Consider the trajectory of a spacecraft in the vicinity of Earth, analyzed within the framework of the restricted two-body problem. At a given time t0, the spacecraft is located at a point with geocentric equatorial coordinates (x, y, z), and the velocity vector of the spacecraft at this moment has components (vx, vy, vz) in the same non-rotating coordinate system. The Earth’s gravitational parameter is denoted by μ = 398600km^3/s^2.

Data: x=400km, y=6100km, z=-3300km, vx=7km/s vy=3km/s vz=4km/s, t0: 02.12.2020 11:00

Objective: Determine the elements of the spacecraft’s orbit:

• Semimajor axis a; (or alternatively, semilatus rectum p);

• Eccentricity e;

• Inclination I;

• Right ascension of the ascending node, RAAN Ω;

• Argument of the periapsis ω;

• True anomaly θ; (or alternatively, time of passage at periapsis tp).

Python code to determine the elements of the spacecraft’s orbit.