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

[danmend]

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 :)

 

[tiny-tim]

Welcome to PF!

Hi danmend ! Welcome to PF!

(try using the X² tag just above the Reply box )

… 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? ​