Design a Telescope Optics for Spy Satellite- Angular Resolution & Mirror Size

[BurnieMac]

Homework Statement

This is a question on my final review.

Imagine you are given the task of designing the telescope in a spy satellite that is
going to be launched into an orbit 500 km above the surface of the Earth. The agency you
are working for wants to be able to clearly see objects as small as 1 inch = 2.5 cm (for
example the headlines on a newspaper).

a.) Calculate the angular resolution needed to achieve this.

b.) Given that diffraction is the ultimate limitation of your telescope, how big will the
primary mirror need to be? Use 500 nm for the wavelength of the light.

c) In one or two sentences, comment on the feasibility of your design. Hint: for
comparison the largest Earth based telescope has a 10 meter diameter mirror, the Hubble
space telescope has a 2.4 meter diameter mirror.

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I am really lost.. My knowledge is very poor for this chapter, I read the chapter earlier and still don't know.

Much help from your bright minds would be appreciated!

Homework Equations

Not sure

The Attempt at a Solution

a. )
Theta = Object height / Object Distance
In that case it is 5.0x10^-8 degrees
b.) How big will the mirror have to be..
I used rayleigh's criterion.
Theta(min) = 1.22(wavelength) / D
Solved for D, giving 12.2m
c.) No idea

 

[Redbelly98]

The Attempt at a Solution

a. )
Theta = Object height / Object Distance
In that case it is 5.0x10^-8 degrees
b.) How big will the mirror have to be..
I used rayleigh's criterion.
Theta(min) = 1.22(wavelength) / D
Solved for D, giving 12.2m
c.) No idea

(a) Okay, but that should be in radians.
(b) Looks good.
(c) Mainly a common-sense question. How feasible is it to launch a telescope 5x larger (and 25x times the area) of Hubble? Or to not only build something larger than any telescope that has ever been built, ever, but launch it into orbit as well?