The Draconid meteor shower occurs at this time every year when dust from Comet 21P/Giacobini-Zinner hits the Earth at high speed, creating a trail of bright ionized gas in the upper atmosphere. This is a meteor, or "shooting star." Unlike the majority of other showers through the year that are best observed after midnight, the Draconids can be observed at nightfall, just after sunset. So if you're not a late owl, and you live in the Northern Hemisphere, this is the shower for you. All you have to do is lie down, with your feet pointing north, while looking toward the constellation Draco (the Dragon).
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Draco is the radiant of this shower (so any meteors you see will appear to emanate from that point), which will be at its highest in the night sky soon after the sun has set, but as the night progresses, the radiant will drop below the horizon, hence why this shower is viewable so early in the night.