There is a circle centered at the origin of a coordinate system S with radius R. Consider a coordinate system S′ moving in the xy plane relative to S such that the relative speed v makes an angle ϕ with respect to the x axis. The circle would appear like an ellipse in S′. Compute the eccentricity o

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There is a circle centered at the origin of a coordinate system S with radius R. Consider a coordinate system S′ moving in the xy plane relative to S such that the relative speed v makes an angle ϕ with respect to the x axis. The circle would appear like an ellipse in S′. Compute the eccentricity of this ellipse. Note: the eccentricity of the ellipse is e=sqrt(1−b^2/a^2) and a and b are the semi-major and semi-minor axes, respectively. You will know that the semi-minor axis is the smaller 'radius' while the semi-major axis is the larger 'radius' for the ellipse.

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