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The three-body problem is a notoriously tricky puzzle in physics and mathematics, and an example of just how complex the natural world is. Two objects orbiting each other, like a lone planet around a star, can be described with just a line or two of mathematical equations. Add a third body, though, and the math becomes much harder. Because each object influences the others with its gravity, calculating a stable orbit where all three objects get along is a complex feat.

Now, an international team of mathematicians claims to have found 12,000 new solutions to the infamous problem — a substantial addition to the hundreds of previously known scenarios. Their work was published as a preprint to the database arXiv, meaning it has not yet undergone peer review.

More than 300 years ago, Isaac Newton wrote down his foundational laws of motion, and mathematicians have been working on solutions to the three-body problem pretty much ever since. There is no single correct answer; instead, there are many orbits that can work within the laws of physics for three orbiting objects. 

Related: The ‘Three-Body Problem’ has perplexed astronomers since Newton formulated it. A.I. cracked it in under a second.

Unlike our planet’s simple loop around the sun, orbits for the three-body problem can look twisted and tangled, like pretzels and scribbles. The 12,000 newly discovered ones are no exception — the three hypothetical objects start at a standstill and, when released, are pulled into various spirals toward one another via gravity. They then fling past one another, moving farther away, until the attraction takes over and they once again come together, repeating this pattern over and over again.

The orbits “have a very beautiful spatial and temporal structure,” lead study author Ivan Hristov, a mathematician at Sofia University in Bulgaria, told  New Scientist. Hristov and colleagues found these orbits using a supercomputer, and he’s confident that with even better tech, he could find “five times more.”

Three-body systems are quite common in the universe; there are plenty of star systems with multiple planets, or even multiple stars orbiting each other. In theory, these new solutions could prove extremely valuable to astronomers trying to explain the cosmos. But they’re only useful if they’re stable, meaning the orbital patterns can repeat over time without breaking apart, flinging one of the component worlds off into space. Just because they’re theoretically stable doesn’t mean they’ll stand up to the many other forces present in a real star system.

“Their physical and astronomical relevance will be better known after the study of stability — it’s very important,” Hristov said.

Juhan Frank, an astronomer at Louisiana State University who wasn’t involved in the work, is skeptical that these orbits will turn out to be stable. They’re “probably never realized in nature,” he told New Scientist. “After a complex and yet predictable orbital interaction, such three-body systems tend to break into a binary and an escaping third body, usually the least massive of the three.”

No matter what, though, these solutions are a mathematical wonder. According to Hristov, “stable or unstable — they are of great theoretical interest.”

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Seven years after it left for the near-Earth asteroid Bennu, NASA’s OSIRIS-REx spacecraft is returning with a celestial souvenir. On the morning of Sunday, September 24, as it passes by Earth the probe will release a canister holding about 9 ounces of space rock. The container will plummet through the atmosphere, its parachute will unfurl, and it will touch down in the Utah desert at about 8:55 am Mountain time.

Assuming its contents survive the journey unscathed, the return will mark a tantalizing step forward for planetary science. Researchers have long salivated over the prospect of examining pristine asteroid fragments. While meteorites—which are often broken chunks of asteroids—fall from the sky all the time, they’re immediately contaminated by the ground they smash into. This will be a rare look at an untainted rock from space, and it will help scientists understand what Bennu is made of and where it came from. If the mission is successful, it will be only the third asteroid sample return in history—following Japanese space agency missions to Ryugu and Itokawa.

To planetary scientist Dante Lauretta, the mission’s principal investigator, it’s also “a little bittersweet,” because the program is now coming to an end. Still, he says, “I’m excited to get it into the laboratory, so we can do all this amazing science.” His University of Arizona team will study the composition of the dust and rock fragments in the container and trace any organic molecules they may harbor. The scientists will also be able to compare samples of Bennu to Ryugu.

But first, the capsule, which is circular and about the size of an ice chest, has to make it safely down to Earth. That will mean slowing from 28,000 miles per hour to just 11. Lockheed Martin built the spacecraft for NASA and is responsible for the capsule recovery. “We have done sample returns before, so we have that experience,” says Sandra Freund, a systems engineer at Lockheed and the OSIRIS-REx program manager, referring to previous NASA missions that collected materials from a comet and the solar wind. “We know we can do this, but there’s always a risk when you’re bringing something back to Earth. You’ve got atmospheric reentry, which is a very fiery experience. You’ve got parachutes that need to deploy. So there are a number of things that need to go just right.”

The capsule’s built-in heat shield is designed to save it from burning up at 5,000 degrees Fahrenheit, as a meteor or unprotected satellite that size hurtling through the atmosphere would. “Any time you want to bring a payload through the atmosphere, you need protection for it. It can be pretty gnarly,” says Todd White, a scientist at NASA Ames Research Center in Mountain View, California, who worked on the spacecraft’s thermal protection system. The heat shield is made of a lightweight chopped carbon fiber infused with resin, and it’s ablative, meaning that it slowly burns off. “It looks nice and brown on the back and white on the front—but when it lands it’ll look charred and crispy,” White says.

First, the capsule will deploy a small drogue chute to keep itself stable. Then seven minutes into its descent, it will open its main parachute and drift to the ground for six more minutes. Recovery helicopters will get the first view of its rapid descent. Relatively soft soil should cushion the impact when it lands within the Department of Defense’s remote Utah Test and Training Range and Dugway Proving Grounds. It’s an active range, though, so before NASA personnel make their approach to retrieve the container, a military representative will check the area to make sure there’s no unexploded ordnance.

OpenAI has announced Dall-E 3, its latest AI art tool. It uses OpenAI’s smash-hit chatbot, ChatGPT, to help create more complex and carefully composed works of art by automatically expanding on a prompt in a way that gives the generator more detailed and coherent instruction.

What’s new with Dall-E 3 is how it removes some of the complexity required with refining the text that is fed to the program—what’s known as “prompt engineering”—and how it allows users to make refinements through ChatGPT’s conversational interface. The new tool could help lower the bar for generating sophisticated AI artwork, and it could help OpenAI stay ahead of the competition thanks to the superior abilities of its chatbot.

AI Art Courtesy of OpenAI

Take this image of the potato king, for example.

This kind of quirky AI-generated art has become commonplace on social media thanks to a number of tools that turn a text prompt into a visual composition. But this one was created with a significant amount of artistic assistance from ChatGPT, which took a short prompt and turned it into a more detailed one, including instructions about how to compose it correctly.

That’s a big step forward not just for Dall-E, but for generative AI art as a whole. Dall-E, a portmanteau of the Pixar character Wall-E and the artist Salvador Dalí that was announced in 2021 and launched in 2022, consists of an algorithm that’s fed huge quantities of labeled images scraped from the web and other sources. It uses what’s known as a diffusion model to predict how to render an image for a given prompt. With sufficiently huge quantities of data this can produce complex, coherent, and aesthetically pleasing imagery. What’s different with Dall-E 3 is in the way humans and machines interact.

AI Art Courtesy of OpenAI

Polaris Spaceplanes, a German aerospace company, has successfully completed a 15-flight test campaign of its MIRA-Light prototype vehicle. 

The test-flights took place over the course of three days, between Aug. 22 and Sep. 8, and were meant to demonstrate the vehicle’s aerodynamics and flight control systems in preparation for a larger-scale spaceplane prototype the company plans to equip with a linear aerospike rocket engine.

MIRA-Light measures just 8.2 feet (2.5 meters) long, and flies using four electric fans. For 10 of MIRA-Light’s 15 flights, the mini-spaceplane was equipped with a mock aerospike engine to simulate its impact on vehicle performance. In total, the prototype accumulated about 40 total minutes of flight time, according to a report from European Spaceflight.

Now, engineers at Polaris Spaceplanes plan to use data collected during the MIRA-Light flights to move forward with a scaled-up, larger MIRA vehicle, which measures nearly 14 feet (4.25 meters). MIRA will be equipped with an actual linear aerospike engine for testing of the vehicle’s integrated flight systems. 

Related: Dream Chaser: Sierra Space’s design for spaceflight

Both MIRA spaceplanes are precursor prototypes to the company’s ultimate demonstration model, NOVA. 

Polaris Spaceplanes plans to scale up the vehicle again after testing MIRA, this time to a length of 22 feet (6.7 meters). NOVA will fly using four kerosene-fueled jet engines, in addition to its functional aerospike engine. This vehicle’s test campaign will involve full rocket-powered flights in Earth’s upper atmosphere happening at supersonic speeds. 

If all goes well with MIRA’s upcoming demonstration missions, Polaris Spaceplanes expects to begin flying NOVA sometime in 2024.

MIRA-Light, MIRA and NOVA succeed three other prototypes that flew from 2020-2022. Polaris Spaceplanes hopes to culminate them all into its multipurpose, hypersonic transport vehicle, AURORA. 

Polaris Spaceplanes’ website markets AURORA’s future design as capable of transporting a payload up to 22,000 pounds (10,000 kilograms) to suborbital velocities, and up to 2,200 pounds (1,000 kilograms) to an orbit of any inclination, according to the company’s website. 

Polaris Spaceplanes hopes to begin flying AURORA sometime in 2026 or 2027.

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Stoke Space successfully landed its reusable second stage rocket system this week, an important demonstration of the company’s innovative engineering concepts.

The test, dubbed Hopper2, saw Stoke Space’s Hopper launch vehicle lift off about 30 feet off the ground and safely return to the ground, landing in its targeted landing zone after flying for about 15 seconds. The test was meant to demonstrate the soundness of several of the rocket’s systems and design elements, including its hydrogen/oxygen engine, coolant-based heat shield and a propulsion system that maneuvers the rocket by throttling its different engines.

Stoke Space is confident that the successful test moves the company towards its goal of  developing fully-reusable rockets. “We’ve also proven that our novel approach to robust and rapidly reusable space vehicles is technically sound, and we’ve obtained an incredible amount of data that will enable us to confidently evolve the vehicle design from a technology demonstrator to a reliable reusable space vehicle,” the company said in a statement.

Related: US Space Force grants 4 companies launch pads at Cape Canaveral

Among the features tested were the rocket’s differential throttle, which is used for attitude control of the vehicle and isn’t widely used in the modern space industry, as well as its regeneratively cooled heat shield, which uses pressurized coolant passing through metal pores in the exterior of the rocket to cool its surface during reentry. 

The latter is especially interesting since this type of shielding was the type of heat shield that Elon Musk originally wanted for SpaceX’s Starship before that plan was abandoned in favor of a more traditional design. While the design has a lot of proponents, no spacecraft has ever attempted reentry into Earth’s atmosphere using the design, so it is still unproven. 

Still, Stoke Space says that “although this vehicle didn’t directly experience the heat from hypersonic atmospheric re-entry, it has successfully operated at 100% of the expected heat load in a simulated environment.”

While the test of the second stage rocket has been a success, Stoke Space has a way to go before reaching its goal of building a 100% reusable rocket with a turnaround time of just 24 hours. Still, the company says it is encouraged by the results so far, and will now turn its attention to developing a reusable first stage rocket.

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: community@space.com.