Question

has been proposed to use an array of infrared telescopes spread over thousands of kilometers of spaceto observe planets orbiting other stars. Consider such an array with an effective diameter of 6000 km, whichobserves infrared radiation at a wavelength of 10m. If it is used to observe a planet orbiting the star 70Virginis, which is 59 light years from our solar system, what is the size of the smallest details that the arraymight resolve on the planet

Answer 1

`\triangle x=1.135 *10^9km`

Step-by-step explanation:

From the question we are told that:

Diameter of array
`d=6000km \approx 6000*10^3`

Infrared wavelength
`\lambda =10m`

Distance of planet
`d=59 light\ years \approx 55.82*10^(16)m`

Generally the equation for Diffraction is mathematically given by

`sin\theta =1.22(\lambda)/(D)`

Given that

`sin\theta=(\triangle x)/(R)`

Therefore

`(\triangle x)/(R)=1.22(\lambda)/(D)`

`\triangle x=1.22(R \lambda)/(D)`

`\triangle x=1.22(10 *55.82*10^(16))/(6000*10^3)`

`\triangle x=1.135 *!0^1^2m`

`\triangle x=1.135 *10^9km`