Question

Determining the distance to stars can be challenging. The parallax method is one way of finding the distance to many stars around us. Your research team measures the parallax of two stars that have a distance of 5 degrees from each other in the night sky: The first star has a parallax of 0.11 arcsec, and the second has a parallax of 0.13 arcsec. How far apart are the two stars from each other? Express your answer in light-years​

Answer 1

To determine the distance to the stars, we need to use the parallax formula:

distance = 1 / (parallax angle in arcseconds)

Let's use this formula to calculate the distances to the two stars:

distance to star 1 = 1 / 0.11 arcsec = 9.09 parsecs

distance to star 2 = 1 / 0.13 arcsec = 7.69 parsecs

Now, we need to determine the distance between the two stars. We can use trigonometry to do this. The angle between the two stars is 5 degrees, which is equivalent to 300 arcminutes or 18,000 arcseconds. Since we know the distance to each star, we can use the tangent function to calculate the distance between them:

tan(5 degrees/2) = (distance to star 1 - distance to star 2) / distance between stars

Simplifying this equation, we get:

distance between stars = (distance to star 1 - distance to star 2) / 2 / tan(5 degrees/2)

Plugging in the values we calculated earlier, we get:

distance between stars = (9.09 parsecs - 7.69 parsecs) / 2 / tan(5 degrees/2) = 5.57 parsecs

Finally, we convert this distance to light-years:

1 parsec = 3.26 light-years

So, the distance between the two stars is:

distance between stars = 5.57 parsecs * 3.26 light-years/parsec = 18.15 light-years

Therefore, the two stars are about 18.15 light-years apart from each other.