# Eclipsing Binary Stars var addthis_config = { services_exclude:"print", ui_508_compliant:true, data_ga_property:"UA-34776817-1", data_ga_social: true };

## INTRODUCTION

Just as the planets rotate about the Sun, two stars can rotate about each other. Actually, in both the planetary case and the binary star case, the objects rotate about their common center of mass. If the stars in a binary system are sufficiently close together and if we are sufficiently close to the plane of their orbit, then the two stars can eclipse each other in turn. Just as with a solar eclipse, we observe the eclipse as a darkening of the light coming from the eclipsed star.

The eclipsing binary project computes the light coming to us from the binary star system as a function of the orbital phase of the stars. During an eclipse, the portion of the eclipsed star that is hidden by the eclipsing star, emits no light seen by the observer.

## THE PROJECT

Compute the positions of the two stars and compute how much light comes from the two stars at several positions throughout the orbital cycle. The program should read the radius of each star, the mass of each star, the brightness of each star, and the angle between the plane of the orbit and the plane of the sky. The program should plot the total light at several positions throughout the orbital cycle. The final product should be a display of the stars' positions relative to the observer and a light curve illustrating the total intensity of light throughout the orbital cycle. As a first approximation you can treat each star as being uniformly bright. In a more realistic approximation the stars are brighter at their centers than at their edges.

Method

Divide the space which two stars can occupy into several rectangles (probably squares) of some size. To compute the area occupied by each star, count the rectangles that the star occupies. The precision of the result can be increased by increasing the number of rectangles. If both stars occupy one of the rectangles, then one of the stars is eclipsed by its companion. In this case, even though both stars occupy the same space, only the light coming from the eclipsing star is counted.

Questions

By observation, it is easy to detect which star has the largest radius, but which star has the largest mass?

Which of the two stars is brighter? How do you know?

Can you estimate the angle between the plane of the orbit and the plane of the sky?

## PROJECT DETAILS

SI 1995

Paul Buerger is the OSC coordinator for the Eclipsing Binary Stars project. Paul's office is in 420G. Please contact Paul to set up appointment(s) for consultation.

For assistance, write si-contact@osc.edu or call 614-292-0890.