Short answers, pulled from the story.
The system integrates equations of motion using Cartesian coordinates represented as x, y, and z values in three-dimensional space. Engineers adjust initial conditions to match modern measurements of planetary positions while accounting for perturbations from all planets and larger asteroids.
August 2013 marked the start of ephemeris DE431 usage within the Horizons system. During the week of the 12th of April 2021, engineers replaced this older solution with DE440 and DE441.
September 2021 initiated a major shift where JPL began moving from common gateway interface protocols to application programming interface standards. This change enhanced automation capabilities by allowing full access via email or Telnet connections alongside existing web interfaces.
Objects following outbound ejection trajectories exceed an eccentricity of one which results in an apoapsis distance value of 9.99E+99 units under standard calculation rules. Galactic tides influence whether weak hyperbolic trajectories result in true ejection while passing stars can gently nudge these objects back inward toward the Sun.
Three distinct pathways exist for accessing the Horizons database today including Web interfaces, Email requests, and Telnet connections. All three methods support automation for batch processing tasks and allow users to generate highly accurate ephemerides for Solar System objects through any channel.