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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: D 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 xrs 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 separationo (measured in seconds of arc - make sure you don't use the parallax!!) so: amry = aD =__trc)(_ pc) =( AU) 5.21 pc x 6.1 arc min = 31.781 AU 3. Now, since we know that the period, T, of the binary stars is 87.3 years, we can now calculate the combined masses of the stars (designated 1 and 2 below) using Kepler's Third Law: AU) (M, - M.) = . -S M

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: D 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 xrs 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 separationo (measured in seconds of arc - make sure you don't use the parallax!!) so: amry = aD =__trc)(_ pc) =( AU) 5.21 pc x 6.1 arc min = 31.781 AU 3. Now, since we know that the period, T, of the binary stars is 87.3 years, we can now calculate the combined masses of the stars (designated 1 and 2 below) using Kepler's Third Law: AU) (M, - M.) = . -S M

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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 vears) It vs 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 separationo (measured in seconds of arc - make sure you don't use the parallax!!) so: aary = aD= ( _arc)_ _pc) = AU) 5.21 pc x 6.1 arc min = 31.781 AU 3. Now, since we know that the period, T, of the binary stars is 87.3 years, we can now calculate the combined masses of the stars (designated 1 and 2 below) using Kepler's Third Law: AU) (M, +M,): M. San
Transcribed Image Text: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 vears) It vs 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 separationo (measured in seconds of arc - make sure you don't use the parallax!!) so: aary = aD= ( _arc)_ _pc) = AU) 5.21 pc x 6.1 arc min = 31.781 AU 3. Now, since we know that the period, T, of the binary stars is 87.3 years, we can now calculate the combined masses of the stars (designated 1 and 2 below) using Kepler's Third Law: AU) (M, +M,): M. San
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