Question

Suppose that two stars in a binary star system are separated by a distance of 80 million kilometers and are located at a distance of 150 light-years from Earth.
A) What is the angular separation of the two stars in degrees?

B) What is the angular separation in arceseconds?

Answer 1

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

$\theta _{rad}=\frac{S}{D}$

Applying values we get

$\theta _{rad}=\frac{80\times 10^{6}}{150\times 9.46\times 10^{12}}\\\\\therefore \theta _{rad}=\frac{1}{18487500}radians$

Now we know that 'π' radians equals 180 degrees thus the above value in degrees shall be equal to

$\therefore \theta _{degrees}=\frac{1}{18487500\times \pi }\times 180^{o}=0.0000031^{o}$

2)

The angular separation in arc- seconds is given by

$\theta ''=\theta ^{o}\times 3600\\\\\theta'' = 0.0000031\times 3600=0.011156"$