Happy Winter, everyone!
I don't know about the weather where you live, but out here on the Great Plains, we've been enjoying the benefits of an Arctic high pressure system that got lost and wandered down from northern Canada, like some misplaced meteorological moose. Yesterday morning, my car thermometer reported a temperature of -20°F when I got in. On the other hand, we now have some gorgeous wind-sculpted snowscapes folding and undulating along the creek banks and roadsides, and when the sky clears we have a sparkly, crystal-clear view of outer space.
Astronomically speaking, we are passing through a few months of relative quiescence, and we can continue to relax and enjoy the simple beauty of the constellations, monitoring their gradual shift with the seasons, and to notice the wandering planets as they gradually rearrange themselves around the sun.
You may recall that a month or two ago, Scorpius was barely beginning to climb out of the sunrise, only managing to get his head above the horizon before the sun rose and drowned out the stars. Now, if you look southeast before dawn begins to take hold, you can see most of the scorpion preceding the sun up into the sky. You may be able to catch the stinger of his tail, and the teapot of Sagittarius as well, low over the horizon just before the stars disappear. The moon has just passed by these two zodiac constellations, and will do so again in early March.
(This represents the view from Iowa. If you live farther north than this, Scorpius and Sagittarius will be even lower in the southern sky, and you may have difficulty finding them. If you live in Canada or Europe, they will probably be blocked from your view completely.)
Jupiter and Saturn have now completely departed the evening skies, passed the sun, and begun to appear in the morning skies, but they are still very low over the sunrise, and I doubt that you will be able to see them yet. However, they will continue to climb higher over the sunrise as the days and weeks go on, so if you are an early riser, you may want to keep your eyes on the eastern pre-dawn horizon, and see who can be the first to find them. Venus continues to descend, and is now very near Jupiter and Saturn, very low over the sunrise, and very hard to find. It will continue to descend, and will eventually pass the sun, but very slowly. It won't reappear in the evenings until April, and won't rise high and begin to really decorate the sunsets until May or June.
The majestic Winter Hexagon still dominates the southern evening skies. Assuming you are already familiar with it, try staring at brilliant Sirius for a few moments, especially if it is still close to the horizon. You should be able to see it twinkle and scintillate powerfully—so powerfully that it actually changes colors! You might also enjoy trying to getting a better look at Orion's Sword, either with binoculars, or as I did with a long-exposure photograph.
This is a 10-second exposure that I took with my DSLR and telephoto lens (in sub-zero temperatures). You may recognize the three stars in the middle as Orion's Belt, and the vertical grouping near the bottom is Orion's Sword. The glowing cloud is the beautiful Orion Nebula, one of the largest and brightest nebulae in the sky, and one of the very few that it is possible to glimpse with the naked eye.
If you wait until the late evening, when Orion and the Hexagon are standing up straight in the south, you can find Leo rising in the east. If you have dark skies and let your eyes adapt fully to the dark, you may be able to pick out another dim fuzzy spot, about halfway between Leo and Gemini. This is not a nebula, but a star cluster—the "Beehive Cluster"—and it, too, might be worth a closer inspection.
The moon will be passing across the southern sky, and through the Winter Hexagon, later this month, and if you keep any kind of journal, you may enjoy noting the moon's passage by various landmarks. Among other things, it will pass very close to a small star, and maybe even eclipse it, as it goes. On Thursday, February 18, the moon will pass nearby Mars, which is now entering Taurus and approaching the Winter Hexagon from the right. On the next day, the 19th, the moon will pass through the "Golden Gate of the Ecliptic" ... meaning it will pass between the two star clusters of the Pleiades and the Hyades. (The Hyades, you may recall, is a group of reddish stars marked by the "V"-shaped portion of Taurus the Bull. And it, too, is lovely in binoculars.) I have watched for this passage in the past, hoping for a beautiful sight, but the moon was nearly full and drowned out the star clusters, and I was a little disappointed. However, this time the moon will be at First Quarter, so I'm optimistic. After passing through the "Golden Gate", the moon will then enter the Hexagon, and will pass across it from the 20th to the 23rd. After sunset on the 23rd, you may want to keep your eye on the moon, because it will pass very close to κ ("kappa") Geminorum, a medium star in Gemini. Whenever the moon passes very close to something, it is a good opportunity to observe the rapid motion of the moon through the stars—depending on circumstances, you should be able to see obvious changes in position in as little as a few minutes. Try observing the speed of the moon as it passes κ Geminorum, especially if you have a good pair of binoculars. (Kappa Geminorum is the "hand" of Pollux. In other words, find the two bright stars of Gemini, pick the lower and brighter of the two, and then look for the medium star just below it. Here's a map.)
A Stellar Eclipse
Actually, if you are lucky, this passage of the moon by κ Geminorum could be unusually dramatic for you—the moon might actually "hit" the star! But you have to live in the right place.
As the moon makes its monthly orbit around the zodiac, it passes through and among all of the stars of the zodiac constellations. Once in awhile, it hits one. More precisely, it eclipses the star, passing in front of it, and hiding it from our view. These eclipses of stars by the moon are formally known as "occultations", and they happen pretty frequently.
Unfortunately, like solar eclipses, each "occultation" is visible only to a small part of the world. The rest of the world just sees the moon pass very close to the star. Furthermore, half of the time the sun is in the sky along with the moon and the star, in which case the star is drowned out by glowing blue air. Finally, the stars most likely to be occulted are the more numerous dimmer ones, and these are often very hard to see when next to the bright moon, especially when the moon is nearly full. And there is always the weather to worry about. Thus, observing these lunar occultations can be a rewarding challenge for avid star-gazers, but it takes some devotion, good timing, and lots of waiting. And luck helps.
As the moon passes through the Winter Hexagon later this month, observers in the southeastern United States will see it "hit" the star Kappa Geminorum shortly after sunset on February the 23rd. For a map and further technical details about this month's occultation of Kappa Geminorum, this page has all the info. (If you live between the white lines on the map, you'll be able to see it. If you live between the red lines, it will happen in your sky, but during the daytime.)
If you'd like a full list of occultations occurring in 2021, this page has a detailed list. The "General Area" column lists the parts of the world where the occultation will be visible, and you can click on each star name for a map with more detail. The "MAG" column lists how bright the star is. Smaller numbers represent brighter stars. I recommended getting excited if you find any with a magnitude number less than around 3 that are visible in your area. How do you know which star will be eclipsed? The "Name" column identifies each star with a three-letter code indicating the constellation, and a Greek letter indicating the star within the constellation. Assuming you can deduce the constellation name from the three-letter code, I suggest consulting the Wikipedia article for that constellation, which will have a map of the constellation. Examine the map, and you should be able to find the star labeled with the corresponding Greek letter.