The first wave of stormy weather from the sun hit Earth on Tuesday, sparking bright northern lights - and an even brighter light show is expected on Thursday when the second wave is due to hit.

Both waves were set off on Sunday, when a solar flare and a whooshing magnetic filament erupted on the sun, as seen in a series of images from NASA's Solar Dynamics Observatory. Forecasters at the National Oceanic and Atmospheric Administration's Space Weather Prediction Center, based in Colorado, say those two events sent two distinct waves of electrically charged particles toward Earth. And some space weather watchers suggest there were as many as four separate blasts of particles sent our way.

The first wave, sparked by the flare, began sweeping over our planet's magnetosphere at about 1 p.m. ET Tuesday and peaked at 3:30 p.m., based on real-time satellite readings of the proton flux. The arrival was heralded by elevated readings from the Advanced Composition Explorer satellite, or ACE. "We can see it hitting the ACE satellite even as we speak," Doug Biesecker, a spokesman for the Space Weather Prediction Center, told me Tuesday.

Biesecker said the relatively low-level magnetic disturbance may have caused some power-grid fluctuations and some weirdness for high-accuracy navigation systems, but he didn't expect the event to have any impact for "the average person on the street."

So how about those auroral displays?

"It bodes well for folks in Canada, at least," Biesecker said. "The strength of this storm is such that it's unlikely that people in the U.S. will have much of a chance. Except Alaska. They always have a chance."

Biesecker acknowledged that auroral displays could be more widespread than he and his colleagues expect. And based on the pictures sent in to SpaceWeather.com, observers in Michigan, Wisconsin and Minnesota as well as Canada and northern Europe had great views of the rippling greenish lights in the sky. Denmark's Jesper Grønne captured some stunning pictures plus a video well worth watching. It's the next best thing to being there.

Speaking of things well worth watching, it's definitely worth watching the skies on Wednesday night as well, even if the northern lights can't be seen from your locale.

After sunset, you can check out the planetary triangle that's forming in western skies. After midnight, you might spot some shooting stars, part of the buildup for this month's Perseid meteor shower. Before sunrise, you could catch the International Space Station as it flies overhead.

The forecast for northern lights is better for Thursday, when space weather forecasters expect another wave of particles from the filament ejection to hit Earth's magnetic field. The second wave is projected to have more of an effect than the first one. "It's a case of priming the pump with the first one," Biesecker explained. "The second one can do a little bit more than it could on its own."

There's a good chance of seeing an aurora from Michigan's Upper Peninsula and the northern parts of Minnesota and North Dakota. In fact, folks across the northern tier of the United States, from Maine and upstate New York to Washington state, could be well-placed to see the cosmic lights.

Aurora-seeking skywatchers in the Carolinas or Georgia are likely to be disappointed, but you never know. Space weather forecasters, like your typical TV meteorologists, don't always nail their predictions 100 percent. Keep an eye on the three-hour Kp index (5 or higher is good for seeing the northern lights, but not so good for satellites). You should also check out these websites for real-time information about geomagnetic activity:

• Day-by-day aurora forecasts from GEDDS at University of Alaska
• Space Weather Prediction Center's aurora-viewing tips
• Map of current auroral activity from prediction center
• Soft Serve News: Aurora borealis activity forecast
• SpaceWeather.com coverage of auroral activity

If you do snap a cool picture of the northern lights, why not share it with the rest of the class? Submit your snapshots via msnbc.com's FirstPerson Web page and I'll pass along the best of the bunch. And feel free to file your skywatching report as a comment below.

Update for 5:09 p.m. ET Aug. 3: Here's another take on the aurora-viewing outlook from Christine Pulliam at the Harvard-Smithsonian Center for Astrophysics.

"We'll have multiple opportunities for a display of the Northern Lights over the next two days. The latest word from the solar scientists is that the sun erupted not just once, but four times. All four coronal mass ejections are headed toward Earth.

"Space weather forecasts are even more challenging than regular weather forecasts. Dr. Leon Golub says a coronal mass ejection is like a hurricane: It's large and fuzzy, and doesn't always move at the same speed. Currently, the estimated arrival times are:

Wednesday, Aug. 4 - 3 a.m. EDT
Wednesday, Aug. 4 - 1 p.m. EDT (aurorae not visible in daylight)
Wednesday, Aug. 4 - 8 p.m. EDT
Thursday, Aug. 5 - 2 a.m. EDT

"Any one of these events may or may not generate an aurora. It depends on details like magnetic field orientation. If the magnetic field in the oncoming solar plasma is directed opposite Earth's magnetic field, the result could be spectacular aurorae. If the fields line up, the coronal mass ejection could slide past our planet with nary a ripple.

"Viewing tips: No fancy equipment is needed to see the Northern Lights. You should seek a viewing location with dark skies, as far from city lights as possible. Then, look to the north. An aurora appears as a ghostly sheen of light, colored green or red, that slowly shimmers and undulates over time. An aurora can disappear within minutes or last for hours."

Latest aurora information from the Center for Astrophysics

Update for 8:30 p.m. ET Aug. 3: One of the puzzles surrounding the sun has to do with the extended period of low activity during the most recent 11-year solar cycle. Why was the sun quiet for so long? An analysis just now being published in Geophysical Research Letters suggests an answer: The sun's conveyor belt took an unusually meandering course, stretching out the solar cycle. The solar conveyor belt transports super-hot plasma around the sun, much as Earth's ocean conveyor belt transports water and heat around our planet. Usually the flow gets no closer to the poles than 60 degrees latitude, but during solar cycle 23, the flow went all the way to the poles. Computer simulations showed that a stretched-out conveyor belt could stretch out the cycle's duration.

Update for 4:30 p.m. ET Aug. 4: The Center for Astrophysics says two waves of charged particles have swept past Earth, and two more are expected in the next 10 hours or so. The way the center's astronomers see it, the peak viewing may come late Wednesday night or early Thursday morning. The University of Alaska's Geophysical Institute expects active aurorae Wednesday and Thursday night, with a sharp fall-off afterward. The Space Weather Prediction Center's maps suggest that Europe once again will get the best light show on Wednesday night.

The northern lights made the news on the MSNBC cable channel today: Watch the video featuring commentary by my colleague, NBC News space analyst James Oberg.

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