  Gravitational waves from binary black hole mergers have allowed us to
directly observe stellar-mass black hole binaries for the first time, and
therefore explore their formation channels. One of the ways to infer how a
binary system is assembled is by measuring the system's orbital eccentricity.
Current methods of parameter estimation do not include all physical effects of
eccentric systems such as spin-induced precession, higher-order modes, and the
initial argument of periapsis: an angle describing the orientation of the
orbital ellipse. We explore how varying the argument of periapsis changes
gravitational waveforms and study its effect on the inference of astrophysical
parameters. We use the eccentric spin-aligned waveforms TEOBResumS and SEOBNRE
to measure the change in the waveforms as the argument of periapsis is changed.
We find that the argument of periapsis could already be impacting analyses
performed with TEOBResumS. However, it is likely to be well-resolvable in the
foreseeable future only for the loudest events observed by LIGO--Virgo--KAGRA.
The systematic error in previous, low-eccentricity analyses that have not
considered the argument of periapsis is likely to be small.
