3. The Hubble Space Telescope has an aperture of 2.4 m and focuses visible light

Question

3. The Hubble Space Telescope has an aperture of 2.4 m and focuses visible light (400-700nm). The Arecibo radio telescope in Puerto Rico is 305m in diameter and focuses radio waves of wavelength 75 cm.
a. Under optimal viewing conditions, what is the smallest crater that each of these telescopes could resolve on the moon?
b. Of the Hubble Space telescope were to be converted to surveillance use, what is the highest orbit above the surface of the Earth it could have and still be able to resolve the license plates (just the plates, not the letters) of a car on the ground?

Explanation / Answer

diameter aperture d = 2.4 m wavelength ? = 400 nm = 400 * 10 ^-9 m distance between earth and moon D = 384,400 km the smallest crater that hubble telescope could resolve on our moon y = 1.22 ?D / d y = 78 m
second: wavelength ? ' = 75 cm = 0.75 m diameter d' = 305 m the smallest crater that Arecibo raio telescope could resolve on our moon y ' = 1.22 ?'D / d' y ' = 1.2*10^6 m


B: y = 1.22?D/d
y=30cm d=2.4 ?= 400 *10^-9
therefore D=1.5*10^3 wavelength ? ' = 75 cm = 0.75 m diameter d' = 305 m the smallest crater that Arecibo raio telescope could resolve on our moon y ' = 1.22 ?'D / d' y ' = 1.2*10^6 m


B: y = 1.22?D/d
y=30cm d=2.4 ?= 400 *10^-9
therefore D=1.5*10^3

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.