The brightness variations for Cepheid variables repeat exactly from one cycle to the next.
This might make them seem unattractive for variable star observers. However, the practice of observing them and seeing how clearly the brightness variations are recorded by visual observations provides an interesting insight into the challenges faced by visual observers when monitoring stars with relatively small amplitudes and also the challenges of observing naked eye variables in particular. It is generally stated that individual visual observations have an uncertainty of +/- 0.1 magnitudes. Over the course of a year, however, observations will be made under a variety of different sky conditions (dark sky, moonlight, streetlighting, haze …) and these factors can add the the spread in the observed magnitudes.
The light curves which follow are based on observations made by Bob Steele, Matthew Barrett and Tracie Heywood.
Delta Cephei is listed as having a magnitude range of 3.4-4.3 and a period of 5.37 days.
The accompanying light curve combines all observations made during 2017 into a single light curve showing one and a half cycles of variation.
Although there is some scatter in the observations, the general pattern of brightness changes can be seen with peak brightness occurring near phase 0. This is followed by a slow fade in brightness until around phase 0.7, followed by a steeper rise in brightness back to maximum.
A finder chart, showing comparison stars to use when monitoring the brightness changes of delta Cephei, can be found here
Zeta Geminorum is listed as having a magnitude range of 3.7-4.2 and a period of 10.15 days. A brightness range of 0.5 magnitudes is generally regarded as being the lower limit for variable stars to be readily followed visually and so observers of zeta Gem are following a star whose changes are borderline for visual study.
The smaller scale on the vertical axis makes the scatter stand out more in the accompanying light curve, but the general pattern of the brightness changes can still be seen however.
In particular, it can be seen that minimum brightness is occurring roughly midway between maxima – this difference in the shape of the light curve is due to the pulsation mode of zeta Gem being different from that of delta Cephei. Most Cepheid variables have light curves similar in shape to that of delta Cephei, but a small number like zeta Gem produce more sinusoidal light curves.
A finder chart, showing comparison stars to use when monitoring the brightness changes of zeta Gem, can be found here