Final answer:
The right of a petty officer to exercise authority is likely found in the U.S. Navy Regulations or the Uniform Code of Military Justice, not directly in the Constitution, which broadly outlines the President's and Congress's powers over military forces.
Step-by-step explanation:
The authority of a petty officer to exert control over subordinate personnel in the U.S. Navy is not directly outlined in the provided text about U.S. Navy Regulations.
However, it is possible that the Navy Regulations themselves prescribe such authority, separate from the constitutional provisions presented here. The Constitution details broader powers, such as those in Article II, Section 2, where it states that the President shall be the Commander in Chief of the Army and Navy, and outline the powers of Congress over military forces, seen in Article I, Section 8. For specific details regarding the authority of non-commissioned officers like petty officers within the Navy, one would need to consult the U.S. Navy Regulations or the Uniform Code of Military Justice (UCMJ), which includes more specific rules governing military personnel.