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I'm pretty sure the questions build on top of each other so I included question 1 but I would like question 2 solved, thank you!

I. Application to Visual Binary Stars Double stars are stars which are close enough and move slowly enough that they orbit each other. Each star is located at the focus of the ellipse of its orbit around the other star. 1. Consider a binary star system which has a semi-major axis of 6.1" arc and a period of 87.3 years. The annual parallax of the stars, p, is 0.192"arc. We call the measure of the angular separation of the two stars, a. [Remember that 1 degree is divided into 60 'arc (read this as 60 minutes of arc) and each l'arc is subdivided into 60"arc (read this as 60 seconds of arc)]. The distance to the binary star system is calculated from its parallax, p, of 0.192"arc, which has been measured carefully over a period of the last 92 years. First we must calculate the distance to the binary system: 1 D pc binary where p is the parallax in seconds of arc giving D in parsecs. How many light years does this correspond to? (Remember that 1 pc = 3.26 It yr) D (in light years) = It MIs D= 1/0.192 pc D= 5.21 pc D= 5.21 x 3.26 light year D= 16.98 light year 2. This angular measure of the semi-major axis of the orbit can be converted to a linear measure of the distance by multiplying the distance, d, to the binary system (measured in parsecs) by the angular separation (measured in seconds of arc - make sure you don't use the parallax!!) so: aD =C "arc) _pc)=_ _AU
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Transcribed Image Text:I. Application to Visual Binary Stars Double stars are stars which are close enough and move slowly enough that they orbit each other. Each star is located at the focus of the ellipse of its orbit around the other star. 1. Consider a binary star system which has a semi-major axis of 6.1" arc and a period of 87.3 years. The annual parallax of the stars, p, is 0.192"arc. We call the measure of the angular separation of the two stars, a. [Remember that 1 degree is divided into 60 'arc (read this as 60 minutes of arc) and each l'arc is subdivided into 60"arc (read this as 60 seconds of arc)]. The distance to the binary star system is calculated from its parallax, p, of 0.192"arc, which has been measured carefully over a period of the last 92 years. First we must calculate the distance to the binary system: 1 D pc binary where p is the parallax in seconds of arc giving D in parsecs. How many light years does this correspond to? (Remember that 1 pc = 3.26 It yr) D (in light years) = It MIs D= 1/0.192 pc D= 5.21 pc D= 5.21 x 3.26 light year D= 16.98 light year 2. This angular measure of the semi-major axis of the orbit can be converted to a linear measure of the distance by multiplying the distance, d, to the binary system (measured in parsecs) by the angular separation (measured in seconds of arc - make sure you don't use the parallax!!) so: aD =C "arc) _pc)=_ _AU
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