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)


../_images/notebooks_Ellipse_on_sphere_8_0.png