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An Old Abstract Field of Math Is Unlocking the Deep Complexity of Spacecraft Orbits

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The original version of this story appeared in Quanta Magazine.

In October, a Falcon Heavy rocket is scheduled to launch from Cape Canaveral in Florida, carrying NASA’s Europa Clipper mission. The $5 billion mission is designed to find out if Europa, Jupiter’s fourth-largest moon, can support life. But because Europa is constantly bombarded by intense radiation created by Jupiter’s magnetic field, the Clipper spacecraft can’t orbit the moon itself. Instead, it will slide into an eccentric orbit around Jupiter and gather data by repeatedly swinging by Europa—53 times in total—before retreating from the worst of the radiation. Every time the spacecraft rounds Jupiter, its path will be slightly different, ensuring that it can take pictures and gather data from Europa’s poles to its equator.

To plan convoluted tours like this one, trajectory planners use computer models that meticulously calculate the trajectory one step at a time. The planning takes hundreds of mission requirements into account, and it’s bolstered by decades of mathematical research into orbits and how to join them into complicated tours. Mathematicians are now developing tools which they hope can be used to create a more systematic understanding of how orbits relate to one another.

“What we have is the previous computations that we’ve done, that guide us as we do the current computations. But it’s not a complete picture of all the options that we have,” said Daniel Scheeres, an aerospace engineer at the University of Colorado, Boulder.

“I think that was my biggest frustration when I was a student,” said Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory. “I know these orbits are there, but I don’t know why.” Given the expense and complexity of missions to the moons of Jupiter and Saturn, not knowing why orbits are where they are is a problem. What if there is a completely different orbit that could get the job done with fewer resources? As Koh said: “Did I find them all? Are there more? I can’t tell that.”

After getting her doctorate from the University of Southern California in 2016, Koh grew interested in how orbits can be cataloged into families. Jovian orbits that are far from Europa form such a family; so do orbits close to Europa. But other families are less obvious. For instance, for any two bodies, like Jupiter and Europa, there is an intermediate point where the two bodies’ gravitational effects balance to create stable points. Spacecraft can orbit this point, even though there is nothing at the center of the orbit. These orbits form a family called Lyapunov orbits. Add a little energy to such an orbit by firing a spacecraft engine, and at first you’ll stay in the same family. But add enough, and you’ll cross over into another family—say, one that includes Jupiter inside its orbits. Some orbit families might require less fuel than others, remain in sunlight at all times, or have other useful features.

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Dayung Koh, an engineer at NASA’s Jet Propulsion Laboratory, is trying to come to a systematic understanding of how orbits in a planetary system relate to one another.

PHOTO: Courtesy of Dayung Koh

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Abstract Midjourney prompts to take your creativity and new directions

Midjourney prompts to take your creativity and new directions

From photorealistic to abstract, to playfully quirky, AI image prompts are transforming the way we create and perceive art. This quick guide has been created to provide further insight into how you can take your creativity in new directions. Exploring and experimentation of various AI image prompts, in the areas of abstract, quirky and realistic prompts revealing what you can expect, their effectiveness and unique interpretations across different AI art generators Such as Midjourney, Adobe Firefly, Stable Diffusion, DallE 3 and more. Providing examples of how you can push your artistic ideas in different directions.

Photorealistic and abstract AI image prompts are at the forefront of this artistic revolution. These prompts offer a blend of hyper-detailed realism and psychedelic dreamscapes, creating a visual experience that is both familiar and otherworldly. The dynamic interplay between realistic and fantastical elements in these prompts results in art that is as captivating as it is thought-provoking.

Surrealistic and dreamy elements are another significant aspect of AI art. These elements, often inspired by the subconscious mind, add a layer of depth and intrigue to the artwork. They transport the viewer into a world where the boundaries of reality are blurred, and the imagination is free to roam. AI art generators are particularly adept at creating these surreal dreamscapes, using complex algorithms to generate images that are as mesmerizing as they are mysterious.

The use of tactile photography in AI art is another fascinating area of exploration. This technique involves the use of forms from the natural world, such as geometric and organic shapes from colored wood pieces. These elements add a tactile quality to the artwork, making it more engaging and immersive. AI image prompts that incorporate tactile photography often result in art that is rich in texture and detail.

Realistic, abstract and quirky Midjourney prompts

 Previous articles we have written that you might be interested in on the subject creating AI art using a variety of different Midjourney prompts :

Shibori, a form of Japanese tie-dye, is another technique that is being incorporated into AI art. This ancient art form, known for its intricate patterns and vibrant colors, adds a unique aesthetic to the artwork. AI image prompts that incorporate Shibori techniques result in art that is visually stunning and culturally rich.

Tessellations and optical illusions are also being used in AI art to create intriguing visual effects. These techniques play with the viewer’s perception, creating images that are both complex and captivating. AI image prompts that incorporate tessellations and optical illusions result in art that is not only visually appealing but also intellectually stimulating.

Neon distorted art is another trend in AI art that is gaining popularity. This style uses bright, neon colors and distorted shapes to create art with depth and dimension. The result is a vibrant, dynamic piece of art that is both visually striking and emotionally evocative.

Midjourney landscape prompts

Surreal 3D landscapes and whimsical chaos are other themes that are being explored in AI art. These themes create a sense of wonder and intrigue, transporting the viewer into a world of fantasy and imagination. AI image prompts that incorporate these themes result in art that is both visually stunning and emotionally engaging.

Anthropomorphic prompts with urban street gear are another interesting trend in AI art. These prompts create images that are both familiar and fantastical, blending elements of the human form with urban street culture. The result is a unique style of art that is both contemporary and edgy. The use of neuron-inspired epoxy propop UV reactive ink in AI art is another innovative technique. This technique creates images that are vibrant and dynamic, with a unique glow that adds a futuristic element to the artwork.

Lastly, the playful use of homonyms or homographs in AI image prompts adds a layer of wit and humor to the artwork. These prompts play with language and meaning, creating art that is not only visually appealing but also intellectually engaging.

It’s seems like that everyday new AI image prompts are taking the latest AI art in new directions, allowing artists to experiment with a diverse range of styles and techniques. From photorealistic to abstract, to playfully quirky, these prompts offer endless possibilities for creativity and innovation. As we continue to explore and experiment with these prompts, we can expect to see even more exciting developments in the world of AI art. Other articles you may find of interest on prompts you can using Midjourney to get a variety of different creative styles :

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