Question

Friedrich Bessel concluded in 1844 that Sirius is a binary star where the companion is "invisible", the two components A and B orbit around each other every 50 years. From decades of observations, it was found that Sirius A is a A1V star with a mass of 2.3 solar masses and Sirius B is a WD with a mass of 1.0 solar mass. Assuming circular orbits, calculate the physical separation between the two stars in AU. The parallax of Sirius

Answer 1

To calculate the physical separation between Sirius A and Sirius B, we can use Kepler's Third Law of planetary motion. By setting up a proportion with the relative masses and periods of the binary system, we can find the average distance between the two stars in AU.

Step-by-step explanation:

From the given information, we know that the sum of the masses of Sirius A and B is 3.2 solar masses. Assuming circular orbits, we can use Kepler's laws of planetary motion to find the physical separation between the two stars. Kepler's Third Law states that the square of the period of revolution of two objects orbiting each other is proportional to the cube of their average distance.

We are given that the period of revolution is 50 years, and we need to find the distance in AU. Since 1 AU is the average distance from Earth to the Sun, we can relate the average distance between Sirius A and B to the average distance between the Sun and Earth.

Using the relative masses and periods, we can set up the following proportion:

(1 AU) / (Average distance between Sirius A and B) = (2.3 solar masses + 1.0 solar mass) / (3.2 solar masses)

Solving for the average distance between Sirius A and B gives us:

Average distance between Sirius A and B = (1 AU) * ((2.3 solar masses + 1.0 solar mass) / (3.2 solar masses))**(1/3)

Using this equation, we can find the average distance between Sirius A and B in AU.