On the night of 3-4 January, look out for enhanced shooting star activity - possibly as many as one a minute - from the Quadrantids meteor shower. Perspective makes the meteors appear to come from a spot in the sky beyond the end of the Great Bear's "tail" (marked on the chart as Ursa Major). This is the site of an old constellation called Quadrans (the quadrant) which no longer appears on modern maps.
This doesn't mean that the meteors have travelled from that constellation. It's simply the Earth's orbit taking it through the remnants of an asteroid which broke up at a particular spot in space. The annual variations in meteor intensity are caused by the fact that space is awfully big - and every time the Earth passes by, its gravity swirls those remnants around a little more.
Despite those displays, only two planets are on show. The ringed world of Saturn is on duty during the early evening, setting in the west at 10pm. The red planet, Mars, then rises in the east and shines through the rest of the night. Because Saturn and Mars are close enough (celestially speaking) to show in the sky as faint discs, they are not blurred by air- currents, so, like all planets, they don't twinkle.
2 Moon at last quarter 1.46am
3-4 Maximum of Quadrantids meteor shower
9 New moon 4.26am
15 Moon at first quarter 8.02pm
23 Full moon 3.11pm
24 Mercury at greatest western elongation
31 Moon at last quarter 7.41pm