# Perifocal to ECI using Argument of Latitude

Suppose a satellite is orbiting Earth in a circular orbit. I know the following orbital elements:

• Inclination i,
• RAAN (Ω),
• Semi-major axis a (or orbit radius given that it is a circular orbit)
• Argument of latitude (u)

I know that the rotation matrices used to obtain the ECI coordinates from Perifocal coordinates require RAAN, Inclination, and Argument of Periapsis.

Since for circular orbits, the argument of periapsis and true anomaly are undefined, we make use of the argument of latitude. IS there a way to do the transformation from Perifocal to ECI frame using the Argument of Latitude instead of the Argument of Periapsis?

I apologize for the noob question but I am new to these topics.

• I though the convention was to use 0 as Argument of Periapsis for inclined circular orbits, and consider the ascending node as an effective periapsis for defining a a usable true anomaly? I think it screws thing up if you're tryin to deal with perturbed circular orbits, but works fine for two-body Keplerian orbits. Commented Jul 11, 2023 at 11:50
• @notovny The problem that I am working on involves iterating on the Argument of latitude value to obtain an optimal transfer trajectory to the Moon. Hence, the above assumption might not work in this case. Commented Jul 11, 2023 at 15:19