Answer: 1) Angular separation equals 0.0000031 degrees
2) Angular separation in arc -seconds equals 0.011156"
Explanation:
For 2 stars separated by a distance 'S' and at a distance 'D' from the earth the angular separation in radians is given
[tex]\theta _{rad}=\frac{S}{D}[/tex]
Applying values we get
[tex]\theta _{rad}=\frac{80\times 10^{6}}{150\times 9.46\times 10^{12}}\\\\\therefore \theta _{rad}=\frac{1}{18487500}radians[/tex]
Now we know that 'π' radians equals 180 degrees thus the above value in degrees shall be equal to
[tex]\therefore \theta _{degrees}=\frac{1}{18487500\times \pi }\times 180^{o}=0.0000031^{o}[/tex]
2)
The angular separation in arc- seconds is given by
[tex]\theta ''=\theta ^{o}\times 3600\\\\\theta'' = 0.0000031\times 3600=0.011156"[/tex]
The angular separation equals of the binary star is equals to the [tex]0.0000031^o[/tex] and the Angular separation in arc -seconds equals [tex]0.011156"[/tex].
A binary star system is a system of two stars that are gravitationally moved in orbit and in the orbit around each other.
Binary stars in the dark sky that are seen as an individual object to the bare eye are ofttimes settled employing a telescope as discrete stars, in which case they are called visual binaries.
(A). Calculation of Angular separation of the two stars in degrees:
We divide the two stars by a distance 'S' and at a distance 'D' from the earth, then
The angular separation in radians is:
Given that, S=80 and D =150.
[tex]\rm{\theta}_{rad}=\dfrac{S}{D}\\\\\rm{\theta}_{rad}=\dfrac{80\times10^6}{150\times9.46\times10^1^2}\\\\\rm{\theta}_{rad}=\dfrac{1}{18487500}\text{radians}\\\\\rm{\theta}_{rad}=\dfrac{1}{18487500}\times180^o\\\\\rm{\theta}_{rad}=0.0000031^0[/tex]
Where, Radians =[tex]180^0[/tex].
Therefore, the Angular separation of the two stars in degrees is [tex]0.0000031^0[/tex]
(B). Computation of angular separation in arceseconds:
[tex]\rm{\theta''}= \theta\times3600\\\\\rm{\theta''}= 0.0000031^0\times3600\\\\\rm{\theta''}= 0.011156''[/tex]
Therefore, angular separation in arceseconds is [tex]0.01156''[/tex].
Learn more about the binary star system, refer to:
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