= Consider a moon of Uranus - if Uranus is currently a distance of 2.08 billion km from Earth, then what diameter telescope would you need (use telescope-resolution formula 1.22, where D is the telescope diameter) in order to clearly resolve the moon Titania in orbit around Uranus if the moon has a period of orbit of T = 8.71 days? (use Kepler's 3rd Law T² = (GMUrave -)³ to relate moon's period T to moon's orbital radius, r) The telescope only needs to resolve the small dot of the moon as distinct from the circle of light which is Uranus, so the orbital resolution is the angular size of the diameter of orbit of Miranda (use the arc-length formula where d is the distance from Earth to Uranus). Take the mass of Uranus as 8.68 x 1025 kg, and the wavelength of light as 490 = nm.

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Consider a moon of Uranus if Uranus is currently a distance of 2.08 billion km from Earth, then
what diameter telescope would you need (use telescope-resolution formula = 1.22, where D
is the telescope diameter) in order to clearly resolve the moon Titania in orbit around Uranus if the
47²
)3 to relate
moon has a period of orbit of T = 8.71 days? (use Kepler's 3rd Law T² = (GMrave
T2
moon's period T to moon's orbital radius, r) The telescope only needs to resolve the small dot of the
moon as distinct from the circle of light which is Uranus, so the orbital resolution is the angular size
of the diameter of orbit of Miranda (use the arc-length formula 0 = 2 where d is the distance from
Earth to Uranus). Take the mass of Uranus as 8.68 × 1025 kg, and the wavelength of light as 490
d
nm.
Transcribed Image Text:Upload a PDF document that shows your work and solution. - Consider a moon of Uranus if Uranus is currently a distance of 2.08 billion km from Earth, then what diameter telescope would you need (use telescope-resolution formula = 1.22, where D is the telescope diameter) in order to clearly resolve the moon Titania in orbit around Uranus if the 47² )3 to relate moon has a period of orbit of T = 8.71 days? (use Kepler's 3rd Law T² = (GMrave T2 moon's period T to moon's orbital radius, r) The telescope only needs to resolve the small dot of the moon as distinct from the circle of light which is Uranus, so the orbital resolution is the angular size of the diameter of orbit of Miranda (use the arc-length formula 0 = 2 where d is the distance from Earth to Uranus). Take the mass of Uranus as 8.68 × 1025 kg, and the wavelength of light as 490 d nm.
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