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But you can go out tonight, or earlier tomorrow night, or on Friday night, too; you just won't see as many meteors (about 10-12 per hour on the nights before and after). Be sure to go somewhere with dark skies, because streetlights will drown out most of the smaller meteors. To eliminate as much sky-glow as possible, go north of your local city so that the city's lights are behind you rather than between you and the show. Also spend some time getting dark-adapted (your pupils take a while to fully embrace the light) before you can expect to see the most meteors - go with friends, camp out, make it a night!
Another great source for info here.
But wait, there's more! The show begins at sundown when Venus, Saturn, Mars, and the thin crescent Moon pop out of the western twilight in tight conjunction. All four heavenly objects fit within a circle about 10 degrees in diameter (smaller than your open hand at arm's length), shining together amid the sunset colors. All of these objects are very bright, so you can view this even with your naked eye. The full show will last until about 10:00pm, when the Moon sets. If you want to use a telescope, that's purely optional, as Mercury and Venus don't look like much more than bright disks, with Moon-like phases depending on where they are in their orbits. Here's a map for Thursday, but they'll be in conjunction starting tonight for the next few days. The line at the bottom is the horizon, and the sun is the clear circle below it:
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So get out there and enjoy this incredible show!
Chris