis,
position angle, the variances and covariance on the parameters

var(A)=sin^{2}(p) a^{2}+ cos^{2}(p) b^{2}var(D)=cos^{2}(p) a^{2}+ sin^{2}(p) b^{2}cov(A,D)=(a^{2}– b^{2}) cos(p) sin(p)

and from there the mean errors and correlation coefficients may be computed knowning that:

σ(A)=sqrt(var(A))σ(D)=sqrt(var(D))ρ=cov(A,D)/(σ(A)⋅σ(D))

© Université de Strasbourg/CNRS

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