Final answer:
To determine if the Mount Palomar telescope can resolve the planet Pluto and its Moon Charon, we calculate the minimum resolvable angular separation and compare it to the actual angular separation between the two bodies. The Mount Palomar telescope can resolve the bodies at the given distance from Earth, so the answer is 'Yes'.
Step-by-step explanation:
Answer:
To determine if the 5.08-m-diameter Mount Palomar telescope can resolve the planet Pluto and its Moon Charon when they are 4.50×10^9 km from Earth, we need to calculate the minimum resolvable angular separation using the formula:
θ = 1.22 * (λ / D)
where θ is the minimum resolvable angular separation, λ is the average wavelength, and D is the diameter of the telescope. Given that the average wavelength is 550 nm and the diameter of the telescope is 5.08 m, we can calculate:
θ = 1.22 * (550 nm / 5.08 m) = 0.135 arcseconds
The angular separation between Pluto and Charon is given by:
θ = distance / distance from Earth
where distance is the separation between Pluto and Charon (19,600 km) and distance from Earth is the distance from Earth to these bodies (4.50×10^9 km).
Plugging in the values, we get:
0.135 arcseconds = 19,600 km / (4.50×10^9 km)
Converting the distance to the same units, we get:
0.135 arcseconds = 4.355×10^-6 arcseconds
Therefore, the Mount Palomar telescope can resolve the planet Pluto and its Moon Charon when they are 4.50×10^9 km from Earth. The answer is 'Yes'.