Tau Ceti and Declination

Partners: Nathan, Mee, Eric


Imagine you are standing outside on a clear night, far away from any sources of light pollution, yet also in the relative vicinity of Palomar Observatory (this will be important later). When you look up, you see a vast array of stars spread out before you.


Now, before you get too distracted by the splendor of the night sky, turn to face north, and find Polaris. Polaris is the North Star, and it is fixed in the heavens (for the next several thousand years, anyway), shining above the northern horizon.


If you watched the area around Polaris for the whole night, you would see the sky appear to rotate around it, with the paths of nearby stars tracing (parts of) circles in the night around the unmoving North Star.


You see, the Earth’s axis of rotation points toward Polaris; therefore, as the Earth rotates during the night, the angle between Polaris, the point of observation, and the observed star changes. So the star in question appears to be at a different point in the sky.


If you shift your observation of the sky to a position south of the area around Polaris, you’ll notice that the stars in this area trace larger circles. If you were able to watch their paths for 24 hours (the Sun tends to be a problem here), you would perhaps see that part of the stars’ paths are blocked by the Earth; their movements take place “behind” the horizon.


Why do the paths get longer as your gaze drifts south? This is a function of declination. This is essentially the same as latitude, and is measured in degrees north or south of the celestial equator (the celestial equator is simply the plane of the Earth’s equator extended out into space). Palomar is at about 30 degrees North; any object directly above it in the sky will have a declination of 30 degrees N (or an object directly above any point on the 30-degree latitude line).


You can also think of the declination as an angle whose vertex is at the Earth’s center, with one line on the celestial equator and one connecting the center of the Earth to the star in question. So Polaris, on the line of Earth’s rotational axis, is perpendicular to the celestial equator. Thus, Polaris’ declination is 90 degrees.


Take another star, Tau Ceti. It has a declination of negative 15 degrees, so it is in the Southern Hemisphere. But it’s close enough to the declination of the equator (0 degrees) that it should be visible in parts of the Northern Hemisphere. Like, say, Palomar.


Suppose that from Palomar’s 30 degrees N, any object with a declination >30 degrees is visible in the sky throughout the day. Everything between -30 and 30 is visible at some times but not others. Everything below -30 is never seen in the sky above Palomar.


Tau Ceti is within the sometimes-visible interval. So, when can we see Tau Ceti? Well, obviously we can’t see it during the day, because there’s an annoyingly close star whose light masks the presence of other stars during the daytime. At this latitude, the Sun is visible for just over 14 ours at the summer solstice, and just over 10 at the winter. Give it an extra two hours for the sky to darken, and you have possibly eight hours of time to see Tau Ceti in the summer and 12 in the winter.


But there is another factor to consider here. As the Earth moves in its orbit around the Sun, the time at which an object reaches the meridian (the highest point it reaches in the sky, and the best point for viewing) changes. Because, when the Earth rotates, it takes 360 degrees to complete one full rotation. But because it is also moving in space, after one full rotation, it must then rotate one extra degree to bring the starting point of the measurement in line with the sun. This extra rotation takes about 4 minutes. Accordingly, a given distant star will rise 4 minutes earlier each subsequent night.


Tau Ceti’s Right Ascension is 1 hour and 44 minutes, so about 2 hours. This is the time after noon (set at 0:00 hours) that a star will reach the meridian in the sky on the Vernal Equinox (known by some as March 20). So in late March, Tau Seti will be in prime viewing position around 2 pm. This is obviously a problem, as the Sun is also in prime viewing position around 2 pm. So when will Tau Ceti peak at a better time?


Every 30 days is about 120 minutes of change, or 2 hours. So around April 20, Tau Ceti will peak around noon. Not better. But by August, it will be peaking at around 4 in the morning. Tau Ceti will reach meridian at midnight in October.


So, if we assume that, because of its declination, Tau Ceti is best viewed around its meridian peak, when it can’t be hidden by the horizon, and that Tau Ceti, like most stars, is best viewed at night, then we can estimate the best times for viewing Tau Ceti as early fall to early winter.


Possibly more to follow, including graphs, if I have time.