I approached the problem with the knowledge that day and night are equal at the equator, using that knowledge to set up a basis for comparison of night and day lengths for the rest of Earth. The foundation graph looked like this:
The next step was to label the sunrise and sunset times for the vernal and autumnal equinoxes because that's when night and day are both 12 hours long. Then I used my experience of the length of day and night during the different to seasons to plot the sunrise and sunset times at the solstices (relative to the base lines in the graph above). I have many winter memories of walking home from practice in the dark at 5:00, so I knew sunset happened earlier in the winter. I also have memories of riding to school at 7:00 in the morning when it was still dark, so sunrise in the winter is later. My experiences also told me that summer is exactly the opposite, which led me to the following graph.
The second part of the problem asked me to sketch a diagram illustrating the times that astronomers can observe AY Sixteenus from the Mt. Hopkins observatory. We* started with a review of right ascension which led to the following picture.
Looking at this picture, and operating under the infinite distance idea described in the last post, we realized that on the vernal equinox, AY Sixteenus comes into the field of view at midnight. Before that, the observatory is facing the wrong half of the night sky to see the star. Twelve hours later, at noon the next day, the observatory is once again facing the wrong side of the sky and the star sets.
We know that one stellar day is equal to four minutes more than exactly 24 hours. Four minutes every day for three months (the length of one season) gives a difference of about six hours. Knowing this, we knew that at every change of season, the starrise and starset would be six hours earlier than they were at the previous change. This idea led to the following graph:
The final parts of the problem asked us to consider how the above graph would change in different situations. If the observatory were at a latitude of -10$^{\circ}$, The lines indicating sunrise and sunset would be closer together in the winter (beginning of the graph) and further apart in the summer. If the observatory were further north than in is at Mt. Hopkins, at a latitude of 60$^{\circ}$, the lines indicating sunrise and sunset would be further apart in the winter and closer together in the summer.
The final part asked whether a higher or lower declination than +32$^{\circ}$ would be better for observation. A higher declination would be better because an observer would have to look through more atmosohere to see anything much lower.
*"We" are Dennis Lee, Delfina Martinez-Pandiani, and me.
Nice explanation of your reasoning. However as in the previous problem I would have liked to see a little more quantitative description of the observability (i.e. label your x and y-axes numerically, and line up the star rise and set times on the graph.) Regarding the part of the problem asking about how the graph changes from observing sites located at different latitudes, you correctly pointed out the changing length of nighttime, but missed an additional point: if you're at -10 degrees of latitude, is Ay Sixteenus still perfectly overhead when it crosses the meridian? Does it still spend exactly 12 hours above the horizon every day? How would this (qualitatively) affect the observability band?
ReplyDeleteWhile you're correct about higher declination being more favorable, it doesn't have to do with the atmosphere thickness, but with how much time the star spends high in the sky...
Finally - good effort with the diagrams, but the transparent background you are using shows up as a squared gray background, which is a little distracting.