Final answer:
Temperature and radius influence a star's luminosity by determining the energy output and surface area for light emission, respectively. Distance and local gravity do not directly affect luminosity but can influence the perceived brightness or have indirect effects over time.
Step-by-step explanation:
Among the options provided, both temperature and radius influence the luminosity of a star. The luminosity of a star is defined by the total energy a star emits per second. The higher the temperature, the more energy the star emits due to increased thermal radiation. Similarly, a larger radius increases the surface area from which light can be emitted, contributing to higher luminosity. However, contrary to what one might initially think, neither distance nor local gravity directly affect a star's intrinsic luminosity; rather, they affect how we perceive the star's brightness from Earth. Distance is crucial for measuring and understanding the apparent brightness, which decreases with the square of the distance to an object. It is by knowing a star's luminosity and its apparent brightness that astronomers can calculate its distance from us. On the other hand, local gravity can influence the physical structure and evolution of the star, which might indirectly affect its luminosity over long timescales.