# Chapter 8 – Starcharts (Stellar Magnitude)

## Stellar Magnitude

Astronomers have a scale to measure the apparent brightness of the stars called magnitude. This was first classified by Hipparchus in 127 bc: he described ‘the brightest stars as magnitude 1’ and ‘the faintest stars as magnitude 6’ with four steps in between. This basic system has been retained ever since, but of course refined and explained mathematically, principally by Pogson in the last century. Pogson ascribed a value of 2.512 to 1 as a ratio between one whole magnitude and the next. This equates to a ratio of 100:1 for a star of first magnitude against a star of sixth magnitude just visible to the naked eye. Pogson also noted that the common logarithm of 2.512 is precisely 0.4, much simplifying computation.

This short program uses a simple FOR/NEXT loop to PRINT to the screen a magnitude range from -26 (the Sun) to +24 (faintest star detected with the 200-inch Hale telescope at Mt Palomar, California). The ratio to the standard star Vega at magnitude 0.0 is also displayed for each whole magnitude step. Our Sun proves to be 1:2.51E10 (25,000,000,000) times brighter than Vega: a magnitude +24 star proves to be about a similar ratio fainter than Vega.

Using a series of conditional PRINT statements the list is punctuated by some mainly familiar objects that match particular magnitudes. The standard star Vega is made to FLASH to identify itself readily.

The Spectrum does not use common logs but natural logs (LN function) to a base of 2.71828 … so Pogson’s neat common log relationship has to be fudged in this program, via Line 80, to give a ratio of 100:1 over five magnitudes.

10 REM Stellar Magnitude
15 PRINT “Mag Name”,”1:ratio”
20 FOR n=-26 TO 24 STEP 1
30 PRINT PAPER 6;(” ” AND ABS n0);n;” “;
37 PAPER 5
40 PRINT “Sun” AND n=-26;
41 PRINT “Full Moon” AND n=-13;
42 PRINT “Venus” AND n=-4;
43 PRINT “Sirius” AND n=-1;
50 PRINT FLASH 1;”Vega-standard” AND n=0;
51 PRINT “Uranus” AND n=5;
52 PRINT “Neptune” AND n=8;
53 PRINT “Barnard’s Star” AND n=10;
60 PRINT “Pluto” AND n=14;
61 PRINT “200”” eye limit” AND n=19;
62 PRINT “200””photolimit” AND n=24;
70 PAPER 7
80 PRINT TAB 18;EXP (LN 2.51193*-n): NEXT n