Interpolation Activity

This is Core Activity 6.2 in the HOA curriculum and is titled Estimating Magnitudes Using Interpolation. It is a good introductory activity, teaching students how to estimate just the magnitudes, or apparent brightness, of stars.

To estimate magnitudes of variable stars, you will need to interpolate. Interpolation is the process of estimating a value between two known values. Near the variable star you will be observing are two or more comparison stars of known magnitude. These stars do not change in brightness and are used to compare the brightness of the variable star. Knowing the values of the magnitudes of the comparison stars and the magnitude range of the variable star itself, you can interpolate or estimate the magnitude of the variable star as it changes over time.

1. Given below are three star fields. The magnitudes of the comparison stars are given. Estimate to the nearest tenth the magnitude of the star (offset by the lines in each field [- -]). Note: In star fields, the decimals are not indicated. A magnitude of 6.4 is written as 64, so that the fields are not cluttered and the decimal points are not mistaken for stars.

   In field A, the magnitude of the variable star seems to lie between 6.1 and 6.4, almost half way, maybe a little closer to 6.1, so the magnitude estimate is 6.2. Your estimate may be different from this and that is okay. Make a table like the one below, and record your estimate.

   Make estimates of the other two star fields. Also, record the estimates made by two of your classmates. Do your estimates differ from theirs?
   

2. Compare your estimated magnitudes with those of the rest of the class. Does everyone have the same answers?
   
   

   	Magnitude (Your own)	Magnitude (classmate 1)	Magnitude (classmate 2)
   (A)
   (B)
   (C)

The lesson then moves into Core Activity 6.3 titled How accurate are your results?. In this lesson students learn how to calculate absolute error/percentage of error, the concept of significant digits, and systematic vs. random error.