Lab:  Determining Distance and Luminosity Using Apparent Brightness

In this activity you will determine the apparent brightness of stars and use this to determine their distance and luminosity.  Light spreads out spherically in all directions, so the star appears dimmer and dimmer the further away it is.  Dimming follows the inverse square rule, the same rule that applies to the strength of the gravitational field of a planet.  Apparent brightness varies directly with the luminosity and inversely with the square of the distance as described in the following equation:

Apparent Brightness  =         _Luminosity
                                              ^{_________________}
                                                    _{4 (3.14) d}²
 

Looking at the following CCD image, we can see 3 stars of varying brightness.  Star A has a brightness count of 444; Star B, 3780; and Star C, 215177.  Assume the distance to the dimmest and brightest stars (A and C) is the same.  Since the stars are on the same image, thus were taken using the same CCD camera and the same observing conditions.  Make a ratio of the counts of the two stars to calculate the ratio of their luminosities.  Star C is ___?___ times more luminous than Star A.

Assume the two brighter stars measured have the same luminosity, but not necessarily the same distance.  Using the formula above, calculate the ratio of their distances.  Star A is _____?_____ times farther away than Star C.
 

The image used was taken through a V filter that lets through predominantly yellow light.  The magnitude of Star C through the V filter is 6.4 and the apparent brightness of 1.00 X 10^-11 watts per square meter.  Calculate the apparent brightness of the other stars in the V.  (Hint:  remember since all the stars are in the same image the ration of the counts equals the ratio of the apparent brightness.

Use the distance values for each star given below to calculate their luminosity in V.  This is the amount of yellow light emitted by the star per second.  Find the luninosity of each star in units of solar luminosity (how many times the luminosity of the sun).  The luminosity of the Sun through a V filter  =  5.7 x 10²⁵ watts.