How does resolving power help astronomers distinguish nearby objects in the sky?

In the context of astronomy, resolving power (or resolution) is the ability of a telescope to form distinguishable images of objects that are separated by a very small angular distance.12

Because light behaves as a wave, it undergoes diffraction when passing through a circular aperture, such as a telescope's lens or mirror. This causes each point source of light to be imaged as a finite diffraction pattern rather than an infinitely small point. Consequently, two closely spaced objects—such as binary stars—can only be seen as separate if their angular separation is greater than the telescope's minimum resolvable angle.34

This limit is defined by the diameter of the telescope's objective ($D$) and the wavelength of light ($\lambda$); generally, a larger aperture decreases the resolvable angular separation, allowing astronomers to distinguish finer details and closely positioned celestial objects. While Earth-based telescopes are often limited by atmospheric turbulence, techniques like adaptive optics and interferometry help overcome these constraints to improve resolution.23