The Three-Body Continuum Coulomb Problem and the 3$alpha$ Structure of $^{12}$C

Three-body Problem1.Loyalty & DefectionYe Wenjie's father was driven to death during the _____ ______ (文革). She herself was exiled to a deserted observatory.By chance she ____ _____ ____(提出，想出) an idea to communicate with aliens - ____ the sun ___(把......用作) a giant signal emitter.___ october 21st, 1979, Ye _____ (收到) a message which said“Don't reply.” Four light years away,in the Centaurus, there were 3 suns and one earth.____ _____(由于) the three suns moves irregularly, the civilization on that earth____ ______(被毁灭)many many times. Their doom was no others but annihilation.____ ______ ___(为了) avoid the fatal destiny, the aliens were trying to find _____ (另一个) earth to live on.Just then they got the message from our Earth. They dispatched high-tech proton named “智子” to the earth. It could ____ _____(不仅) send all the overheard information back to “三体”____ ____(而且) emit false figures to block the ____________________________ (科技发展) on the Earth.2.Religion & Belief___________ (既然) we know 三体人's plot. ____________(一些人) ____ (创造) their own religion to welcome it. ______(另一些人)wanted 三体人to conquer the Earth. Still most people called for independence.But what should we do? Since the development was blocked and we are monitored by 智子，How could we ______(保护) our home Earth?After ______(讨论), we came up with a plan. We _____(选择) four people. They can use all resources______ (不用) telling others _________(是什么计划).3.The law of Dark ForestThe universe is just like a dark forest. _________ __ (各种各样的) civilisation are hunters________(在森林里等待着) like ghosts.They grope secretly without _______ (发出任何噪音). Because they know there are other hunters hiding in the forest.If he finds other living things, no matter it is a hunter or an angel or a devil, _________(唯一的事) they will do is: Shoot!! To destroy any threats, to kill all other looters.Because the resource in the universe is limited but human's greed never stops.4. The Chain of SuspicionOne kind of civilisation cannot tell _______(是否) the other civilisation is good or evil.One kind of civilisation cannot tell______(是否) they will be attacked by the other civilisation or not.Because every civilisation may experience science and technology burst, No body knows whether a seemingly weak civilisation will become a threat.One of the four candidates was president in a country. He made more than 2000 tons of nuclear weapons. unluckily, three people failed.Only a Chinese called 罗辑left. 三体人tried many times to kill him. Why?Many years passed, We created enormous space warships.Would we win?5.The Universal WarWe waited and waited...but only found a drop of water.However，it was the drop of water that destroyed the whole space warship! Within a very short time!! Without sweat!!!That was the first universal war of the last day. 三体's high-tech let us know the ______ (真相) of the universe_____________(第一次). We just like frightened children shaking in the darkness. We had thought we were adults, actually we were toddlers. We had thought we knew the secret to exist, actually we even had no right to compete!!We paid great loss for our arrogance.At the same time, 罗辑worked out the secret of “the chain of suspicion”and “the law of dark forest”.In the whole universe there are many kinds of super civilisations.For fear of science and technology burst, they would destroy whatever they find.If the position of 三体was given out, ______ the Earth ____ (两个都) 三体will be destroyed inevitably.罗辑got the signal emitter. 三体人had no other choices but retreat.We were saved by 罗辑！！！6.The DoomHappy time seldom lasts long.We were in peace with 三体人for_____ ______ (一段时间).Then they destroyed all the emitters on the Earth all of a sudden.So the Earth was conquered.All the people ____ ____ (send) to Australia. Then they destroyed all the farms and factories.We had nothing to eat ______(除了) other people!!!Only one space ship escaped. It was a giant emitter itself.With no hesitation, it emitted signal to the universe.Thus the position of 三体was given out.So in a very short time 三体were ______(毁灭) completely by higher civilisation.Now ________________(轮到我们了)...。

托福写作备考：议论文段落写作三部曲朗阁托福考试研究中心在英语学习过程中，大家能够尝试着用英文来谢谢日记其实是锻炼英语文笔的一个不错的方法，但是像托福雅思这种应试型的议论文写作中就与我们平常写的方式就有所不同了，通常这些文章都遵循introduction- body-conclusion（引言段-主体段-结论段）的“三步曲”，但我们平常的练笔就显得有些随意性了。

一般来说，一篇议论文必须包含至少两个主体段。

每个主体段都必须有明确的主题句“topic sentence”和若干支持句“supporting sentences”。

他们共同组成文章的理由段，对全文的论点提供理由支持。

下面我们就来分析一下这三部曲的各部分注意要点，相信一定会对你的托福议论文写作有一定的帮助的哦！我们首先要说的是Body（主体）段落，这个部分的内容提供了论证观点的理由，是整个文章的主体，在评分中占有很大的比重。

例如一篇满分的雅思作文（9分）必须“presents a fully developed position in answer to the question with relevant, fully extended and well supported ideas”。

这里的“fully extended / well supported”，必须通过主体段来体现。

新托福的满分作文（5分）也要求“is well organized and well developed, using clearly appropriate explanations, exemplifications, and/or details”，同样必须通过主体段落发展来实现。

朗阁托福考试研究中心建议初学者在练习议论文写作时，必须遵循理由段发展的几个简单原则，这对迅速完成理由段、构建连贯和理由充分的议论文大有帮助。

这几个简单原则包括：1. Write a topic sentence for each paragraph you plan to write. Each topic sentenceshould relate to your thesis statement and introduce what the paragraph will be about.If you find that the topics you want to discuss do not support the thesis statement you have written, revise your thesis statement or reconsider your topic sentences.（每个主体段都必须有一个明确的主题句）2. Write ideas that support your topic sentences. The topic sentence for eachHobbies are important for many reasons. First, a hobby can be educational. Forexample, if the hobby is stamp collecting, the person can learn about the countries of the world and even some of their history. Second, engaging in a hobby can lead to meeting other people with the same interests. A person can also meet other people by going to the school. Third, a person's free time is being used in a positive way. The person has no time to be bored or get into mischief while engaged in the hobby.Finally, some hobbies can lead to a future job. A person who enjoys a hobby-related job is more satisfied with life.这段话的topic sentence很明显-“Hobbies are important for many reasons”，之后的支持句从三方面阐述hobby的重要性（first, second, third），但段中这句话"A person can also meet other people by going the school"与hobby重要的原因没有关系，因此削弱了整个段落的连贯性与统一性，应该被去掉。

《三体》英语书评：A Journey ThroughTime and SpaceIn the vast expanse of the universe, where the boundaries of science and imagination intersect, LiuCixin's "Three-Body Problem" stands as a monumental testament to the power of human creativity and curiosity. This groundbreaking science fiction novel, a winner of numerous awards and accolades, weaves a complex tapestry of ideas, ranging from astrophysics to philosophy, into a captivating narrative that takes readers on a thrillingride through the cosmos.The story begins with a mysterious signal received by Earth from a distant civilization, the Trisolaris. This signal heralds the beginning of a chain of events that upend our understanding of the universe and our placewithin it. The Trisolaris, facing extinction in their own star system, seek a new home and view Earth as a potential candidate. As the Trisolaris' technology and influence grow, so does the threat to humanity, leading to a race against time for Earth's scientists and politicians to find a wayto survive.The narrative is told through multiple perspectives, giving readers a rich and nuanced understanding of the characters and their动机. The scientific details are meticulously crafted, yet accessible to the lay reader, making the complex concepts of cosmology and quantum physics engaging and understandable. Liu's writing style is both powerful and poetic, evoking a sense of awe and wonder that is both exhilarating and thought-provoking.One of the most remarkable aspects of "Three-Body Problem" is its ability to blur the lines between science and fiction. Liu seamlessly integrates cutting-edge scientific theories and hypothetical scenarios into the narrative, creating a world that feels both real and fantastical. This blend of science and fiction not only enhances the story's credibility but also encourages readers to question their own understanding of the universe and the limits of human knowledge.The themes explored in "Three-Body Problem" are as vast and complex as the universe itself. The novel raises questions about the nature of intelligence, the role of technology in society, and the ethics of survival in theface of existential threats. Through these themes, Liu challenges readers to consider the biggest questions of our time: What is our purpose in the universe? How far shouldwe push the boundaries of science and technology? What are the costs of survival?The impact of "Three-Body Problem" extends beyond the pages of the book. It has sparked widespread interest in science fiction and astrophysics, inspiring a generation of readers to pursue further study in these fields. Thenovel's influence has also extended to the global stage,with its English translation winning numerous awards and recognition, further solidifying Liu's status as a leading figure in science fiction literature.In conclusion, "Three-Body Problem" is a remarkablefeat of literary and scientific genius. Liu Cixin'svisionary storytelling and profound insights into the human condition make this novel a must-read for anyone interested in science fiction, astrophysics, or the intersection of these fields with human thought and culture. "Three-Body Problem" is not just a story about survival in the universe; it is a story about the survival of the human spirit in theface of insurmountable challenges and the limitless possibilities of the human imagination.**《三体》英语书评：穿越时空的旅程**在宇宙的辽阔无垠中，科学与想象力的边界交汇，刘慈欣的《三体》作为人类创造力和好奇心的壮丽见证，屹立不倒。

创新学院剑桥大学定制课程解剖学课程考核1. The three basic body planes are [单选题] *transverse, horizontal and axialtransverse, sagittal and coronal(正确答案)coronal, sagittal and parasagittalcoronal, oblique and frontal2. Which of the following statements about bone dynamics is incorrect? [单选题] *the epiphysis of long bones consists mainly of compact bone(正确答案)both the periosteum and endosteum possess osteogenic potentialtrabecular bone accounts for up to 20% of the total mass of the adult skeletonthe periosteum acts as an anchoring point for tendons and ligaments3. A young patient is brought in to A&E with reduced GCS after being hit in the temple with a cricket ball during a match. A CT head shows a fracture adjacent to the pterion. What pattern of haemorrhage would you expect to see? [单选题] *blood in a crescent-shape between the dura mater and the arachnoid mater of the meningesbiconvex region of blood between the dura mater and skull(正确答案)blood in the circle of Willis, fissures and cisternsblood in parenchyma and ventricles4. Which of the following statement is correct regarding function of the visual system [单选题] *homonymous hemianopia is caused by an optic chiasm lesionmonocular hemianopia is caused by an optic tract lesionbitemporal hemianopia is caused by an optic nerve or retinal lesion ophthalmoplegia is caused by a lesion to cranial nerve III, IV and/or VI(正确答案)5. Preganglionic sympathetic neurons release [单选题] *acetylcholine(正确答案)noradrenalinedopamineserotonin6. In Guillain-Barre syndrome, [单选题] *symptoms generally develop over many years, occuring in isolated attackssymptoms begin proximally and progress distallysymptoms are generally unilateralsymptoms classically start with pain, numbness and/or tingling(正确答案)7. Travelling away from the heart of an individual with normal anatomy, the aortic arch branches into the [单选题] *left subclavian artery, followed by the brachiocephalic trunk and then the left common carotid arteryleft common carotid artery, followed by the left subclavian artery and then the brachiocephalic trunkbrachiocephalic trunk, followed by the left subclavian artery and then the left common carotid arterybrachiocephalic trunk, followed by the left common carotid artery and then the left subclavian artery(正确答案)8. The nerve supply causing bronchoconstriction of the lungs comes from the [单选题] * vagus nerve(正确答案)thoracic sympathetic chainphrenic nerveazygous nerve9. The arterial supply of the different parts of the GI tract is [单选题] *foregut - superior mesenteric artery; midgut - inferior mesenteric artery; hindgut - coeliac trunkforegut - left colic artery; midgut - superior mesenteric artery; hindgut - inferior mesenteric arteryforegut - coeliac trunk; midgut - superior mesenteric artery; hindgut - inferior mesenteric artery(正确答案)foregut - superior mesenteric artery; midgut - inferior mesenteric artery; hindgut - ileocolic artery10. Which of the following is a correct statement about the testes [单选题] *the testicular artery is a direct branch of the aorta(正确答案)there is no sympathetic nerve supplyvenous drainage is via the internal iliac veinsthe broad ligament of the ovary is the female equivalent of the male gubernaculum11. The uterus [单选题] *is usually anteverted and retroflexedreceives a sympathetic nerve supply from S2-4receives an arterial supply from both uterine and ovarian arteries(正确答案)drains lymph to para-aortic nodes12. A healthy female undergoes puberty at 12 years with an oocyte pool of 300,000. Assuming linear reduction in the pool at the ages and rates described in the lecture, approximately how many oocytes would remain when she is 33 years and 6months? [单选题] *274,200171,00042,000(正确答案)4,20013. Vertebral levels of structures in the neck: ______ is at the level of C3, the ______ sits around C5-T1 and the ______ is at the level of C6 [单选题] *The thyroid gland, cricoid cartilage, larynxThe thyroid cartilage, pharynx, hyoid boneThe hyoid bone, thyroid gland, cricoid cartilage(正确答案)Sternocleidomastoid, oesophagus, parathyroid14. Bell's palsy is caused by the dysfunction of which nerve? [单选题] *phrenic nervecranial nerve VII(正确答案)cranial nerve Vvagus nerve15. Which vein in the cubital fossa is often used for venepuncture? [单选题] *antecubital vein (median cubital vein)(正确答案)axillary veincephalic veinsubclavian vein16. Which three muscles are located in the anterior compartment of the arm? [单选题] *triceps brachii, brachialis and coracobrachialistriceps brachiibiceps brachii, brachialis and coracobrachialis(正确答案)biceps brachii, brachioradialis and anconeus17. The boundaries of the carpal tunnel are the _____ and _____. It contains _____ and the _____. [单选题] *flexor retinaculum; deep carpal arch; nine tendons; median nerve(正确答案)flexor carpi ulnaris; pronator teres; three arteries; musculocutaneous nervepronator quadratus; flexor retinaculum; four nerves; radial arterypronator teres; pronator quadratus; nine tendons; median cubital vein18. A patient with no pre-existing condition or abnormality is involved in a major road traffic collision, during which the dashboard causes limb amputations at the left radio-carpal joint and the right mid-lower leg. How many complete bones does the patient have remaining? [单选题] *55151(正确答案)18915519. The structures passing posterior to the medial malleolus are the ______, the ______ and the ______. [单选题] *sciatic nerve; posterior tibial vein; posterior tibial arterypopliteal vein; tibial nerve; sciatic nerveposterior tibial artery; tibial nerve; tendons of tibialis posterior, flexor digitorum longus and flexor hallicus longus(正确答案)anterior tibial vein; fibular artery; tibial nerve20. Trendelenberg gait is the result of the ineffective action of which two muscles? [单选题] *gluteus maximus and tensor fascia lataobturator internus and quadratus femorisgluteus maximus and gluteus minimusgluteus minimus and gluteus medius(正确答案)21. What are the effects of weight loss on plasma concentrations of following three hormones? [单选题] *Weight loss lowers plasma insulin levels and increases plasma leptin and ghrelin levels. Weight loss lowers plasma insulin and ghrelin levels and increases plasma leptin levels. Weight loss lowers plasma insulin and leptin levels and increases plasma ghrelin levels.(正确答案)Weight loss lowers plasma levels of all three hormones.22. Which of the following active metabolites are generated by the colonic microbiota through fermentation? [单选题] *Short-chain fatty acids (SCFAs) and lipopolysaccharide (LPS).Short-chain fatty acids (SCFAs), indole, γ-aminobutyric acid (GABA) and lipopolysaccharide (LPS).(正确答案)Indole, γ-aminobutyric acid (GABA) and lipopolysaccharide (LPS).Short-chain fatty acids (SCFAs) and γ-aminobutyric acid (GABA).23. Which of the following populations of neurons inhibit food intake? [单选题] *AGRP-expressing neurons located in the hypothalamic arcuate nucleus (ARC).POMC-expressing neurons located in the in the paraventricular nucleus (PVN).AGRP-expressing neurons located in the nucleus of the solitary tract (NTS).POMC-expressing neurons located in the hypothalamic arcuate nucleus (ARC).(正确答案)24. Which of the following statements is not a characteristic of epicardial fat? [单选题] *Epicardial fat produces cytokines that modulates the function of the myocardium. Epicardial fat has the greatest rates of lipogenesis and fatty acid metabolism among visceral fat depots.Epicardial fat is vascularized by noncoronary arteries.(正确答案)Epicardial fat is located between the myocardium and the visceral layer of the pericardium.25. Which of the following statements regarding brown and beige adipocytes is false? [单选题] *Both cell types express UCP1 protein.Both cell types have multiple lipid droplets.They originate from distinct precursors during cell diffentiation.Both cell types produce heat through Ca2+ cycling via endoplasmic reticulum.(正确答案)26. A woman with BMI 33 and 1.70 cm height has 30% fat content. After losing weight, her new BMI becomes 28, and her fat content 25%. How much fat did she lose (chose the closest value in kg)? [单选题] *8.5 kg(正确答案)5.5 kg10 kg12 kg27. Please chose the organs that are the main source for the following secreted factors, in the order listed here: FGF21, irisin, leptin, GLP1. [单选题] *Fat, gut, liver, muscle.Mucle, liver, gut, fat.Gut, mucle, fat, liver.Liver, muscle, fat, gut.(正确答案)28. Which tissue/organ is major source of circulating microRNAs in the circulation? [单选题] *LiverFat(正确答案)MucleBone29. Which of the following statements related to the role of indoxyl sulfate in inter-organ communication is true? [单选题] *Indole is created in the gut, via the metabolism of valine by the gut microbiota.Indole is taken up by the kidney, where it is metabolized to indoxyl sulfate.Indoxyl sulfate signals in various tissues through the aryl hydrocarbon receptor (AHR).(正确答案)Indoxyl sulfate is ultimately excreted by the kidney through transporters located in the distal tubule epithelium.30. Where in the brain is the central clock located? [单选题] *In the hypothalamic suprachiasmatic nucleus (SCN).(正确答案)In the nucleus of the solitary tract (NTS).In the hypothalamic arcuate nucleus (ARC).In the paraventricular nucleus (PVN).31. Which of the following statements regarding the molecular organization of the circadian clock is false? [单选题] *The transcriptional-translational regulatory loops of the circadian clock are operating in most cells and control a large fraction of the mammalian genome.The transcriptional activators CLOCK and BMAL1 dimerize to stimulate the expression of many genes with E-box elements in their promoters.At night, REV-ERBα protein amounts are low, allowing Bmal1 transcription to take place.PERs and CRYs protein levels become high during the day.(正确答案)32. To minimize the effects of jet lag for eastward travel across six time zones, administration of melatonin is recommended at which time of the day? [单选题] *In the early morning hours at the arrival zone.In the early morning hours at departure zone.In the afternoon hours at the departure zone.(正确答案)At departure, irrespective of the time of the day.33. Which of the following changes is not a phisiological adaptation to pregnancy? [单选题] *Enhanced production of glucose by the liver.Increased circulating lipids.Hemodilution.Improved peripheral insulin sensitivity.(正确答案)34. Which of the following factors implicated in regulating β-cell adaptations during pregnancy acts in an autocrine manner? [单选题] *Prolactin.Serotonin.(正确答案)Kisspeptin.Urocortin.35. Which of the following hormones peaks at the end of the first trimester in human pregnancy? [单选题] *Human chorionic gonadotropin.(正确答案)Estrogen.Progesterone.Insulin.36. Which areas of the adult human brain do not contain neuronal stem cells? [单选题] *The striatum.The hypothalamic arcuate nucleus (ARC).(正确答案)The dentate gyrus of the hippocampus.The subventricular zone (SVZ).37. Which of the following cell types are intestinal stem cells? [单选题] *Paneth cells.Tuft cells.LGR5-positive crypt-base columnar cells (CBCs).(正确答案)Goblet cells.38. Which of the following characteristics define adult hematopoietic stem cells (HSC)? [单选题] *HSC reside in bone marrow, are multipotent, can differentiate into all mature blood cells and express markers such as c-Kit and CD34.(正确答案)HSC reside in bone marrow, are pluripotent, can differentiate into all mature blood cells and express markers such as c-Kit and CD34.HSC reside in bone marrow, are pluripotent, can differentiate into all mature blood cells and express markers such as OCT4 and SOX2.HSC reside in bone marrow, are multipotent, can differentiate into all mature blood cells and express markers such as OCT4 and SOX2.HSC reside in bone marrow, are multipotent, can differentiate into all mature blood cells and express markers such as OCT4 and SOX2.39. Which of the following statement regarding sex-related differences is false? [单选题] *Lipid storage capacity of visceral adipose tissue is higher in men.During the reproductive years, males have a higher blood pressure (BP) than females. Women show faster cognitive decline after diagnosis of mild cognitive impairment (MCI) or Alzheimer disease (AD) dementia.Morphine is a less effective analgesic in men.(正确答案)40. A study performed across 9 nations from the beginning of the current pandemic until June 21, 2020 found the following data: 77,652 men and 59,591 women died due to COVID-19 from an estimated population of 194,349,591 men and 201,715,364 women. What was the overall female to male mortality sex ratio? [单选题] *1.20.74(正确答案)0.891.35。

- 51 -①中国人民解放军海军第九七一医院　山东　青岛　266000双歧杆菌三联活菌联合美沙拉嗪治疗溃疡性结肠炎的效果 孙海源①　苑刚①　孙波①【摘要】　目的：以溃疡性结肠炎（UC）患者为研究对象，分析双歧杆菌三联活菌联合美沙拉嗪的治疗效果。

方法：选取2020年3月—2021年3月中国人民解放军海军第九七一医院收治的94例UC 患者为研究对象，按照随机数表法分为两组，各47例。

对照组采用美沙拉嗪治疗，观察组采用双歧杆菌三联活菌联合美沙拉嗪治疗。

比较两组患者临床疗效、T 淋巴细胞亚群水平、血浆纤维蛋白原（FIB）水平、炎症因子水平、不良反应。

结果：观察组总有效率（95.74%）显著高于对照组（82.98%），差异有统计学意义（P <0.05）；治疗后，观察组T 淋巴细胞亚群水平显著高于对照组，血浆纤维蛋白原（FIB）水平及炎症因子水平显著低于对照组，差异有统计学意义（P <0.05）；两组不良反应发生率（6.38% vs 10.64%）比较，差异无统计学意义（P >0.05）。

结论：采用双歧杆菌三联活菌联合美沙拉嗪治疗UC，可明显改善患者病情，提高机体免疫力，减轻炎症反应，不增加不良反应。

【关键词】　溃疡性结肠炎　双歧杆菌三联活菌　美沙拉嗪　炎症因子　免疫力 doi：10.14033/ki.cfmr.2024.01.013 文献标识码　B 文章编号　1674-6805（2024）01-0051-04 Effect of Bifidobacterium Triple Live Bacteria Combined with Mesalazine in Patients with Ulcerative Colitis/SUN Haiyuan, YUAN Gang, SUN Bo. //Chinese and Foreign Medical Research, 2024, 22(1): 51-54 [Abstract]　Objective: To analyze the therapeutic effect of Bifidobacterium Triple Live Bacteria combined with Mesalazine in patients with ulcerative colitis (UC). Method: A total of 94 UC patients admitted to the 971th Hospital of the Chinese People's Liberation Army Navy from March 2020 to March 2021 were selected as the study objects, and they were divided into two groups according to the random number table method, 47 cases in each group. The control group was treated with Mesalazine, while the observation group was treated with Bifidobacterium Triple Live Bacteria combined with Mesalazine. The clinical efficacy, T lymphocyte subpopulation levels, plasma fibrinogen (FIB) levels, inflammatory factor levels and adverse reactions between two groups were compared. Result: The clinical efficacy of the observation group (95.74%) was significantly higher than that of the control group (82.98%), the difference was statistically significant (P <0.05). After treatment, the levels of T lymphocyte subsets in the observation group were significantly higher than those in the control group, while the levels of plasma FIB and inflammatory factors were significantly lower than those in the control group, the differences were statistically significant (P <0.05). There was no statistically significant difference in the incidence of adverse reactions (6.38% vs 10.64%) between the groups (P >0.05). Conclusion: The use of Bifidobacterium Triple Live Bacteria combined with Mesalazine in the treatment of UC can significantly improve the patients' condition, enhance the body's immunity, reduce inflammatory reactions, and do not increase the adverse reaction. [Key words]　Ulcerative colitis　Bifidobacterium Triple Live Bacteria　Mesalazine　Inflammatory factors　Immunity First-author's address: The 971th Hospital of the Chinese People's Liberation Army Navy, Qingdao 266000, China 溃疡性结肠炎（UC）是在结直肠中高发的非特异性慢性炎症性疾病，患者多表现出腹痛、腹泻、乏力、脓血便、食欲不振等症状，对患者身体健康造成严重危害[1]。

三体英文原版单词量Title: The Word Count of "The Three-Body Problem" English Original VersionIntroduction:"The Three-Body Problem" is a renowned science fiction novel written by Liu Cixin. It has gained global recognition and has been translated into multiple languages. In this article, we will explore the word count of the English original version and its implications for readers.Word Count Significance:The word count of a novel provides insights into its complexity, depth, and reading difficulty. It reflects the author's ability to craft a compelling narrative while maintaining readers' engagement. Understanding the word count of "The Three-Body Problem" can shed light on the language proficiency required to fully grasp the story.The Word Count of "The Three-Body Problem":"The Three-Body Problem" English original version, including all three volumes, has a word count of approximately 416,000 words. The first volume contains around 135,000 words, the second volume has 140,000 words, and the final volume consists of approximately 141,000 words. The significant word count indicates the extensive storyline, intricate world-building, and comprehensive character development within the series.Reading Difficulty:Due to its substantial word count, "The Three-Body Problem" poses a considerable reading challenge. The novel delves deep into scientific concepts, exploring complex themes such as astrophysics and advanced theoretical physics. Readers should possess a solid grasp of English language proficiency, particularly in scientific and technical terms, to fully comprehend the intricacies of the narrative.Vocabulary Enhancement:Reading "The Three-Body Problem" can significantly contribute to expanding one's vocabulary. Liu Cixin employs a rich and diverse range of vocabulary, including scientific terminology and descriptive language. As readers engage with the novel, they will encounter new words, phrases, and expressions that can enhance their overall language proficiency.Cultural Exchange:"The Three-Body Problem" has been translated into multiple languages, facilitating cultural exchange and promoting understanding between different communities. The availability of the English original version allows readers worldwide to immerse themselves in the unique narrative and experience the story as close to its original form as possible.Language Learning:For English language learners, "The Three-Body Problem" English original version can serve as an excellent resource for language acquisition and improvement. Through reading and analyzing the novel, learners can strengthen their reading comprehension skills, expand their vocabulary, and gain a deeper understanding of the English language.Impact on the Science Fiction Genre:"The Three-Body Problem" has revolutionized the science fiction genre and has become a milestone in contemporary literature. Its English original version further solidifies the novel's global impact, making it accessible to a broader audience. The extensive word count reinforces the depth and complexity of the story, contributing to its reputation as a modern science fiction masterpiece.Conclusion:"The Three-Body Problem" English original version captivates readers with its intricate and thought-provoking narrative. The significant word count reflects the novel's depth, complexity, and extensive world-building. While posing a reading challenge, it offers an enriching experience for those interested in science fiction, language learning, and cultural exchange.。

The ThreeBody ProblemJoakim Hirvonen Gr¨u tzeliusKarlstad University December26,2004 Department of Engineeringsciences,Physics and MathematicsAnalytical Mechanics5pExaminator:Prof J¨u rgen F¨u chsAbstractThe main topic of this project is to give a mathematical description of the three body problem.A direct application to this problem is a rotating two-body system such as Sun-Jupiter,this rotating system is going to be treated in detail.At the end of the project there is a short discussion about the Ascending nodes and the Lagrangian points.Contents1Historical Background21.1Origin of The Three Body Problem (2)1.2Introduction to The Three Body Problem (2)2Mathematical Description of The Three Body Problem32.1The differential equations of the problem (3)2.2Reduction to the6th Order (4)3The Restricted Three Body Problem6A Ascending Node8B Lagrangian Points91Historical Background1.1Origin of The Three Body ProblemSince bodies in the solar system are approximately spherical and their dimensions extremely small when compared with the distances between them,they can be considered as point masses.Hence the origin of the problem can be thought of as being synonymous with the foundation of modern dynamical astronomy.This part of celestial mechanics,which connects the mechanical and physical causes with the observed phe-nomena,began with the introduction of Newton’s theory of gravitation. From the time of the publication of the Principia in1687,it became important to verify whether Newton’s law alone was capable of render-ing a complete understanding of how celestial bodies move in space.In order to pursue this line of investigation,it was necessary to ascertain the relative motion of n bodies attracting one another according to the Newtonian law.Newton himself had geometrically solved the problem of the two bodies for two spheres moving under their mutual gravitational attrac-tion,and in1710Johann Bernoulli had proved that the motion of one particle with respect to the other is described by a conic section.In 1734Daniel Bernoulli won a French academy prize for his analytical treatment of the two body problem,and the problem was solved in detail by Euler1744.Meanwhile work was already in progress on the higher dimensional problem.Driven by the needs of navigation for knowledge about the motion of the moon,researchers scrutinized the system formed by the sun,the earth and the moon,and the lunar theory quickly dominated the early research into the problem.1.2Introduction to The Three Body ProblemThe three body problem,which was described by Whittaker as”the most celebrated of all dynamical problems”[1]and which fulfilled for Hilbert the necessary criteria for a good mathematical problem,can be simply stated:three particles move in space under their mutual gravitational attraction;given their initial conditions,determine their subsequent motion.Like many mathematical problems,the simplicity of its statement belies the complexity of its solution.For although the one and two body problems can be solved in closed form by means of elementary functions,the three body problem is a complicated linear problem,and no similar type of solution exists.Apart from its intrinsic appeal as a simple-to-state problem,the three body problem has a further attribute which has contributed to its attraction for potential solvers:its intimate link with the funda-mental question of the stability of the solar system.Over the years attempts tofind a solution spawned a wealth of research,and between 1750and the beginning of the twentieth century more than800papersrelating to the problem were published,invoking a roll call of many distinguished mathematicians and astronomers.And hence,as is often the case with such problems,its importance is now perceived as much in the mathematical advances generated by attempts at its solution as in the actual problem itself.These advances have come in many different fields,including,in recent times,the theory of dynamical problems.To clarify the mathematical difficulties associated with the problem we will begin with a mathematical description.2Mathematical Description of The Three Body Problem2.1The differential equations of the problemLet us suppose that the three bodies under consideration to be at the points P i,with masses m i and coordinates q ij in an inertial reference frame(i,j=1,2,3).The distance between them are large,so we can think of them as point particles.We denote the distance between them as P ij=r ij,where r ij=|q i−q j|.Due to Newton’s law of gravitation,the force of attraction between the i th and j th becomes Gm i m j/r2ij ,andthe corresponding term in the potential energy becomes−Gm i m j/r ij. Then the potential energy of the hole system isV=−Gm1m2r12+m1m3r13+m2m3r23(1)where G is the gravitational constant.With the help of Newtons equa-tion of motion and that F=−∂V∂r ,then choosing units so that G isequal to one,the equations of motion becomem1d2q1idt2=−∂V∂q1i(2)m2d2q2idt2=−∂V∂q2i(3)m3d2q3idt2=−∂V∂q3i(4)ord2q1i dt2=m2(q2i−q1i)r312+m3(q3i−q1i)r313(5)d2q2i dt2=m1(q1i−q2i)r321+m3(q3i−q2i)r323(6)d2q3i dt2=m1(q1i−q3i)r331+m2(q2i−q3i)r332(7)where i=1,2,3.The problem is therefore described by nine second-order differential equations or by18equations of thefirst orderdq1i dt =˙q1i,dq2idt=˙q2i,dq3idt=˙q3im1d˙q1idt=−∂V∂q1i,m2d˙q2idt=−∂V∂q2i,m3d˙q3idt=−∂V∂q3i(8)So for a closed solution to the problem,the system needs18independent integrals.However,it is only possible tofind12such integrals,and the system can therefore only be reduced to one of order six.As will be shown below,this is achived through the use of the so-called ten classic integrals,the six integrals of the motion of the centre of mass,the three integrals of angular momentum,and the energy integral,together with the elimination of the time and the elimination of what is called the ascending node.Illustration of the ascending node and other orbital parameters can be found in appendix A.2.2Reduction to the6th OrderWhen multiplying equation(5),(6)and(7)by m i a summation can be performed to give three equations3i=1m id2q ijdt2=0,(j=1,2,3),(9)if we integrate these equation twice we get the equations3i=1m i q ij=A j t+B j,(j=1,2,3),(10)in which the A j and B j are constants of integration.These equations show that the centre of mass of the three particles either remains at rest or moves uniformly in space in a straight line.This is expected since there are no forces acting except the mutual attractions of the particles.The six constants serve to describe the motion of the centre of mass in the original arbitrary inertial coordinate system and play no part in the motion of the bodies about the centre of mass.If thefirst equation of(5)multiplied by−q12,thefirst equation of (6)by−q22and thefirst equation of(7)by−q32,and in equation(5) the second equation is multiplied by q11,the second equation of(6)by q21,and the second equation of(7)by q31,and these two sets are added together,this will give us3i=1m i q i1d2q i2dt2−3i=1m i q i2d2q i1dt2=0,(11)and two similar equations can be obtained by a cyclic change of the variables(x,y,z).The three equations can then be integrated to give3i=1m iq i2dq i3dt−q i3dq i2dt=C1(12)3i=1m iq i3dq i1dt−q i1dq i3dt=C2(13)3i=1m iq i1dq i2dt−q i2dq i1dt=C3.(14)These equations represent the conservation of angular momentum for the system.That is,they show that the angular momentum of the three particles around each of the coordinate axes is constant throughout the motion.Equation(5),(6)and(7)can be written in the formm i d2q ijdt2=−∂V∂q ij.(15)Multiplying by dq ijdt and summing gives,since V is a function of thecoordinates only,3i,j=1p ijd2q ijdt2=−dVdt.(16)This equation can then be integrated to give3 i,j=1p2ij2m i=−V+C,(17)where C is a constant of integration.Furthermore,since the left-hand side of the equation represents the kinetic energy T of the system, the integral can be put in the form T+V=C,which expresses the conservation of energy.Twofinal reductions can then be made to the order of the system. First,the time can be eliminated by using one of the dependent vari-ables as an independent variable which is used in the section treating the restricted three body problem,and,second,a reduction can be made by the so called elimination of the nodes.Thus through use of the classical integrals and these last two inte-grals,the original system of order18can be reduced to a system of order six.Furthermore,this result can be generalised to the n body problem.In this case the differential equations constitute a system of order6n.By using the same integrals this system can be reduced to a system of order(6n−12).3The Restricted Three Body ProblemIf we consider a body of unit mass(e.g.,an asteroid)moving in the field of a heavy body of mass M(e.g.,the Sun)and a much lighter body(e.g.,Jupiter)of mass m.Also assume that the heavy bodies are in circular orbit around each other with angular frequencyΩ;the effect of the light body on them is negligible.All three bodies move in the same plane.This is the restricted three body problem.When ignoring the effect of the asteroid,we can solve the two body problem to getMm M+m RΩ2=GMmR2,⇒Ω2=G(M+m)R3.(18)When we choose the center of mass of the heavy bodies as the ori-gin of a polar coordinate system.Then the position of the Sun is at (νR,π−Ωt)and Jupiter is at((1−ν)R,Ωt),where R is the distancebetween them,andν=mM+m .The distance from the asteroid to theSun isρ1(t)=r2+ν2R2+2νrR cos(θ−Ωt)(19)and to Jupiter isρ2(t)=r2+(1−ν)2R2+2(1−ν)rR cos(θ−Ωt).(20)The Lagrangian for the motion of the asteroid isL=12˙r2+12r2˙θ2+G(M+m)1−νρ1(t)+νρ2(t).(21)In this coordinate system the Lagrangian has an explicit time depen-dence:the Hamiltonian is not conserved.We change variables to χ=θ−Ωt to getL=12˙r2+12r2(˙χ+Ω)2+G(M+m)1−νr1+νr2(22)wherer1=r2+ν2R2+2νrR cosχ(23)andr2=r2+(1−ν)2R2−2(1−ν)rR cosχ(24)are now independent of time.Now the Hamiltonian in the rotating frame,H=˙r ∂L∂˙r+˙χ∂L∂˙χ−L=12˙r2+12r2˙χ2−G(M+m)r22R3+1−νr1+νr2(25)is a constant of the motion.This is called the Jacobi integral in classical literature.The Hamiltonian is of the form H=T+V where T is the kinetic energy and V is an effective potential energy:V(r,χ)=−G(M+m)r22R3+1−νr1+νr2.(26)It consist of the gravitational potential energy plus a term due to the centrifugal barrier,since we are in a rotating coordinate system.The effective potential V(r,χ)is conveniently expressed in terms of the distances to the massive bodies,V(r1,r2)=−GMr212R3+1r1+mr222R3+1r2(27)using the identity1νr21+11−νr22=1ν(1−ν)r22+R2.(28)(We have removed an irrelevant constant from the potential).Sometimes it is convenient to use cartesian coordinates,in which the lagrangian and hamiltonian areL=12˙x2+12˙y2+Ω(x˙y−y˙x)−V(x,y).(29) H=12˙x2+12˙y2+V(x,y).(30)It is obvious from the above formula for the potential as a function of r1and r2that r1=r2=R is an extremum of the potential.There are two ways this can happen:the asteroid can form an equilateral triangle with the Sun and Jupiter on either side of the line joining them.These are the Lagrange points L4and L5.These are actually maxima of the potential.In spite of this fact,they correspond to stable equilibrium points because of the effect of the velocity dependent forces.A discussion of the Lagrangian points can be found in appendix B.[2].A Ascending NodeThe ascending node is one of the orbital nodes,a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion.Because of this,the ascending node of the orbit of the Earth’s moon is one of only two places where a lunar or solar eclipse can occur.The line of nodes is the intersection of the object’s orbital plane with the ecliptic,and runs between the ascending and descending nodes.Figure1:Illustration of orbital parameters.B Lagrangian PointsA location in space around a rotating two-body system(such as the Earth-Moon or Sun-Jupiter)where the pulls of the gravitating bodies combine to form a point at which a third body of negligible mass would be stationary relative to the two bodies.There arefive Lagrangian points in all,which can be seen infigure1below,three of which areFigure2:Illustration of the Lagrangian points.unstable because the slightest disturbance to any object located at one of them causes the object to drift away permanently.Until recently,this meant that the unstable Lagrangian points seemed to have no practical application for spaceflight.Now,however,they are known to have immense significance and have become the basis for chaotic control.In addition,growing numbers of spacecraft are being placed in halo orbits around the L1and L2points;station-keeping,in the form of regular thrusterfirings,are needed to maintain these orbits(which are around empty points in space!).The NASA Sun-observing probes SOHO and ACE currently orbit around L1,while future spacecraft to be placed in L2halo orbits include the Next Generation Space Telescope and the European Space Agency’s Herschel,GAIA,and Darwin spacecraft.In many ways these points are ideal for observing both near and far reaches of space since spacecraft can orbit around them far from disturbing influences,such as that of Earth’s magnetosphere.L1is well-suited to solar observations;L2offers uninterrupted observations of deep space, since the spacecraft can be oriented so that the Earth,Moon and Sun remain”behind”it at all times,and enables the entire celestial sphere to be observed over the course of one year.L3hasn’t been utilized for spaceflight because it lies on the opposide side of the Sun from Earth. The remaining two Lagrangian points,L4and L5,lie at the vertices of equilateral triangles formed with the two main gravitating masses and in their orbital plane.They are also referred to as libration points since if any objects located at them are disturbed,the objects simply wobble back and forth,or librate.References[1]A treatise on the analytical dynamics of particles and rigid bodies,4th edition,E.T Whittaker,Cambridge University Press(1937).[2]Methods of Celestial Mechanics,D.Brouwer and G.M.Clemence,Academic Press,NY(1961)[3]Poincar´e and the three body problem,June Barrow-Green,Amer-ican Mathematical Society,Printed in USA(1997).[4]/encyclopedia/L/Lagpoint.html[5]Dynamical systems,G.D.Birkhoff,American mathematical society1927.。