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You need them all, but can omit Mean Anomaly at Epoch and Epoch if you don't care where the object is at any given time, and just care about the orbit itself. Inclination and Right Ascension of the As …

Given the radial distance $r$, velocity $v$, flight path angle $\gamma$ in radians, gravitational parameter $\mu$, and specific orbital energy $\epsilon$, the specific relative angular momentum is $ …

I believe the answer is yes, given one focus, and three coplanar points on the orbit, you can define the orbital shape, and obtain semi-major axis, orbital eccentricity, and the direction of the peria …

No, one focus, two points on the orbit, and the orbital eccentricity is not enough information to determine the velocity vector. Attached below are images of two different ellipses that share the sam …

In the situation where the orbit is not inclined, the convention generally is that the Argument of Periapsis is the angle from the Reference Direction (in your case, the x-axis) to the Periapsis. Th …

Partial Answer: For the extreme special case of the parabolic trajectory, where Orbital Eccentricity = $e=1$, the semi-major axis hits a singularity at $a=\pm\infty$, whereas the semi-latus rectum rem …

If you have all the orbital parameters of the new orbit, and you also have the radial distance from the central body of the spacecraft after the maneuver, and the orbit isn't circular you have enough …

This is not enough information. All you have is the eccentricity vector and the orbital inclination. (Declination of apoapsis is derivable from the eccentricity vector's direction, as the eccentricity …

True anomaly ($f$) is always measured in the direction of travel around the orbit; if, in your 2d simulation, the spacecraft is moving counterclockwise, then true anomaly is also measured countercloc …

True Anomaly is the angle from periapsis, through the center of the body being orbited, to a designated orbital position, measured in the plane of the orbit, with the positive direction designated as …

The two parameters are independent; any combination of non-negative semi-major axis and eccentricity between 0 and 1 results in a valid ellipse. Semi-major axis for an ellipse is half the longest dime …

The eccentricity vector has a magnitude equivalent to the orbital eccentricity of the ellipse, and points along the line of apsides in the direction from the central body towards the periapsis. Given …

I can answer the question of why Semimajor Axis and Eccentricity aren't included in the calculation, at least. What you have here are the main Keplerian Orbital Elements that define the plane of you …

Given Parameter Symbol Units Position Vector $\vec{r}$ distance Orbital Inclination $i$ radians Orbital speed at position vector $v$ distance/time Eccentricity Vector $\vec{e}$ Requ …

Yes, it is possible to determine the orbital inclination from the Longitude of the Ascending Node , and a position vector that is not the Ascending node or the Descending Node, because both the ascend …