Question

The Event Horizon Telescope needs a 22 micro-arcsecond resolution to view the event horizon regions around black holes. If the average wavelength is a 1.3 mm radio wave, (A) what is the diameter of the effective primary objective? (B) How can astronomers build a telescope this big? Defend your answers.

Answer 1

14869817.395 m

Step-by-step explanation:

`\theta`=22 microarcsecond

λ = Wavelength = 1.3 mm

Converting to radians we get

`22* 10^(-6)(\pi)/(180* 3600)\ radians`

From Rayleigh Criterion

`\theta=1.22(\lambda)/(D)\\\Rightarrow D=1.22(\lambda)/(\theta)\\\Rightarrow D=1.22(1.3* 10^(-3))/(22* 10^(-6)(\pi)/(180* 3600))\\\Rightarrow D=14869817.395\ m`

Diameter of the effective primary objective is 14869817.395 m

It is not possible to build one telescope with a diameter of 14869817.395 m. But, we need this type of telescope. So, astronomers use an array of radio telescopes to achieve a virtual diameter in order to observe objects that are the size of supermassive black hole's event horizon.