An eclipsing binary has an orbital period of 2d 22h the dura

An eclipsing binary has an orbital period of 2d 22h, the duration of each eclipse is 18h, and totality lasts 4h. If spectroscopic data indicate a relative orbital speed v of 200 km s^1, what are the stellar radii? Express your answers in both kilometers and solar radii. Requirement: Draw and clearly label a schematic of the light curve as part of your answer.

Solution

Given:-

T= 2days 22 hrs= 2*24 hrs+ 22hrs= 70 hrs= 252000 s

t=18 hrs= 64800 s

v= 200 km/s= 2*10⁵ m/s

T= 2pie/w= 2* 3.14* r/v

r= Tv/2* 3.14= 252000 s*2*10⁵ m/s / 6.28

r=8.03*10 ⁶ km

[Solar radius is a unit of distance used to express the size of stars in astronomy equal to the current radius of the Sun:1R= 6.955*10⁵km]

r= 1.15 R [in solar radii]