Actual and osculating elements
The following graphs show some Parker Solar Probe orbital parameters.
The reference plane is the mean ecliptic of J2000; the reference direction is the mean equinox of J2000. The gravitational parameter of the Sun used for the calculations is 0.0002959122082855911 AU3/day2 (it's the value used to integrate the JPL planetary and lunar ephemeris DE/LE430).
The following graph shows both the osculating and actual eccentricity and the osculating orbital inclination.
The actual eccentricity is represented by the blue points and it is calculated as (Ra - Rp) / (Ra + Rp), where Ra is the aphelion radius vector and Rp is the perihelion radius vector. The points are plotted at the time of the aphelion (if you hover the mouse over a point, the popup label that shows the actual eccentricity also shows the time of the aphelion).
The following graph shows both the osculating and actual orbital period and semi-major axis. The actual semi-major axis is calculated as the mean radius vector for 1 orbit and is obtained by numerical integration of the inverse of the radius vector as a function of the time (the result is the same as that obtained by integrating the radius vector as a function of the eccentric anomaly, but integrating against the time is much easier). Here an orbit conventionally starts at one ascending node and ends at the next ascending node. The points are plotted halfway between two consecutive ascending nodes.
The following graph shows both the osculating and actual R.A. of the ascending node and argument of perihelion.
The actual values are calculated as follows. The program starts the search for the first perihelion after a given starting epoch (2018-08-12 09:00 UTC). Then the search goes backwards until the ascending node is found. The RAAN is calculated as the angle from the mean equinox of J2000 to the direction of the ascending node, measured on the mean ecliptic of J2000 plane. The AoP is calculated as the angle from the ascending node to the perihelion in the direction of the s/c motion on the orbital plane. The popup label that shows the actual AoP also shows the time of the perihelion.