Final answer:
The latitude of the ship's current position is -41 degrees. The sidereal time cannot be determined without the Right Ascension of the star. The longitude of the ship cannot be calculated without the sidereal time.
Step-by-step explanation:
The latitude of the ship's current position can be determined by the declination (-41 degrees) of the star at the zenith. The declination is equal to the latitude of the observer, so the ship's latitude is also -41 degrees.
To determine the sidereal time when the researcher makes the observations, we need to know the Right Ascension (RA) of the star. Unfortunately, the RA of the star is not provided in the question.
To calculate the longitude of the ship given the time on the Cape Town solar clock (19:56), we need to know the difference between the local solar time and the sidereal time. Without the sidereal time, it is not possible to calculate the longitude of the ship.