Question

For an oblate elliptical galaxy with intrinsic axis ratio β=B/A viewed at inclination i, the apparent axis ratio q is given by

q²=β²sin²i+cos²i

Show that the apprent ellipticity ε=1-q is given by

sin²i(1-β²)=1-q²≈2ε, when ε<<1

What result would you get for a prolate ellipsoid

Answer 1

The aaparent axis ratio q for elliptical galaxies is defined as -

Oblate :

Prolate :

Thus apparent ellipticity will be given as -

Oblate:

since,

and

Thus

For prolate,

which gives,