(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two stars, S_{1}and S_{2}, with effective temperature of T_{e,1}=25000 K and T_{e,2}= 2000 K and photospheric radius of R_{1}=R_{sun}/100 and R_{2}=50 R_{sun}make a binary system.

If the Star S_{2}is in circular orbit around the S_{1}with revolution period of P=180 days (1 day=24 hours), and S_{1}has a mass of M_{1}=1.3 M_{sun}, while the inclination angle i is the angle between the normal to orbital plane toward the observer and the visual line of the terrestrial observer (0°<i<90°), calculate:

(i) the limit angle, beyond which there will be occultation between the two stars;

(ii) if there is occultation, is the primary eclipse (more diminution of bolometric luminosity) when S_{s}is between S_{1}and the observer, or viceversa?

(iii) if i=90° how long the total eclipse is?

2. Relevant equations

R_{sun}and M_{sun}are given.

Third Keplero's Law: P^{2}(M_{1}+M_{2})=$1frac{4\pi^2}{G}$d^{3}where P is the period and d the distance between the two stars.

3. The attempt at a solution

Of course, an eclipse/occultation can occur if i ≈ 90°.

The exact angle depends on the stars dimension, i guess.

Bigger the star is (in radius), lower the angle can be.

However, i can't understand how to relate the radii and the angle.

Any suggestion please?

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# Homework Help: Binary star system

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