How to calculate the time to apoapsis & periapsis, given the orbital elements?

Question

I have the 6 orbital elements (excluding Time of Periapsis Passage, obviously), 2 state vectors, and a lot of other parameters like orbital period. I am looking to use them to calculate the time to periapsis and time to apoapsis.

To give you a better idea of the values I already have, here is my code calculating all the data related to the orbit:

 void CalculateOrbitalData(Vector3 pos1, Vector3 vel1, float m1) {
    Vector3 pos2 = planet.position;
    Vector3 vel2 = planet.velocity;
    float m2 = planet.mass;

    //Relative Position Vector
    Vector3 r = pos1 - pos2;

    //Distance between bodies
    float rmag = r.magnitude;

    //Relative Velocity Vector
    Vector3 v = vel1 - vel2;

    //Specific Angular Momentum
    Vector3 h = Vector3.Cross(r, v);

    //Standard Gravitational Parameter
    float µ = World.G * m2;

    //Eccentricity Vector
    Vector3 evec = (Vector3.Cross(v, h) / µ) - (r / Vector3.Magnitude(r));

    //Eccentricity
    float e = Vector3.Magnitude(evec);

    //Vector to Ascending Node
    Vector3 n = new Vector3(-h.x, h.z, 0);

    //True Anomaly
    float t = Mathf.Acos((Vector3.Dot(evec, r)) / (e * Vector3.Magnitude(r)));
    if (Vector3.Dot(r, v) < 0)
        t = (2 * Mathf.PI) - t;

    //Longitude of Ascending Node (2D)
    float Ω = 0;

    //Inclination (2D)
    float i = 0;

    //Argument of Periapsis
    float ω = Mathf.Atan2(evec.y, evec.x);
    float ωdegrees = ω * (180 / Mathf.PI);
    if (e == 0) {
        ω = 0;
        ωdegrees = 0;
    }

    //Eccentric Anomaly
    float E = 2 * Mathf.Atan(Mathf.Tan(t / 2) / Mathf.Sqrt((1 + e) / (1 - e)));

    //Mean Anomaly 
    float M = E - (e * Mathf.Sin(E));

    //Semi-Major Axis
    float a = 1 / ((2 / Vector3.Magnitude(r)) - (Mathf.Pow(Vector3.Magnitude(v), 2) / µ));

    //Apoapsis
    float ap = a * (1 + e);

    //Periapsis
    float pe = a * (1 - e);

    //Orbital Period
    float T = (2 * Mathf.PI) * Mathf.Sqrt(Mathf.Pow(a, 3) / µ) / 60;
    //patch orbital period to stay in line with unity timestep
    float fT = T * 1.205f;

    //Mean motion
    float m = (2 * Mathf.PI) / fT;

    //Perifocal distance
    float rp = (Vector3.Dot(h, h) / µ) / e + 1;
}

Answer 1

You seem to be looking for the time equation:

$$t=\sqrt{a^3\over\mu}\left(\tau-e\sin\tau\right)$$

where $t$ is time and $\tau$ is the eccentric anomaly. It looks like you have the eccentric anomaly at the "current" time. You can just plug that in to see the time relative to periapsis, which is at $t=0$ and $\tau=0$. For the time at apoapsis, plug in $\tau=\pi$. An orbit period is $\tau$ running over a range of $2\pi$, so the period is:

$$T=2\pi\sqrt{a^3\over\mu}$$

So your time since periapsis is $t$, and your time to the next periapsis is $T-t$ (assuming that $\tau$ is in $0$ to $2\pi$).