Course Contents Homework26_ResolutionGratings ResolvingStars.problem Evaluate a
ID: 2032065 • Letter: C
Question
Course Contents Homework26_ResolutionGratings ResolvingStars.problem Evaluate a Feedback-' Print e, lnfo Timer Notes The three stars of a triple star system lie at a distance of 5.5×1016 m from Earth. The two brightest stars, A and B, are separated by a distance of 3.8x109 m, while the third star, C, is separated from the first two by a distance of 2.1x1012. Assume that the lines between the stars are all perpendicular to the line from Earth to the star system. What is the angular separation (in radians) between the A/B binary system and star C? Submit Answer Tries 0/4 If you observe the stars with a filter that only allows through light with a wavelength of 6x107 m, what is the minimum diameter of your telescope that is required to distinguish the A/B binary from star C? Submit Answer Tries 0/4 What is the angular separation (in radians) between stars A and B? Submit Answer Tries 0/4 What is the minimum diameter of your telescope required to distinguish star A from star B? Assume you are using the same filter as described above. Submit Answer Tries 0/4 If you were to repeat your observation of the A/B binary system, but this time using ultraviolet light with a wavelength of 1.1x107 m, what is the minimum diameter of your telescope required to distinguish star A from star B? Tries 0/4 Submit AnswerExplanation / Answer
a) angular separation between the A/B binary system and star C = 2.1*10^12/(5.5*10^16)
= 3.8*10^-5 radians
b) using Reyliegh's cryteria, theta = 1.22*lamda/d
d = 1.22*lamda/theta
= 1.22*6*10^-7/(3.8*10^-5)
= 0.0193 m
c) angular separation between stars A and B = 3.8*10^9/(5.5*10^16)
= 6.91*10^-8 m
d) using Reyliegh's cryteria, theta = 1.22*lamda/d
d = 1.22*lamda/theta
= 1.22*6*10^-7/(6.91*10^-8)
= 10.6 m
e)
d = 1.22*lamda/theta
= 1.22*1.1*10^-7/(6.91*10^-8)
= 1.94 m