What are the initial 15 corrections to make in sequence following an observer's spotting?

The correct choice identifies the initial corrections an observer must provide after spotting in the field artillery context. Following an observer's spotting, the process begins by establishing the Observer Target Direction, which serves as a reference point for the fire mission. This is crucial because it aligns the artillery with the observed target.

The second part of this choice focuses on the importance of danger close and canceling danger close. This is a critical safety consideration when artillery is fired in proximity to friendly forces or other units. Understanding the parameters for danger close ensures the mission adheres to safety protocols and minimizes risk to friendly personnel.

The final aspect of this correct option addresses the trajectory. An adequate understanding of the trajectory is essential to ensure that the projectile is fired in a manner that accurately meets the target’s needs and adjusts for environmental factors.

In summary, this choice effectively captures the essential components of the observer's responsibilities in the sequence of corrections following a spotting, highlighting the significance of target direction, safety measures, and trajectory in executing a successful artillery mission.