Question

The width of a telescope aperture is important because it determines what you will be able to resolve.

(a) You are out stargazing with your 13.6-cm telescope. You point your telescope at an interesting formation in the sky, which you think is a binary star system. A binary star system consists of two stars in orbit around each other. You guess that the average wavelength coming from the stars is 528 nm. What is the minimum angular separation between the two stars required for your telescope to resolve the two stars of the binary system? ___ rad

(b) Having graduated with a degree in astronomy, you seek a job at the Arecibo radio telescope. You use a large radio telescope (300-m diameter) to observe the same binary system that you observed in part (a). You estimate that the average radio emissions from the system have a wavelength of 4.66 cm. What is the minimum angular separation required for the Arecibo telescope to resolve the two stars of the binary system? ___ rad

Answer 1

Solution:

Minimum angular separation between two stars required for telescope to resolve the two stars in binary system is

Theta=(1.22*Lamda)/D ------(i)

Where D= diameter of telescope

Lamda=wavelength of Light.

(a) given , diameter of telescope = 13.6 c.m

Wavelength coming from stars = 528 nm =528×10^-7 c.m.

From equation (i) substitute the values to find out minimum angular separation between two stars is (1.22×528×10^-7)/13.6 =4.73×10^-6 radian.

Hence, minimum angular separation between two stars required for telescope is 4.73×10^-6 radian.

(b) given , diameter of telescope = 300 meter

Wavelength = 4.66 c.m =4.66 ×10^-2 meter

Now substitute the given values in equation(i) to find out minimum angular separation between two stars is (1.22 ×4.66×10^-2)/300 =1.89×10^-4 radian.

Hence, minimum angular separation between two stars required for telescope to resolve between two stars is 1.89×10^-4 radian.