How Is Angular Resolution Used to Determine the Distance Between Two Stars?

AI Thread Summary
Angular resolution is crucial for determining the distance between two stars observed by a radio telescope, which in this case operates at a wavelength of 20.0 cm and has a diameter of 20.0 km. The minimum angle of resolution is calculated using the formula theta(min) = 1.22 * wavelength / diameter, resulting in a value converted to degrees for easier understanding. The initial calculation led to an incorrect distance of 6.99x10^13 m, while the correct distance is 1.22x10^12 m. The discussion highlights the importance of using radians for calculations to avoid confusion and errors. Accurate angular resolution is essential for precise astronomical measurements.
danmend
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Homework Statement


A radio telescope observes two stars orbiting each other, using radio waves of wavelength 20.0 cm. The stars are 10^7m away from the Earth. The telescope, which has a diameter of 20.0km, can just resolve the two stars. What is the distance between the two stars?

Homework Equations



theta(min) = 1.22* wavelength/Diameter of circular aperture

The Attempt at a Solution



I got 1.22(0.2)/20000 = theta (min). Then I changed it into degrees because I'm more comfortable using them. I got 0.000699 degrees. Then I divided that by half to get the angle to one of the stars. Using the small angle approximation I got 0.000699*10^17m = 3.49x10^13. Then I doubled it to get the distance between the stars 6.99x10^13m. The answer is apparently 1.22x10^12m. Help please :)
 
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Welcome to PF!

Hi danmend ! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)
danmend said:
… Then I changed it into degrees because I'm more comfortable using them.
…
6.99x10^13m. The answer is apparently 1.22x10^12m. Help please :)

6.99x1013 divided by 1.22x1012 = 57.29 = 180/π …

now do you see why it's so much easier to use radians? :smile:​
 
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