Answer to Question #122925 in Astronomy | Astrophysics for SODIQ ADIO KAREEM

Question

The e star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared to

the more distant star Tau Ceti, which has an absolute magnitude of 5.69.

(a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude.

(b) Calculate the apparent magnitude of the star Tau Ceti.

(c) Find the distance between the Earth and Tau Ceti.

Answer 1

(a) Apparent magnitude $m$ is the brightness of a star as it is observed from the earth.

Absolute magnitude $M$ is the apparent magnitude of an object as if it is located 10% away from the observer.

Bolometric magnitude takes into account electromagnetic radiation at all possible wavelengths. 

(b) The apparent magnitude of the star Tau Ceti can be found according to the following equation:

$$\frac{b1}{b_2}=\sqrt[5]{100^{(m_2-m_1)}},\\\space\\ m_2=m_1+2.5\text{ lg}\frac{b_1}{b_2}=-1.46+2.5\text{ lg}(95)=0.518.$$

(c) The distance can be found from the following equation:

$$m-M=5\text{ lg } d-5,\\\space\\ d=10^\frac{m-M+5}{5}=10^\frac{0.518-5.69+5}{5}=0.92\text{ parsec}.$$