If astronomers assume isotropy (equal random stellar motions in all directions), what critical uncertainty remains when trying to constrain the exact 3D shape of an elliptical galaxy from observed velocity data?
Answer
The mass distribution cannot be uniquely constrained alongside the 3D shape.
Without making simplifying assumptions about stellar orbits, observed line-of-sight velocity dispersions and rotation velocities are insufficient data to uniquely determine both the mass distribution and the exact three-dimensional shape simultaneously.
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