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# The 300 m diameter Arecibo radio telescope is observing the Andromeda galaxy at a wavelength of 29 cm. show answer No Attempt 50% Part (a) W

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The 300 m diameter Arecibo radio telescope is observing the Andromeda galaxy at a wavelength of 29 cm. show answer No Attempt 50% Part (a) What is the angle between two just-resolvable stars for this telescope in radians

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2021-08-31T22:07:18+00:00
2021-08-31T22:07:18+00:00 1 Answers
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Answer:The angle between two just-resolvable stars for the Arecibo telescope is [tex]1.179×10^{-3}rad[/tex].

Explanation:The resulting image in a telescope obtained from an object is a diffraction pattern.

That diffraction pattern is obtained because the light encounters different obstacles on its path inside the telescope (interact with the walls and edges of the instrument).

The diffraction pattern is composed by a central disk, called Airy disk, and diffraction rings.

The angular resolution is defined as the minimal separation at which two sources can be resolved one for another, or in other words, when the distance between the two diffraction patterns maxima is greater than the radius of the Airy disk.

The angular resolution can be determined in an analytical way by means of the Rayleigh criterion.

[tex]\theta = 1.22\frac{\lambda}{D}[/tex]

(1)Where [tex]\lambda[/tex] is the wavelength and D is the diameter of the telescope.

Notice that it is necessary to express the wavelength in the same units than the diameter.

[tex]\lambda = 29cm \cdot \frac{1m}{100cm}[/tex] ⇒ [tex]0.29m[/tex]

Finally, equation 1 can be used.

[tex]\theta = 1.22(\frac{0.29m}{300m})[/tex]

[tex]\theta = 1.179×10^{-3}rad[/tex]

Hence, the angle between two just-resolvable stars for the Arecibo telescope is [tex]1.179×10^{-3}rad[/tex]