Question

Can an astronaut orbiting Earth in a satellite at a distance of 180 km from the surface distinguish two skyscrapers that are 20 m apart? Assume that the pupils of the astronaut’s eyes have a diameter of 5.0 mm and that most of the light is centered around 500 nm.

Answer 1

The ability to distinguish two close objects is determined by the resolution of the observer's eye, which can be calculated using the Rayleigh criterion. The angular resolution of the eye is based on the wavelength of light and the diameter of the pupil. By applying these calculations, we can determine if an astronaut orbiting Earth can distinguish two skyscrapers at a given distance.

Step-by-step explanation:

The ability to distinguish two objects that are close together is determined by the resolution of the observer's eye. In this case, the astronaut in the satellite is trying to distinguish two skyscrapers that are 20 m apart from a distance of 180 km.

The resolution of the eye can be determined using the Rayleigh criterion, which states that two objects can be resolved if the angle between them is greater than the angular resolution of the eye.

Angular resolution can be calculated using the formula:

angular resolution = 1.22 * (wavelength / diameter of the pupil)

Using the given values of wavelength (500 nm) and diameter of the pupil (5.0 mm), we can calculate the angular resolution of the eye. Then, we can find the distance between the two skyscrapers that can be resolved at that angular resolution.