Sensitivity of Gamma Astroparticle Experiments to the Detection of Photon Oscillations

新托福听力十大主题词汇分享：天文词汇1主题之一: 天文Theme One: Astronomyastronomer astronomical astronautastrology observatory telescopesolar system cosmic rays cosmosinterstellar intergalactic galaxyThe Milky Way The Big Bang cometasteroid satellite meteormeteorite revolution rotationradiation constellation clusterlunar eclipse velocitycorona terrestrial planetaryexploration hypothesis assumecollision supernova novalight year gravitation nebula1 astronomern. 天文学家During his own tenure as astronomer royal， from 1720 to 1742，Halley studiously tracked the moon.2 astronomicala. 天文学的，天文数字的，庞大的A man-made clock would certainly prove a useful accessory to astronomical reckoning but could never stand in its stead.3 astronaut n. 太空人，宇航员，太空旅行者In their most visible work， astronauts will let loose a retrievable satellite carrying a coffin-sized inflatable antenna.4 astrologyn. 占星学，占星术Racing expert John Randall phoned a friend on the £1million astrology question on Monday.5 observatoryn. 天文台，气象台The accuracy of global field models depends on the worldwide network of magnetic observatories.6 telescopen. 望远镜Details on the moon’s surface can be seen through a telescope.7 solar systemn. 太阳系的美女编辑们A less-co ntrived example involves the relation between Kepler’s theory of the solar system and Newton’s.8 cosmic raysn. 宇宙射线A stray cosmic ray might do the same thing.9 cosmosn. （被视作和谐体系的）宇宙Among the factors that stand out in the Orphic construal of a cosmos is the nature of time.10 interstellara. 星际的It is possible that we have traces of interstellar dust in meteorites.11galaxyn. 星系。

基于星敏感器和陀螺的卫星定姿新方法艾奇;葛升民【摘要】Aiming at the problem of unable to choose suitable filtering mode for errors accumulated and noise distribution changed, the body coordinate system, a augmented measure composed of measurements of star-sensor and gyro in the inertial coordinate is proposed and the attitude determination is modeled to a nonlinear filter problem. Because the nonlinear filters used commonly may have a good performance both in accuracy and real time, UKF is introduced to estimate the attitude parameters and the gyro drift Further, the situation of unknown or time-varied sensor accuracy is considered, and the IMMUKF algorithm is proposed. The simulation results show the efficiency and accuracy of the method. It has a high practical value.%针对本体坐标系下对卫星姿态进行线性滤波存在误差累积和噪声分布改变无法正确选择滤波模型的问题,利用惯性坐标系下的星敏感器和陀螺原始测量构建系统扩维测量,将卫星姿态确定问题建模为非线性滤波过程.针对常用的非线性滤波方法无法同时兼顾精度和实时性的问题,采用无迹滤波(UKF)对卫星的姿态参数和陀螺常值漂移同时进行估计,实现了对卫星精确定姿.进一步考虑实际情况中,敏感器测量误差未知或随时间变化的情况,提出了交互式多模型无迹滤波(IMMUKF)方法.仿真实验结果表明了该算法的有效性和优越性,具有较高的实际应用价值.【期刊名称】《现代电子技术》【年(卷),期】2012(035)004【总页数】5页(P13-17)【关键词】姿态确定;星敏感器;陀螺仪;无迹滤波;交互式多模型【作者】艾奇;葛升民【作者单位】哈尔滨工业大学控制科学与工程系,黑龙江哈尔滨 150001;哈尔滨工业大学控制科学与工程系,黑龙江哈尔滨 150001【正文语种】中文【中图分类】TN911-34;V448.22卫星姿态确定系统是卫星姿态控制系统中的重要组成部分，其精度是影响姿态控制系统精度水平的决定性因素。

天文知识的英文作文Title: Voyaging Through the Cosmos: An Exploration of Astronomical WondersThe study of astronomy, a scientific journey that delves into the mysteries of the universe, is a testament to humanity's insatiable quest for knowledge and understanding beyond our terrestrial confines. It unfolds a narrative where time and space intertwine, revealing the majestic tapestry of stars, galaxies, planets, and phenomena that comprise the cosmic arena. This celestial exploration is not just an accumulation of facts but a voyage into the depths of existence, shedding light on our origins and our place in the grand scheme.At the heart of astronomical inquiry lies an array of celestial bodies, each offering unique insights into the workings of the universe. Stars, the luminous beacons in the velvet darkness of space, are born from vast clouds of gas and dust, undergoing a life cycle marked by stages of stability, explosion, and, sometimes, black hole creation. Their lifespan and characteristics, ranging from size to brightness, provide astronomers with valuable information about stellar evolution and the dynamics of celestial mechanics.Galaxies, vast island-like structures in the universe, arecomposed of billions of stars, nebulae, and dark matter, bound together by gravity. They come in diverse shapes and sizes, from spiral to elliptical, each telling a different story of cosmic evolution. The study of galaxies aids in comprehending the large-scale structure of the universe and the processes that drive cosmic evolution over aeons.Planets, both within and beyond our solar system, offer a more tangible glimpse into the variety of conditions that support life or alter its course. From the extreme climates of Venus to the potential oceans beneath the icy surface of Europa, a moon of Jupiter, these celestial bodies serve as laboratories for understanding the possibilities of life in environments vastly different from Earth.Astronomy also unveils a plethora of cosmic phenomena that challenge the limits of human understanding. Black holes, with their intense gravitational pull that not even light can escape, pose questions about the nature of spacetime and the destiny of matter. Comets, with their brilliant tails, are frozen relics from the formation of the solar system, providing invaluable insights into its early history.The exploration of astronomical wonders culminates in the search for extraterrestrial life, a quest that has captivatedimaginations and propelled scientific endeavor. The discovery of exoplanets, orbiting stars other than our Sun, has expanded the realm of possibility, offering candidates for potentially habitable worlds. The search for signals amidst the cosmic radio noise and the probing of exoplanet atmospheres for signs of biological activity embody our innate curiosity and our longing for a cosmic companionship.In conclusion, the journey through astronomical knowledge is an epic that unfolds the intricate saga of the universe, from the birth of stars to the potential for life among the stars. It transcends the boundaries of mere academic pursuit, touching the philosophical and existential aspects of human consciousness. As we continue to unravel the mysteries of the cosmos, we find reflections of our own being and the universality of our quest for understanding. The study of astronomy thus becomes a metaphor for our shared human adventure, seeking connections and finding awe in the vast, mysterious, and beautiful universe that is our home.。

Certainly! Here’s an essay exploring the conjectures about extraterrestrial civilizations, delving into the scientific, philosophical, and speculative aspects of the topic. Extraterrestrial Civilizations: The Great Beyond and Our Place in the CosmosThe universe, vast and ancient, stretches its arms across 93 billion light-years of observable space, containing billions of galaxies, each with billions of stars. Within this cosmic tapestry, the question of whether we are alone has captivated human minds for centuries. This essay explores the conjectures surrounding extraterrestrial civilizations, from the scientific theories to the speculative musings that fuel our imaginations.The Drake Equation: A Mathematical Framework for SpeculationAt the heart of the search for extraterrestrial intelligence (SETI) lies the Drake equation, formulated by astronomer Frank Drake in 1961. This mathematical framework attempts to estimate the number of active, communicative civilizations in the Milky Way galaxy. Variables include the rate of star formation, the fraction of stars with planetary systems, the number of planets capable of supporting life, the fraction of those planets where life actually emerges, the fraction of those life-bearing planets that develop intelligent life, the fraction of those that develop a civilization with technology, and the length of time such civilizations release detectable signals into space. While many of these variables remain unknown, the Drake equation serves as a tool for structured speculation and highlights the immense challenge in estimating the likelihood of extraterrestrial life.The Fermi Paradox: Where Are They?The Fermi paradox, named after physicist Enrico Fermi, poses a compelling question: Given the vastness of the universe and the high probability of habitable worlds, why have we not encountered any evidence of extraterrestrial civilizations? This paradox has led to numerous hypotheses. Perhaps civilizations tend to destroy themselves before achieving interstellar communication. Or, advanced civilizations might exist but choose to avoid contact with less developed species, adhering to a cosmic form of the “prime directive” seen in science fiction. Alternatively, the distances between stars could simply be too great for practical interstellar travel or communication, making detection exceedingly difficult.The Search for TechnosignaturesIn the quest for extraterrestrial intelligence, scientists have focused on detecting technosignatures—signs of technology that might indicate the presence of a civilization elsewhere in the universe. These include radio signals, laser pulses, or the dimming of stars due to megastructures like Dyson spheres. SETI projects, such as the Allen Telescope Array and Breakthrough Listen, scan the skies for anomalous signals that could be attributed to alien technology. While no definitive technosignatures have been found to date, the search continues, driven by advances in technology and a growing understanding of the cosmos.Astrobiology: Life Beyond EarthAstrobiology, the study of the origin, evolution, distribution, and future of life in the universe, offers insights into the conditions necessary for life. Research in astrobiology has revealed that life can thrive in extreme environments on Earth, suggesting that the conditions for life might be more widespread in the universe than previously thought. The discovery of exoplanets in the habitable zones of their stars, where liquid water can exist, increases the probability of finding environments suitable for life.Continued exploration of our solar system, particularly of Mars and the icy moons of Jupiter and Saturn, holds promise for uncovering signs of past or present microbial life. The Philosophical ImplicationsThe possibility of extraterrestrial civilizations raises profound philosophical questions about humanity’s place in the universe. Encountering another intelligence would force us to reevaluate our understanding of consciousness, culture, and ethics. It could lead to a new era of global unity as humanity comes together to face the challenges and opportunities of interstellar diplomacy. Conversely, it might also highlight our vulnerabilities and prompt introspection on our stewardship of the planet and our responsibilities as members of the cosmic community.Concluding ThoughtsWhile the existence of extraterrestrial civilizations remains a conjecture, the pursuit of answers has expanded our understanding of the universe and our place within it. The search for life beyond Earth is not just a scientific endeavor; it is a philosophical journey that challenges us to consider our origins, our destiny, and our role in the vast cosmic drama unfolding around us. Whether we find ourselves alone or part of a galactic community, the quest for knowledge about the universe and our place in it is one of humanity’s most enduring and inspiring pursuits.This essay explores various aspects of the conjectures surrounding extraterrestrial civilizations, from the scientific frameworks used to estimate their likelihood to the philosophical implications of their existence. If you have specific areas of interest within this broad topic, feel free to ask for further elaboration! If you have any further questions or need additional details on specific topics related to extraterrestrial life or astrobiology, please let me know!。

老师看不出是抄的我的奇思妙想英语作文全文共3篇示例，供读者参考篇1My Wildest Dreams and FantasiesYou know that feeling when your mind starts to wander and suddenly the most peculiar thoughts take over? It's like being transported to another dimension where reality is bent and anything is possible. Well, let me take you on a journey through the untamed wilderness of my imagination. Buckle up, because this ride is about to get weird!Imagine a world where dogs could talk. Not just bark or whine, but engage in full-blown conversations. I'm picturing myself strolling through the park, casually chatting with a pack of Golden Retrievers about the latest bone-chilling thriller they've been digging into (pun very much intended). We'd debate the finer points of storytelling, critique the character development, and maybe even exchange a few doggy puns for good measure. Who knows, I might even get some writing tips from thesefour-legged literary critics!Now, let's take a sharp left turn into the realm of the utterly absurd. What if clouds were made of cotton candy? Imagine gazing up at the sky, watching those fluffy, sugary formations drifting lazily overhead. I can almost taste the sweetness on my tongue as I reach up to pluck a handful of cloud-candy, savoring the delightful flavor bursting in my mouth. Of course, this could lead to some sticky situations – quite literally. Rainclouds would shower us with sugary syrup, and thunderstorms would be an absolute mess. But hey, at least we'd never run out of dessert!Speaking of food, have you ever wondered what it would be like if vegetables could scream? Imagine the horror of biting into a juicy tomato, only to be met with a blood-curdling shriek emanating from its fleshy interior. Chopping an onion would become a form of cruel and unusual punishment, unleashing a torrent of anguished wails. Cooking would be a traumatic experience, filled with the agonized cries of defenseless veggies begging for mercy. On second thought, maybe we should stick to a strict candy diet in this fantastical world.Now, let's drift into the realm of the truly outlandish. What if the moon was made of cheese? Not just any cheese, mind you, but the gooiest, most mouth-watering cheddar you can imagine. Imagine gazing up at that golden, celestial disc, its craters filledwith pools of melted deliciousness. Astronauts would be replaced by cheese connoisseurs, embarking on expeditions to mine the lunar surface for the finest, most aged varieties. The only downside? Lunar eclipses would be a real letdown, blotting out that tantalizing sight with the dull hunk of rock we call Earth.But wait, there's more! How about a world where gravity was reversed? Instead of being pulled down, we'd find ourselves constantly floating upwards, desperately clinging to anything anchored to the ground. Imagine the chaos of trying to have a casual conversation, both parties drifting lazily towards the ceiling as they exchange pleasantries. Eating would be a messy affair, with food and utensils constantly escaping our grasp and disappearing into the stratosphere. And let's not even talk about the challenges of using the restroom in such an environment. On second thought, maybe we should just stick to the ground for that particular activity.Of course, no journey through the bizarre would be complete without exploring the idea of animals walking on their hind legs. Picture yourself strolling down the street, only to encounter a group of upright dogs engaged in a lively discussion about the latest trends in chew toys. Or perhaps you'd stumble upon a gathering of bipedal cats, sipping daintily from tinyteacups as they gossip about the neighborhood's most eligible toms. It would be a surreal sight, to say the least, but also strangely endearing in its own peculiar way.As our adventure through the whimsical reaches of my mind comes to a close, I can't help but feel a sense of wonder and excitement. The ability to imagine the impossible, to dream up scenarios that defy logic and reason, is what makes the human experience so rich and fascinating. So, the next time your thoughts start to wander down an unconventional path, don't shy away from the absurdity. Embrace the weird, the wacky, and the downright bizarre. Who knows? You might just stumble upon your own personal wonderland, filled with talking dogs, cotton candy clouds, and a moon made of cheese.篇2My Wildest DreamsAs I lay in bed last night, staring at the glow-in-the-dark stars stuck to my ceiling, my mind started to wander. I found myself pondering the vast mysteries of the universe and imagining what incredibilities could exist out in the great cosmic unknown. The more I thought about it, the more my imagination ran wild with fanciful possibilities.What if there was another Earth-like planet out there with intelligent life forms vastly different from humans? Maybe there's a planet made entirely of candy with lollipop trees and cookie crumble mountains. Or a world with floating cities held aloft by anti-gravity technology. Anything seems possible when you really open your mind to the mysteries of existence.I started imagining myself on a journey through the cosmos, exploring strange new worlds. On the candy planet, I'd be able to bite into a chocolate mansion or drink from a river of root beer without any consequences. The floating cities would be glorious metropolises suspended in perpetual motion among the clouds and stars.Maybe there's even a planet made up of pure energy where life takes the form of concentrated beams of light and heat. How wild would it be to see cities built of plasma and lightning? I could soar effortlessly by bending radiation around me like a surfboard on a wave.As my mind continued racing with these fanciful ideas, I found myself hoping that somewhere out there, such extraordinary places truly exist. If nothing else, it's fun to imagine the possibilities of what could be.Of course, I'm not naive enough to think there's a real candy planet or cities of pure energy. But who's to say there aren't other planets with forms of life we can scarcely comprehend from our limited human perspective? With how little we know about the larger cosmos, anything seems possible if you allow your imagination to run free.I started pondering how life could evolve in ways entirely different from what we understand. On Earth, carbon-based life emerged from the primordial soup, slowly developing into complex multi-cellular organisms over billions of years. But what if a planet existed where life arose from pure energy or something entirely different and unexpected?There could be civilizations made up of sentient machines that have evolved their artificial intelligence to become a new form of technological life. Or what about a world where life emerged from complex neutron flows, forming itself into something akin to what we'd perceive as neutron stars that can somehow think and reason? The possibilities are endless when you shed your anthropocentric biases.My mind then drifted to what kind of unfathomable technologies could exist across the vastness of space and time. We humans have built some incredible devices like computers,rockets, and particle colliders. But those surely pale in comparison to what could be out there across the galaxies.I imagined a civilization that had mastered teleportation and could effortlessly travel between star systems in the blink of an eye. Or a race of beings that had unlocked the secrets of wormhole physics to create shortcuts across the cosmos. Maybe there are advanced species that long ago transcended physical forms altogether to become purely energetic beings capable of riding the very fabric of space-time itself.As a sci-fi fan, I'm quite familiar with concepts like hyperdrives, warp drives, and other fanciful means offaster-than-light travel that skirt around the cosmic speed limit of light speed. But who's to say more intelligent and ancient alien species haven't already cracked the code to achieve something like that or far crazier things we can't yet conceive?I then found myself wondering just how old some alien civilizations could truly be across this mind-bogglingly vast universe of ours. Our own human history only stretches back a few thousand years from an evolutionary standpoint. But there could be races of xenomorphs out there that are billion, if not trillions of years more ancient than we are.What unfathomable wisdom and technologies could they have amassed over such cosmically vast timescales? There's a chance some could be old enough to have originated during the earliest epochs after the Big Bang itself when the universe was an entirely different place. That's enough to make your head spin if you think about it too much.Of course, these are all wild thoughts and fanciful ideas with no grounding in scientific facts or evidence. I'm just an awestruck teenager allowing my imagination to run rampant across the celestial expanses of my mind's eye. But that's precisely what drives the wonderment of science and human curiosity.While the concepts I'm dreaming up are firmly rooted in the realms of science fiction and fantasy for now, the truth is we simply don't know what actual marvels could exist across this mind-bendingly massive universe of ours. It was once thought the sun revolved around the Earth and that our planet was the center of all creation. Just a few centuries ago, atoms and electromagnetic waves were still unknown to humankind.As our scientific understanding of the cosmos continues advancing by leaps and bounds, who's to say what shocking revelations tomorrow may bring? What we consider to be the wildest fiction today could turn out to be tame reality in thedecades and centuries to come. Keeping an open mind to the seemingly impossible is what continually expands the frontiers of knowledge and discovery.While my restless mind conjured up elaborate alien worlds and unfathomable cosmic technologies in my latest reverie, I realize how little we truly understand about this vast universe surrounding us. Our knowledge is but a drop in the ocean compared to the mysteries still left to be unraveled. But that ultimate uncertainty and sense of wonderment is what keeps driving humanity to explore, question, and push the boundaries of our perception.As my eyelids grew heavy from an all-nighter of vivid cosmic daydreaming, the last whimsical thought I remember before succumbing to sleep's embrace was: What if there's another universe out there entirely parallel to our own, filled with duplicates of every person and civilization? A vast multiverse of infinite realities coexisting across a baffling higher-dimensional expanse?Perhaps in another universe, a different version of me is writing down his own celestial reveries and wildest dreams. Or maybe the latest realms of my subconscious imagination have revealed glimpses of something startling yet to be discoveredabout this endlessly fascinating cosmos of ours. Either way, I can't wait to find out more and to keep exploring the depths of reality and fantasy alike.篇3The Cosmic DreamweaverI can still vividly recall the night everything changed – the night I met the Cosmic Dreamweaver. It was a sultry summer evening, the kind where the thick air seems to wrap around you like a stifling blanket. I had retreated to the solitude of my backyard, seeking refuge from the oppressive heat trapped inside the house. As I flopped onto the weathered wooden bench, I gazed up at the inky black canvas of the night sky, mesmerized by the twinkling diamonds strewn across its expanse.Suddenly, something caught my eye – a shooting star streaked across the heavens, burning brighter than any I'd ever witnessed before. But this was no ordinary meteor. As I watched, transfixed, the blazing streak shifted course, looping and pirouetting through the stars in mesmerizing patterns. My eyes must have been playing tricks on me, I reasoned, rubbing themfuriously. When I opened them again, the fiery trail had ceased its celestial dance and was hurtling directly towards me!I threw my arms up in a feeble attempt at self-defense, bracing for catastrophic impact. But instead of a searing demise, I felt an odd tingling spreading from the top of my head down to the soles of my feet. The tingling intensified until my entire being seemed to dissolve into a blinding kaleidoscope of color and sound. I slipped into a state of transfixed delirium, my consciousness unraveling and reweaving itself into strange new patterns.When my senses sluggishly rejoined, I found myself no longer in the confines of my backyard, but adrift in a realm of breathtaking alien splendor. Colossal spirals of multihued energy undulated all around me, emanating waves of pure harmonic resonance that reverberated through my very soul. Gargantuan celestial structures, their surfaces sculpted into fractal cities of hypnotic complexity, materialized and dematerialized in the cosmic expanse. I felt utterly minuscule, a solitary speck of near-nothingness amid the grandeur of this ineffable wonderland.As I spun about, gawking in open-mouthed awe, something drifted into my field of perception – an entity that defiedcomprehension, yet filled me with a strange sense of tranquility. It was an ever-shifting kaleidoscope of light and form, its visage cycling through a mesmerizing array of avatars: one moment an ascended astral being, brimming with arcane power; the next, a humble woodlands creature; a living fractal; a swirling nebula birth new worlds..."Do not be afraid, Earthchild," a warm voice reverberated through my psyche. "I am the Cosmic Dreamweaver. I have summoned you here to share with you the ultimate gift.""G-gift?" I stammered, utterly confounded. "What gift? Where... where is 'here?'"The entity's avatar shimmered and contorted, resolving into a wizened humanoid form that nonetheless thrummed with latent cosmic power."This place exists beyond the boundaries of your physical universe, in a realm of pure potentiality woven into the fabric of existence itself. And my gift to you is the ability to shape and reshape reality to your wildest imaginings."With an outstretched hand, the Cosmic Dreamweaver released an incandescent torrent of pure creative energy that engulfed my being. I felt my mind expanding immeasurably,blazing new neural pathways flaring open to accept the incomprehensible secrets of this strange place. Images, insights, and alien epiphanies flooded my consciousness in a deluge of pure inspiration."You now possess the power to reach into the dreamscapes of potential and pluck forth entire worlds from your thoughts," intoned the Dreamweaver. "Shape them through force of will and concentration alone into any form you can envisage. Let your imagination be your guide, and the only boundaries will be those you conceive for yourself."The being's avatar contracted into a shimmering sphere that hovered before me, dreamlike whispers echoing fromall sides: "Embrace your innermost fancies and yearnings... All is possible in the realm of dreamweavers..."With those parting words, the strange sphere imploded in a silent blossoming of spectral light. When the brilliance cleared, I found myself once again beneath the familiar night sky, on the worn bench where I'd been stargazing. Had it all been an fever dream hallucination brought on by the heat? I started to convince myself of that logical conclusion when a tinyalpha-numericticker tape began unfurlingitself from my mind'seye. It crystallized into a coherent stream of code – new neural programming granting me impossible abilities.I let the alien algorithms and fractal ciphers wash over me, integrating the incredible power into the core of my being. Taking a deep, centering breath, I focused my newly opened mindand willed my consciousness to expand outward, perceiving and interacting with the Potentiality Matrix underlying all of existence.Suddenly, the backyard scene distorted and fragmented into coruscating wings of light and shadow. A kaleidoscopic vortex spiraled into being, drawing me inward onto a vast formless expanse awash in the primal waters of creation. Here, in the nexus of conceptual potentials, my abilities as a Dreamweaver blossomed into full actualization.I imagined a twisting spire of glimmering crystal, and it effloresced before me. I envisioned floating isles crafted from woven condensed sunlight, and they shimmered into ethereal reality. Great migrating beasts with translucent bodies and metallic carapaces shimmered into existence, buoyed by levitating electrocycles that supercharged the prism-clouds that served as their propulsion...Over what seemed an eternity compressed into a singularity of subjective time, I unleashed my unbridled musings into evermore baroque expressions of pure, distilled dream-fancy. Cities crafted from living infiniglass, their axiro-latticed ziggurats straddling interdimensional continua. Vast sparkling rivers of thought that carried philosophies and mindstreams between shimmershrine arcologies. Fractal-generated megafauna forming symbiological relationships with hyper-sentient botanical canopies and roiling biomechondrial seas...At long last, my manic creative fervor found itself sated...at least for the moment. With an oblique sense of closure, I initiated a return vector to my own humble plane of existence, where the trappings of terrestrial familiarity gradually coalesced around me once again. But everything now seemed just the slightest bit...skewed, as if the molecules of reality itself had been subtly rearranged by the force of my re-imaginings.As I surveyed my surroundings anew through dreamweaver's eyes, I was struck by the boundless possibilities now laid before me. No longer was I bound by the strictures of mundane physics or constraints of preconceived possibility. Every wish, whimsy and unbridled imagining was now within my grasp to actualize through sheer creative force of will. The entirecosmos was my lumenoietic canvas to rearrange and recompose in whatever ever-shifting patterns I could envision.With my first foray into the Metaversal Dreamrealms now complete, I felt a curious synergy of potential and uncertainty well up within me. Where would my burgeoning abilities as a Dreamweaver lead? What breathtaking or terrifying new emanations would I call forth into substantive existence from the morphaevic aethers? Perhaps it was best I didn't know just yet what audacious, improbable, fantastic, and wondrous feats of reconstructive meta-genesis awaited...。

a r X i v :g r -q c /0411082v 1 16 N o v 2004Laser Ranging to the Moon,Mars and BeyondSlava G.Turyshev,James G.Williams,Michael Shao,John D.AndersonJet Propulsion Laboratory,California Institute of Technology,4800Oak Grove Drive,Pasadena,CA 91109,USAKenneth L.Nordtvedt,Jr.Northwest Analysis,118Sourdough Ridge Road,Bozeman,MT 59715USA Thomas W.Murphy,Jr.Physics Department,University of California,San Diego 9500Gilman Dr.,La Jolla,CA 92093USA Abstract Current and future optical technologies will aid exploration of the Moon and Mars while advancing fundamental physics research in the solar system.Technologies and possible improvements in the laser-enabled tests of various physical phenomena are considered along with a space architecture that could be the cornerstone for robotic and human exploration of the solar system.In particular,accurate ranging to the Moon and Mars would not only lead to construction of a new space communication infrastructure enabling an improved navigational accuracy,but will also provide a significant improvement in several tests of gravitational theory:the equivalence principle,geodetic precession,PPN parameters βand γ,and possible variation of the gravitational constant G .Other tests would become possible with an optical architecture that would allow proceeding from meter to centimeter to millimeter range accuracies on interplanetary distances.This paper discusses the current state and the future improvements in the tests of relativistic gravity with Lunar Laser Ranging (LLR).We also consider precision gravitational tests with the future laser rangingto Mars and discuss optical design of the proposed Laser Astrometric Test of Relativity (LATOR)mission.We emphasize that already existing capabilities can offer significant improvements not only in the tests of fundamental physics,but may also establish the infrastructure for space exploration in the near future.Looking to future exploration,what characteristics are desired for the next generation of ranging devices,what is the optimal architecture that would benefit both space exploration and fundamental physics,and what fundamental questions can be investigated?We try to answer these questions.1IntroductionThe recent progress in fundamental physics research was enabled by significant advancements in many technological areas with one of the examples being the continuing development of the NASA Deep Space Network –critical infrastructure for precision navigation and communication in space.A demonstration of such a progress is the recent Cassini solar conjunction experiment[8,6]that was possible only because of the use of Ka-band(∼33.4GHz)spacecraft radio-tracking capabilities.The experiment was part of the ancillary science program–a by-product of this new radio-tracking technology.Becasue of a much higher data rate transmission and, thus,larger data volume delivered from large distances the higher communication frequency was a very important mission capability.The higher frequencies are also less affected by the dispersion in the solar plasma,thus allowing a more extensive coverage,when depp space navigation is concerned.There is still a possibility of moving to even higher radio-frequencies, say to∼60GHz,however,this would put us closer to the limit that the Earth’s atmosphere imposes on signal transmission.Beyond these frequencies radio communication with distant spacecraft will be inefficient.The next step is switching to optical communication.Lasers—with their spatial coherence,narrow spectral emission,high power,and well-defined spatial modes—are highly useful for many space applications.While in free-space,optical laser communication(lasercomm)would have an advantage as opposed to the conventional radio-communication sercomm would provide not only significantly higher data rates(on the order of a few Gbps),it would also allow a more precise navigation and attitude control.The latter is of great importance for manned missions in accord the“Moon,Mars and Beyond”Space Exploration Initiative.In fact,precision navigation,attitude control,landing,resource location, 3-dimensional imaging,surface scanning,formationflying and many other areas are thought only in terms of laser-enabled technologies.Here we investigate how a near-future free-space optical communication architecture might benefit progress in gravitational and fundamental physics experiments performed in the solar system.This paper focuses on current and future optical technologies and methods that will advance fundamental physics research in the context of solar system exploration.There are many activities that focused on the design on an optical transceiver system which will work at the distance comparable to that between the Earth and Mars,and test it on the Moon.This paper summarizes required capabilities for such a system.In particular,we discuss how accurate laser ranging to the neighboring celestial bodies,the Moon and Mars,would not only lead to construction of a new space communication infrastructure with much improved navigational accuracy,it will also provide a significant improvement in several tests of gravitational theory. Looking to future exploration,we address the characteristics that are desired for the next generation of ranging devices;we will focus on optimal architecture that would benefit both space exploration and fundamental physics,and discuss the questions of critical importance that can be investigated.This paper is organized as follows:Section2discusses the current state and future per-formance expected with the LLR technology.Section3addresses the possibility of improving tests of gravitational theories with laser ranging to Mars.Section4addresses the next logical step—interplanetary laser ranging.We discuss the mission proposal for the Laser Astrometric Test of Relativity(LATOR).We present a design for its optical receiver system.Section5 addresses a proposal for new multi-purpose space architecture based on optical communica-tion.We present a preliminary design and discuss implications of this new proposal for tests of fundamental physics.We close with a summary and recommendations.2LLR Contribution to Fundamental PhysicsDuring more than35years of its existence lunar laser ranging has become a critical technique available for precision tests of gravitational theory.The20th century progress in three seem-ingly unrelated areas of human exploration–quantum optics,astronomy,and human spaceexploration,led to the construction of this unique interplanetary instrument to conduct very precise tests of fundamental physics.In this section we will discuss the current state in LLR tests of relativistic gravity and explore what could be possible in the near future.2.1Motivation for Precision Tests of GravityThe nature of gravity is fundamental to our understanding of the structure and evolution of the universe.This importance motivates various precision tests of gravity both in laboratories and in space.Most of the experimental underpinning for theoretical gravitation has come from experiments conducted in the solar system.Einstein’s general theory of relativity(GR)began its empirical success in1915by explaining the anomalous perihelion precession of Mercury’s orbit,using no adjustable theoretical parameters.Eddington’s observations of the gravitational deflection of light during a solar eclipse in1919confirmed the doubling of the deflection angles predicted by GR as compared to Newtonian and Equivalence Principle(EP)arguments.Follow-ing these beginnings,the general theory of relativity has been verified at ever-higher accuracy. Thus,microwave ranging to the Viking landers on Mars yielded an accuracy of∼0.2%from the gravitational time-delay tests of GR[48,44,49,50].Recent spacecraft and planetary mi-crowave radar observations reached an accuracy of∼0.15%[4,5].The astrometric observations of the deflection of quasar positions with respect to the Sun performed with Very-Long Base-line Interferometry(VLBI)improved the accuracy of the tests of gravity to∼0.045%[45,51]. Lunar Laser Ranging(LLR),the continuing legacy of the Apollo program,has provided ver-ification of GR improving an accuracy to∼0.011%via precision measurements of the lunar orbit[62,63,30,31,32,35,24,36,4,68].The recent time-delay experiments with the Cassini spacecraft at a solar conjunction have tested gravity to a remarkable accuracy of0.0023%[8] in measuring deflection of microwaves by solar gravity.Thus,almost ninety years after general relativity was born,Einstein’s theory has survived every test.This rare longevity and the absence of any adjustable parameters,does not mean that this theory is absolutely correct,but it serves to motivate more sensitive tests searching for its expected violation.The solar conjunction experiments with the Cassini spacecraft have dramatically improved the accuracy in the solar system tests of GR[8].The reported accuracy of2.3×10−5in measuring the Eddington parameterγ,opens a new realm for gravitational tests,especially those motivated by the on-going progress in scalar-tensor theories of gravity.1 In particular,scalar-tensor extensions of gravity that are consistent with present cosmological models[15,16,17,18,19,20,39]predict deviations of this parameter from its GR value of unity at levels of10−5to10−7.Furthermore,the continuing inability to unify gravity with the other forces indicates that GR should be violated at some level.The Cassini result together with these theoretical predictions motivate new searches for possible GR violations;they also provide a robust theoretical paradigm and constructive guidance for experiments that would push beyond the present experimental accuracy for parameterized post-Newtonian(PPN)parameters(for details on the PPN formalism see[60]).Thus,in addition to experiments that probe the GR prediction for the curvature of the gravityfield(given by parameterγ),any experiment pushingthe accuracy in measuring the degree of non-linearity of gravity superposition(given by anotherEddington parameterβ)will also be of great interest.This is a powerful motive for tests ofgravitational physics phenomena at improved accuracies.Analyses of laser ranges to the Moon have provided increasingly stringent limits on anyviolation of the Equivalence Principle(EP);they also enabled very accurate measurements fora number of relativistic gravity parameters.2.2LLR History and Scientific BackgroundLLR has a distinguished history[24,9]dating back to the placement of a retroreflector array onthe lunar surface by the Apollo11astronauts.Additional reflectors were left by the Apollo14and Apollo15astronauts,and two French-built reflector arrays were placed on the Moon by theSoviet Luna17and Luna21missions.Figure1shows the weighted RMS residual for each year.Early accuracies using the McDonald Observatory’s2.7m telescope hovered around25cm. Equipment improvements decreased the ranging uncertainty to∼15cm later in the1970s.In1985the2.7m ranging system was replaced with the McDonald Laser Ranging System(MLRS).In the1980s ranges were also received from Haleakala Observatory on the island of Maui in theHawaiian chain and the Observatoire de la Cote d’Azur(OCA)in France.Haleakala ceasedoperations in1990.A sequence of technical improvements decreased the range uncertainty tothe current∼2cm.The2.7m telescope had a greater light gathering capability than thenewer smaller aperture systems,but the newer systemsfired more frequently and had a muchimproved range accuracy.The new systems do not distinguish returning photons against thebright background near full Moon,which the2.7m telescope could do,though there are somemodern eclipse observations.The lasers currently used in the ranging operate at10Hz,with a pulse width of about200 psec;each pulse contains∼1018photons.Under favorable observing conditions a single reflectedphoton is detected once every few seconds.For data processing,the ranges represented by thereturned photons are statistically combined into normal points,each normal point comprisingup to∼100photons.There are15553normal points are collected until March2004.Themeasured round-trip travel times∆t are two way,but in this paper equivalent ranges in lengthunits are c∆t/2.The conversion between time and length(for distance,residuals,and dataaccuracy)uses1nsec=15cm.The ranges of the early1970s had accuracies of approximately25cm.By1976the accuracies of the ranges had improved to about15cm.Accuracies improvedfurther in the mid-1980s;by1987they were4cm,and the present accuracies are∼2cm.One immediate result of lunar ranging was the great improvement in the accuracy of the lunarephemeris[62]and lunar science[67].LLR measures the range from an observatory on the Earth to a retroreflector on the Moon. For the Earth and Moon orbiting the Sun,the scale of relativistic effects is set by the ratio(GM/rc2)≃v2/c2∼10−8.The center-to-center distance of the Moon from the Earth,with mean value385,000km,is variable due to such things as eccentricity,the attraction of the Sun,planets,and the Earth’s bulge,and relativistic corrections.In addition to the lunar orbit,therange from an observatory on the Earth to a retroreflector on the Moon depends on the positionin space of the ranging observatory and the targeted lunar retroreflector.Thus,orientation ofthe rotation axes and the rotation angles of both bodies are important with tidal distortions,plate motion,and relativistic transformations also coming into play.To extract the gravitationalphysics information of interest it is necessary to accurately model a variety of effects[68].For a general review of LLR see[24].A comprehensive paper on tests of gravitationalphysics is[62].A recent test of the EP is in[4]and other GR tests are in[64].An overviewFigure1:Historical accuracy of LLR data from1970to2004.of the LLR gravitational physics tests is given by Nordtvedt[37].Reviews of various tests of relativity,including the contribution by LLR,are given in[58,60].Our recent paper describes the model improvements needed to achieve mm-level accuracy for LLR[66].The most recent LLR results are given in[68].2.3Tests of Relativistic Gravity with LLRLLR offers very accurate laser ranging(weighted rms currently∼2cm or∼5×10−11in frac-tional accuracy)to retroreflectors on the Moon.Analysis of these very precise data contributes to many areas of fundamental and gravitational physics.Thus,these high-precision studies of the Earth-Moon-Sun system provide the most sensitive tests of several key properties of weak-field gravity,including Einstein’s Strong Equivalence Principle(SEP)on which general relativity rests(in fact,LLR is the only current test of the SEP).LLR data yielded the strongest limits to date on variability of the gravitational constant(the way gravity is affected by the expansion of the universe),and the best measurement of the de Sitter precession rate.In this Section we discuss these tests in more details.2.3.1Tests of the Equivalence PrincipleThe Equivalence Principle,the exact correspondence of gravitational and inertial masses,is a central assumption of general relativity and a unique feature of gravitation.EP tests can therefore be viewed in two contexts:tests of the foundations of general relativity,or as searches for new physics.As emphasized by Damour[12,13],almost all extensions to the standard modelof particle physics(with best known extension offered by string theory)generically predict newforces that would show up as apparent violations of the EP.The weak form the EP(the WEP)states that the gravitational properties of strong and electro-weak interactions obey the EP.In this case the relevant test-body differences are their fractional nuclear-binding differences,their neutron-to-proton ratios,their atomic charges,etc. General relativity,as well as other metric theories of gravity,predict that the WEP is exact. However,extensions of the Standard Model of Particle Physics that contain new macroscopic-range quantumfields predict quantum exchange forces that will generically violate the WEP because they couple to generalized‘charges’rather than to mass/energy as does gravity[17,18]. WEP tests can be conducted with laboratory or astronomical bodies,because the relevant differences are in the test-body compositions.Easily the most precise tests of the EP are made by simply comparing the free fall accelerations,a1and a2,of different test bodies.For the case when the self-gravity of the test bodies is negligible and for a uniform external gravityfield, with the bodies at the same distance from the source of the gravity,the expression for the Equivalence Principle takes the most elegant form:∆a= M G M I 2(1)(a1+a2)where M G and M I represent gravitational and inertial masses of each body.The sensitivity of the EP test is determined by the precision of the differential acceleration measurement divided by the degree to which the test bodies differ(position).The strong form of the EP(the SEP)extends the principle to cover the gravitational properties of gravitational energy itself.In other words it is an assumption about the way that gravity begets gravity,i.e.about the non-linear property of gravitation.Although general relativity assumes that the SEP is exact,alternate metric theories of gravity such as those involving scalarfields,and other extensions of gravity theory,typically violate the SEP[30,31, 32,35].For the SEP case,the relevant test body differences are the fractional contributions to their masses by gravitational self-energy.Because of the extreme weakness of gravity,SEP test bodies that differ significantly must have astronomical sizes.Currently the Earth-Moon-Sun system provides the best arena for testing the SEP.The development of the parameterized post-Newtonian formalism[31,56,57],allows one to describe within the common framework the motion of celestial bodies in external gravitational fields within a wide class of metric theories of gravity.Over the last35years,the PPN formalism has become a useful framework for testing the SEP for extended bodies.In that formalism,the ratio of passive gravitational to inertial mass to thefirst order is given by[30,31]:M GMc2 ,(2) whereηis the SEP violation parameter(discussed below),M is the mass of a body and E is its gravitational binding or self-energy:E2Mc2 V B d3x d3yρB(x)ρB(y)EMc2 E=−4.64×10−10andwhere the subscripts E and m denote the Earth and Moon,respectively.The relatively small size bodies used in the laboratory experiments possess a negligible amount of gravitational self-energy and therefore such experiments indicate nothing about the equality of gravitational self-energy contributions to the inertial and passive gravitational masses of the bodies [30].TotesttheSEP onemustutilize planet-sizedextendedbodiesinwhichcase theratioEq.(3)is considerably higher.Dynamics of the three-body Sun-Earth-Moon system in the solar system barycentric inertial frame was used to search for the effect of a possible violation of the Equivalence Principle.In this frame,the quasi-Newtonian acceleration of the Moon (m )with respect to the Earth (E ),a =a m −a E ,is calculated to be:a =−µ∗rM I m µS r SEr 3Sm + M G M I m µS r SEr 3+µS r SEr 3Sm +η E Mc 2 m µS r SEMc 2 E − E n 2−(n −n ′)2n ′2a ′cos[(n −n ′)t +D 0].(8)Here,n denotes the sidereal mean motion of the Moon around the Earth,n ′the sidereal mean motion of the Earth around the Sun,and a ′denotes the radius of the orbit of the Earth around the Sun (assumed circular).The argument D =(n −n ′)t +D 0with near synodic period is the mean longitude of the Moon minus the mean longitude of the Sun and is zero at new Moon.(For a more precise derivation of the lunar range perturbation due to the SEP violation acceleration term in Eq.(6)consult [62].)Any anomalous radial perturbation will be proportional to cos D .Expressed in terms ofη,the radial perturbation in Eq.(8)isδr∼13ηcos D meters [38,21,22].This effect,generalized to all similar three body situations,the“SEP-polarization effect.”LLR investigates the SEP by looking for a displacement of the lunar orbit along the direction to the Sun.The equivalence principle can be split into two parts:the weak equivalence principle tests the sensitivity to composition and the strong equivalence principle checks the dependence on mass.There are laboratory investigations of the weak equivalence principle(at University of Washington)which are about as accurate as LLR[7,1].LLR is the dominant test of the strong equivalence principle.The most accurate test of the SEP violation effect is presently provided by LLR[61,48,23],and also in[24,62,63,4].Recent analysis of LLR data test the EP of∆(M G/M I)EP=(−1.0±1.4)×10−13[68].This result corresponds to a test of the SEP of∆(M G/M I)SEP=(−2.0±2.0)×10−13with the SEP violation parameter η=4β−γ−3found to beη=(4.4±4.5)×10−ing the recent Cassini result for the PPN parameterγ,PPN parameterβis determined at the level ofβ−1=(1.2±1.1)×10−4.2.3.2Other Tests of Gravity with LLRLLR data yielded the strongest limits to date on variability of the gravitational constant(the way gravity is affected by the expansion of the universe),the best measurement of the de Sitter precession rate,and is relied upon to generate accurate astronomical ephemerides.The possibility of a time variation of the gravitational constant,G,wasfirst considered by Dirac in1938on the basis of his large number hypothesis,and later developed by Brans and Dicke in their theory of gravitation(for more details consult[59,60]).Variation might be related to the expansion of the Universe,in which case˙G/G=σH0,where H0is the Hubble constant, andσis a dimensionless parameter whose value depends on both the gravitational constant and the cosmological model considered.Revival of interest in Brans-Dicke-like theories,with a variable G,was partially motivated by the appearance of superstring theories where G is considered to be a dynamical quantity[26].Two limits on a change of G come from LLR and planetary ranging.This is the second most important gravitational physics result that LLR provides.GR does not predict a changing G,but some other theories do,thus testing for this effect is important.The current LLR ˙G/G=(4±9)×10−13yr−1is the most accurate limit published[68].The˙G/G uncertaintyis83times smaller than the inverse age of the universe,t0=13.4Gyr with the value for Hubble constant H0=72km/sec/Mpc from the WMAP data[52].The uncertainty for˙G/G is improving rapidly because its sensitivity depends on the square of the data span.This fact puts LLR,with its more then35years of history,in a clear advantage as opposed to other experiments.LLR has also provided the only accurate determination of the geodetic precession.Ref.[68]reports a test of geodetic precession,which expressed as a relative deviation from GR,is K gp=−0.0019±0.0064.The GP-B satellite should provide improved accuracy over this value, if that mission is successfully completed.LLR also has the capability of determining PPNβandγdirectly from the point-mass orbit perturbations.A future possibility is detection of the solar J2from LLR data combined with the planetary ranging data.Also possible are dark matter tests,looking for any departure from the inverse square law of gravity,and checking for a variation of the speed of light.The accurate LLR data has been able to quickly eliminate several suggested alterations of physical laws.The precisely measured lunar motion is a reality that any proposed laws of attraction and motion must satisfy.The above investigations are important to gravitational physics.The future LLR data will improve the above investigations.Thus,future LLR data of current accuracy would con-tinue to shrink the uncertainty of˙G because of the quadratic dependence on data span.The equivalence principle results would improve more slowly.To make a big improvement in the equivalence principle uncertainty requires improved range accuracy,and that is the motivation for constructing the APOLLO ranging facility in New Mexico.2.4Future LLR Data and APOLLO facilityIt is essential that acquisition of the new LLR data will continue in the future.Accuracies∼2cm are now achieved,and further very useful improvement is expected.Inclusion of improved data into LLR analyses would allow a correspondingly more precise determination of the gravitational physics parameters under study.LLR has remained a viable experiment with fresh results over35years because the data accuracies have improved by an order of magnitude(see Figure1).There are prospects for future LLR station that would provide another order of magnitude improvement.The Apache Point Observatory Lunar Laser-ranging Operation(APOLLO)is a new LLR effort designed to achieve mm range precision and corresponding order-of-magnitude gains in measurements of fundamental physics parameters.For thefirst time in the LLR history,using a3.5m telescope the APOLLO facility will push LLR into a new regime of multiple photon returns with each pulse,enabling millimeter range precision to be achieved[29,66].The anticipated mm-level range accuracy,expected from APOLLO,has a potential to test the EP with a sensitivity approaching10−14.This accuracy would yield sensitivity for parameterβat the level of∼5×10−5and measurements of the relative change in the gravitational constant,˙G/G, would be∼0.1%the inverse age of the universe.The overwhelming advantage APOLLO has over current LLR operations is a3.5m astro-nomical quality telescope at a good site.The site in southern New Mexico offers high altitude (2780m)and very good atmospheric“seeing”and image quality,with a median image resolu-tion of1.1arcseconds.Both the image sharpness and large aperture conspire to deliver more photons onto the lunar retroreflector and receive more of the photons returning from the re-flectors,pared to current operations that receive,on average,fewer than0.01 photons per pulse,APOLLO should be well into the multi-photon regime,with perhaps5–10 return photons per pulse.With this signal rate,APOLLO will be efficient atfinding and track-ing the lunar return,yielding hundreds of times more photons in an observation than current√operations deliver.In addition to the significant reduction in statistical error(useful).These new reflectors on the Moon(and later on Mars)can offer significant navigational accuracy for many space vehicles on their approach to the lunar surface or during theirflight around the Moon,but they also will contribute significantly to fundamental physics research.The future of lunar ranging might take two forms,namely passive retroreflectors and active transponders.The advantages of new installations of passive retroreflector arrays are their long life and simplicity.The disadvantages are the weak returned signal and the spread of the reflected pulse arising from lunar librations(apparent changes in orientation of up to10 degrees).Insofar as the photon timing error budget is dominated by the libration-induced pulse spread—as is the case in modern lunar ranging—the laser and timing system parameters do√not influence the net measurement uncertainty,which simply scales as1/3Laser Ranging to MarsThere are three different experiments that can be done with accurate ranges to Mars:a test of the SEP(similar to LLR),a solar conjunction experiment measuring the deflection of light in the solar gravity,similar to the Cassini experiment,and a search for temporal variation in the gravitational constant G.The Earth-Mars-Sun-Jupiter system allows for a sensitive test of the SEP which is qualitatively different from that provided by LLR[3].Furthermore,the outcome of these ranging experiments has the potential to improve the values of the two relativistic parameters—a combination of PPN parametersη(via test of SEP)and a direct observation of the PPN parameterγ(via Shapiro time delay or solar conjunction experiments).(This is quite different compared to LLR,as the small variation of Shapiro time delay prohibits very accurate independent determination of the parameterγ).The Earth-Mars range would also provide for a very accurate test of˙G/G.This section qualitatively addresses the near-term possibility of laser ranging to Mars and addresses the above three effects.3.1Planetary Test of the SEP with Ranging to MarsEarth-Mars ranging data can provide a useful estimate of the SEP parameterηgiven by Eq.(7). It was demonstrated in[3]that if future Mars missions provide ranging measurements with an accuracy ofσcentimeters,after ten years of ranging the expected accuracy for the SEP parameterηmay be of orderσ×10−6.These ranging measurements will also provide the most accurate determination of the mass of Jupiter,independent of the SEP effect test.It has been observed previously that a measurement of the Sun’s gravitational to inertial mass ratio can be performed using the Sun-Jupiter-Mars or Sun-Jupiter-Earth system[33,47,3]. The question we would like to answer here is how accurately can we do the SEP test given the accurate ranging to Mars?We emphasize that the Sun-Mars-Earth-Jupiter system,though governed basically by the same equations of motion as Sun-Earth-Moon system,is significantly different physically.For a given value of SEP parameterηthe polarization effects on the Earth and Mars orbits are almost two orders of magnitude larger than on the lunar orbit.Below we examine the SEP effect on the Earth-Mars range,which has been measured as part of the Mariner9and Viking missions with ranging accuracy∼7m[48,44,41,43].The main motivation for our analysis is the near-future Mars missions that should yield ranging data, accurate to∼1cm.This accuracy would bring additional capabilities for the precision tests of fundamental and gravitational physics.3.1.1Analytical Background for a Planetary SEP TestThe dynamics of the four-body Sun-Mars-Earth-Jupiter system in the Solar system barycentric inertial frame were considered.The quasi-Newtonian acceleration of the Earth(E)with respect to the Sun(S),a SE=a E−a S,is straightforwardly calculated to be:a SE=−µ∗SE·r SE MI Eb=M,Jµb r bS r3bE + M G M I E b=M,Jµb r bS。

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