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## Main Question or Discussion Point

halo

I will start with ,ellipse in polar coordinates.

bold mean=vectors

polar equation:ellipse in 3d

major axis = a rem:a>b

minor axis = b

angle = theta

info angle between two lines

1e line : focus and point on the ellipse

2e line : focus and perihelion

u,v are unit vector

u is direction major axis

v is direction minor axis

c is vector (orgin to the center of the ellipse)

rem: center different from focus for ellipse

rem: center=focus only for circle

x is vector (orgin to point on the ellipse)

? how can you find the relation between euler angles and (1).

? how unit u,v vector related to euler angles.

? how (1) is related to real observation on the sky.

I will start with ,ellipse in polar coordinates.

bold mean=vectors

polar equation:ellipse in 3d

major axis = a rem:a>b

minor axis = b

angle = theta

info angle between two lines

1e line : focus and point on the ellipse

2e line : focus and perihelion

u,v are unit vector

u is direction major axis

v is direction minor axis

c is vector (orgin to the center of the ellipse)

rem: center different from focus for ellipse

rem: center=focus only for circle

x is vector (orgin to point on the ellipse)

**x**=**c**+a*cos(theta)**u**+b*sin(theta)**v**(1)? how can you find the relation between euler angles and (1).

? how unit u,v vector related to euler angles.

? how (1) is related to real observation on the sky.