Question

(a) The dwarf planet Pluto and its moon, Charon, are separated by 19,600 km. Neglecting atmospheric effects, should the 5.08-m-diameter Palomar Mountain telescope be able to resolve these bodies when they are 4.50×10⁹km from Earth? Assume an average wavelength of 550 nm.

(b) In actuality, it is just barely possible to discern that Pluto and Charon are separate bodies using a ground-based telescope. What are the reasons for this?

Answer 1

Theoretically, the Palomar Mountain Telescope's resolution limit might allow it to resolve Pluto and Charon, but atmospheric distortions and other factors prevent it from reaching this theoretical resolution, making the task challenging for ground-based telescopes.

Step-by-step explanation:

Regarding the resolution of Pluto and its moon Charon by the Palomar Mountain Telescope.

1. To determine if the telescope can resolve Pluto and Charon, we would normally calculate the telescope's angular resolution limit using Rayleigh's criterion and compare that to the angular size of the two objects in the sky.
2. Given the distance to Pluto and the size of the telescope's mirror, we could calculate the minimum resolvable angle, but due to atmospheric interference and other practical limitations, the theoretical resolvability may not translate to actual observations.
3. In reality, the process is complicated by the fact that Earth's atmosphere introduces distortions, known as seeing, which can prevent telescopes from reaching their theoretical resolution limit.

Other factors may include light pollution, telescope optical imperfections, and the adaptive optics system's limitations. This means that even without atmospheric effects, resolving Pluto and Charon would be challenging with ground-based telescopes, and typically only specialized observatories with advanced technology can come close to achieving this.