How far apart are the telescopes?

Question

If astronomers use an interferometer observing the wavelength of 1000 nm to measure the angular diameter of a planet like Jupiter orbiting a star 10 light-years from Earth, How far apart are the telescopes?

A. 50 m

B. 100 m

C. 200 m

D. 400 m

E. 800 m

Please help

Answer 1

We set the angular size (in radians) of this hypothetical planet equal to the expression for the Rayleigh Limit (for resolution), the wavelength of light used (1x10^-6 meters) and solve for the diameter. Using the equatorial diameter of the Jupiter-sized planet of 143000 km and the distance to it of 10 ly, we compute the angular size (in radians) to be arctan (143000/(10*3600*24*365.25*2.99E5)) = 1.515E^-9 R

1.515E^-9 = 1.22 Lambda/Diameter; solving for D, we get 805 meters. The appropriate choice is thus E, 800 m.