# Ellipse on sphere

[3]:

# Parameters
func_name = "Ellipse_on_sphere"


## Description

[5]:

func.display()

• description: An ellipse function on a sphere (in spherical coordinates)
• formula: $$f(\vec{x}) = \left(\frac{180}{\pi}\right)^2 \frac{1}{\pi~ a b} ~\left\{\begin{matrix} 1 & {\rm if}& {\rm | \vec{x} - \vec{x}_{f1}| + | \vec{x} - \vec{x}_{f2}| \le {\rm 2a}} \\ 0 & {\rm if}& {\rm | \vec{x} - \vec{x}_{f1}| + | \vec{x} - \vec{x}_{f2}| > {\rm 2a}} \end{matrix}\right.$$
• parameters:
• lon0:
• value: 0.0
• desc: Longitude of the center of the source
• min_value: 0.0
• max_value: 360.0
• unit:
• is_normalization: False
• delta: 0.1
• free: True
• lat0:
• value: 0.0
• desc: Latitude of the center of the source
• min_value: -90.0
• max_value: 90.0
• unit:
• is_normalization: False
• delta: 0.1
• free: True
• a:
• value: 15.0
• desc: semimajor axis of the ellipse
• min_value: 0.0
• max_value: 20.0
• unit:
• is_normalization: False
• delta: 1.5
• free: True
• e:
• value: 0.9
• desc: eccentricity of ellipse
• min_value: 0.0
• max_value: 1.0
• unit:
• is_normalization: False
• delta: 0.09000000000000001
• free: True
• theta:
• value: 0.0
• desc: inclination of semimajoraxis to a line of constant latitude
• min_value: -90.0
• max_value: 90.0
• unit:
• is_normalization: False
• delta: 0.1
• free: True

## Shape

The shape of the function on the sky.

[6]:

m=func(ra, dec)
hp.mollview(m, title=func_name, cmap="magma")
hp.graticule(color="grey", lw=2)