- #1

RHK

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## Homework Statement

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?

## Homework 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.

## 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?