Final answer:
The student's question relates to the precision in observer-target direction reporting which implies principles of relativity, such as time dilation and length contraction. Specific numeric values weren't provided, but the context indicates high precision is required to account for relativistic effects seen by different observers in motion relative to one another.
Step-by-step explanation:
The student's question pertains to the precision required for an observer to relay the observer-target direction in scenarios involving high accuracy and the effects of relativity, such as in satellite synchronization or light path observations. While a specific numeric value was sought for in the original question (the change in degrees required before updating the observer-target direction), the information provided does not contain the precise quantitative value needed to complete the answer. Nevertheless, the context does suggest a relationship with physics principles related to the constancy of the speed of light (c), the synchronization of clocks to account for relativistic effects, and the differing perceptions of time and distance between moving observers.
The examples provided demonstrate how time and distance can appear different to separate observers, particularly when one is in motion relative to the other, due to the finite speed of light. For instance, the astronaut sees the light travel a shorter path compared to the Earth-bound observer, because the astronaut is moving with the ship. As a result, time dilation and length contraction are fundamental concepts in explaining these observations, which are critical in high precision measurements such as those made by satellites for Global Positioning Systems (GPS).