## Solution

We can express the various quantities in solar units. Taking ratios, we can use equation (5.44) to give

R/R0 = (L/L0) 1/2(T/T0)-2 = (80) 1/2(1.69) -2 = 3.1

Eclipsing binaries (such as in Fig. 5.1) provide us with another means of determining stellar radii. This method involves analysis of the shape of the light curve and a knowledge of the orbital velocities from Doppler shift measurements. (In an eclipsing binary, we don't have to worry about the inclination of the orbit.) Particularly important is the rate at which the light level decreases and increases at the beginning and end of eclipses.

We can also estimate the radii of rotating stars. If there are surface irregularities, such as hot spots or cool spots, the brightness of the star will depend on whether these spots are facing us or are turned away from us. The brightness variations give us the rotation period P. From the broadening of spectral lines, due to the Doppler shift, we can determine the rotation speed v. This speed is equal to the circumference 2-n-R, divided by the period. Solving for the radius gives

Sometimes the Moon passes in front of a star bright enough and close enough for detailed study. An analysis of these lunar occultations tells us about the radius of the star. The larger the star is, the longer it takes the light to go from maximum value to zero as the lunar edge passes in front of the star. Actually, since light is a wave, there are diffraction effects as the starlight passes the lunar limb. The light level oscillates as the star disappears. The nature of these oscillations tells us about the radius of the star.

There is another observational technique, called speckle interferometry, that has been quite successful recently. If it were not for the seeing fluctuations in the Earth's atmosphere, we would be able to obtain images of stellar disks down to the diffraction limits of large telescopes. However, the atmosphere is stable for short periods of

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