Final answer:
The luminosity of the star is one-trillionth of the Sun's luminosity.
Step-by-step explanation:
To determine the luminosity of the star compared to the Sun's luminosity, we can use the flux and parallax shift provided.
The flux, which is the energy received per unit area per unit time, is given as one-trillionth of the Sun's flux. Since luminosity is directly related to flux, we can conclude that the star's luminosity is also one-trillionth of the Sun's.
As for the parallax shift of 0.027 arcseconds, it is a measure of the star's distance from us. However, it doesn't directly relate to luminosity. Therefore, the luminosity of the star would still be one-trillionth of the Sun's luminosity.