Concept explainers
The minimum diameter of the earth based telescope’s aperture to obtain the image of the star and the planet system.
Answer to Problem 51P
Solution:
The minimum diameter of the telescope’s aperture required to obtain the image of the planet-star system is 17 cm.
Explanation of Solution
The nearest star to the Sun is at a distance s from the solar system and a planet orbits the star in an orbit of radius R. therefore, the distance between the star and the planet is R. The star- planet system subtends an angle to the telescope mounted on Earth.
Therefore,
The star- planet system will be resolved if the angular resolution of the telescope is equal to the angle subtended by the star- planet system to the objective of the telescope.
The angular resolution of a telescope is given by,
Equating both the expressions,
Given:
The distance between the sun and the star
The radius of the orbit of the planet around the star
The wavelength of light
Formula:
Calculation:
Substitute the given values of , s and R in the expression and calculate the diameter.
Chapter 25 Solutions
Physics: Principles with Applications
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