# Solving Eclipsing Binary Homework

In summary, the conversation discusses the properties of two main sequence stars, including their apparent magnitude, effective wavelength, and radius. It also poses a question about calculating the apparent brightness of the system when one star is in front of the other, and how to calculate the B-V colors of the stars. The equations used in the solution include the relation of fluxes, Wien's displacement law, and the B-V color equation.

## Homework Statement

Two main sequence stars have the following properties:
#1: apparent magnitude m_v=2.5, λ_eff = 551nm radius r=1.6R_sun
#2: m_v = 5.77, r = 1.25R_sun

1) Calculate the apparent brightness of the system when #2 is in front of #1. Assuming that #1 has constant apparent brightness, what radius is required for #1 to make the depth of the primary eclipse equal to that of the secondary eclipse (the properties of #2 don't change).

2)Further: B-V colors of the two stars have to be calculated

## Homework Equations

a) m_v1 - m_v2 = -2.5*log(F_1/F_2)
b) λ_max = 2898/T
c) B-V= m_b - m_v =-0.865+(8540/T)

## The Attempt at a Solution

1)I already calculated the apparent brightness of the binary system, when there is no eclipse, using eq. a and the relation of fluxes (m_system=m_2+2.5*log(F_2/F_system).

2)for #1 I did the following:
using Wien's displacement law (eq. b) I calculated T (not sure if I can use the effective wavelength as max wavelength), and then calculated B-V using eq. c. From that I calculated m_b. But how to calculate B-V of #2 with only m_v given?Thanks for any suggestions!

1)I already calculated the apparent brightness of the binary system, when there is no eclipse, using eq. a and the relation of fluxes (m_system=m_2+2.5*log(F_2/F_system).
That's not what the question is asking.
But how to calculate B-V of #2 with only m_v given?
You also know the radius, and the star is at the same distance as the other star. You can find some relations to calculate λeff.

1.

## What is an eclipsing binary system?

An eclipsing binary system is a pair of stars that orbit around each other in a way that causes one star to pass in front of the other from our perspective on Earth. This results in a periodic dimming of the combined brightness of the two stars, known as an eclipse.

2.

## Why is solving eclipsing binary homework important?

Solving eclipsing binary homework is important because it allows us to understand the properties and behavior of binary star systems. These systems are valuable for studying stellar evolution, as well as for determining the masses, radii, and other characteristics of individual stars.

3.

## What methods are used to solve eclipsing binary homework?

The most common method for solving eclipsing binary homework is through photometric observations, which involve measuring the light output of the binary system over time. Other methods include spectroscopy, which analyzes the characteristics of the light emitted by the stars, and astrometry, which measures the precise positions of the stars in the binary system.

4.

## What challenges are involved in solving eclipsing binary homework?

Solving eclipsing binary homework can be challenging due to the complexity of the orbital motion of the stars and the effects of factors such as stellar activity and gravitational interactions with other nearby stars. Additionally, accurate measurements and precise data analysis are crucial for obtaining reliable results.

5.

## What can we learn from solving eclipsing binary homework?

Solving eclipsing binary homework can provide valuable insights into the properties and evolution of stars, as well as the dynamics of binary systems. By studying eclipsing binaries, we can also gain a better understanding of the processes that govern the formation and evolution of galaxies and the universe as a whole.