Question

Suppose that two stars in a binary star system are separated by

a distance of 100 million kilometers and are located at a distance
of 180 light-years from Earth.
a) What is the angular separation of the two stars? Give
your answer in degrees.
Express your answer in degrees to two significant figures.
b) What is the angular separation of the two stars? Give
your answer in arcseconds.
Express your answer in arcseconds two significant figures.

Answer 1

To calculate the angular separation in degrees, we use the formula Angular separation = Linear separation / Distance to the stars. Then we convert the angular separation from degrees to arcseconds using the conversion factor 1 degree = 3600 arcseconds.

Step-by-step explanation:

The angular separation of two stars can be calculated using trigonometry. We can use the formula:

Angular separation = Linear separation / Distance to the stars

To calculate the angular separation in degrees, we need to convert the linear separation from kilometers to the same unit as the distance to the stars. Since the distance is in light-years, we need to convert the linear separation to kilometers. Since there are 9.461 × 10^12 kilometers in a light-year, we can calculate the linear separation as follows:

Linear separation = 100 million kilometers × (1 light-year / 9.461 × 10^12 kilometers)

Using this value, we can calculate the angular separation in degrees:

Angular separation = Linear separation / Distance to the stars

Angular separation = Linear separation / (180 light-years × 9.461 × 10^12 kilometers/light-year)

Finally, we can convert the angular separation from degrees to arcseconds using the following conversion factor:

1 degree = 3600 arcseconds