Eridanus: The River
Somewhere near Orion's foot, a river starts, and it does not stop for a long time. Eridanus meanders south across a huge stretch of sky, farther than almost any other constellation bothers to travel, before it finally ends at one of the brightest and strangest-shaped stars visible from Earth.
A reckless ride ends in this river, according to the Greeks
The myth behind Eridanus belongs to Phaethon, son of the sun god, who begged to drive his father's chariot across the sky for a day. He lost control of the horses almost immediately. The chariot scorched the earth as it swung wildly off course, and Zeus finally struck Phaethon down to stop the damage before the whole world burned. He fell from the sky into the river Eridanus, which ancient writers identified with the real, earthly Po river in northern Italy. It is one of the sky's more brutal myths: a boy who wanted one glorious day and paid for it with everything.
The river's four stars trace its whole meandering length
Cursa, Beta Eridani, marks the river's source, sitting near Rigel in Orion at magnitude 2.79, a white star right at the point where the story begins. Theta Eridani, called Acamar, is a wide double star at magnitude 2.88 that was once considered the river's end, before better charting pushed the boundary further south. Zaurak, Gamma Eridani, is a red giant at magnitude 2.97 sitting partway down the length of the river. And Achernar, Alpha Eridani, marks the actual southern end at magnitude 0.46, a hot blue star spinning so fast that it has visibly flattened itself at the poles. Achernar is by a wide margin the brightest thing in the whole constellation, brilliant enough that it earns its Alpha designation without any of the ambiguity that shows up in some other shapes.
A barred spiral and a nebula lit by a neighbor's glow
Eridanus carries two notable deep-sky objects. NGC 1300 is a textbook barred spiral galaxy, the kind of clean, symmetric structure that shows up in astronomy textbooks precisely because it is such a good example of the type. The Witch Head Nebula, catalogued as IC 2118, is a faint reflection nebula, lit not by any star inside itself but by the light of nearby Rigel, borrowing its glow from a neighbor in Orion rather than generating its own.
The Witch Head Nebula's position is a nice detail on its own. It sits inside Eridanus's boundary, near the river's source close to Rigel, which means the very same star that helps you find Cursa is also the reason the nebula has any light at all. NGC 1300, by contrast, has nothing to do with any of Eridanus's own stars. It is simply a distant galaxy that happens to fall within the river's long, winding outline, unrelated to the myth or the named stars in every way except geography.
What this means for you tonight
Eridanus comes to its best in December and stretches from near Orion all the way down into the deep south, so how much of it you can see depends heavily on where you are standing. Start at Orion, find Rigel, and look just to its side for Cursa; that is the river's beginning, and it is the one part of Eridanus almost everyone north of the equator has a real shot at seeing. Achernar, at the far end, sits so far south that it is out of reach for a lot of the northern hemisphere entirely, which is worth knowing before you go hunting for the brightest star in the constellation and cannot find it.
Because Achernar and Cursa differ by more than two magnitudes, this is a genuinely good constellation for practicing your eye against the numbers; how star brightness works explains why a gap that size is easy to see even for a casual observer, unlike the near-ties you will run into elsewhere on the sky map. And if the Witch Head Nebula refuses to show itself, check light pollution and the Bortle scale before assuming your eyes or your optics are the problem; a nebula that only shines by reflected light from a neighboring star is one of the first things any amount of sky glow erases.