Question

Suppose that two stars in a binary star system are separated by a distance of 60 million kilometers and are located at a distance of 180 light-years from Earth.
What is the angular separation of the two stars? Give your answer in degrees.

Express your answer using two significant figures.

Answer 1

Answer:The angular seperation is $\theta =3.6\times 10^{-4}$

Explanation:

For two objects separated by a distance 's' and at a distance 'd' from the observer the angular separation ignoring the physical effects is given by

$\theta =\frac{s}{d}$

In the given question

$s=60\times 10^{6}km$

$d=180$ light years

We know that in 1 light year there are $9.5\times 10^{12}km$

Using the calculated values we get

$\theta =\frac{60\times 10^{6}}{9.5\times 10^{12}}\\\\\theta = 6.315\times10^{-6}radians$

Since π radians equals 180 degrees thus we have

$\\\\\theta =\frac{6.315\times 10^{-6}\times 180}{\pi }degrees=3.6\times 10^{-4}degrees$