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The Eastern Han astronomer Zhang Heng compiled. It states: "Among the officials inside and outside, there are one hundred and twenty-four that are always bright, three hundred and twenty that can be named, and two thousand five hundred stars, but the divinations of the seafarers are not included. The number of faint stars is about eleven thousand five hundred and twenty." This shows that in the two to three hundred years after Sima Qian, the number of stars observed and recorded by Chinese astronomers greatly increased. It also points out: "Moonlight is born from the illumination of the sun, and the dark part is born from the shadow of the sun. When facing the sun, the light is full; when approaching the sun, the light disappears... When opposite the sun, the light is often not complete because it is obscured by the earth, which is called 'dark void'. In stars, it makes the stars faint; when it encounters the moon, it causes a lunar eclipse." This explains that moonlight is the result of reflecting sunlight and the principles behind the waxing and waning of the moon. Additionally, it proposes: "The surface of the universe is boundless, and the end of time is infinite." It suggests that the world we inhabit is finite, but beyond our world, there are infinite realms.

Zhang Heng also discussed the origin of heaven and earth in Lingxian: "Before Taisu, it was dark, clear, mysterious, and silent, formless and imageless. Within it was only emptiness, and outside it was only nothingness, and this state lasted for a long time. This is called 'Mingxing', the root of the Dao. Once the root of the Dao was established, being arose from non-being, and Taisu began to sprout, sprouting without form, with unified qi and color, chaotic and undifferentiated. Therefore, the words of the 'Dao Zhi' say: 'There is a thing formed in chaos, born before heaven and earth.' Its qi and form were not yet discernible, and its speed was not yet recordable. This state lasted for a long time, and this is called 'Panghong', the trunk of the Dao. Once the trunk of the Dao was nurtured, all things took form, and then the original qi divided, hardness and softness began to separate, clarity and turbidity took their positions, with nothingness forming outside and the earth solidifying inside. The heavenly body is yang, hence round and moving; the earthly body is yin, hence flat and still. Movement leads to action, stillness leads to transformation, and through the interaction of yin and yang, all things are nurtured. This is called 'Tianyuan', the fruit of the Dao." Zhang Heng divided the generation and evolution of heaven, earth, and all things into three stages, called 'Mingxing', 'Panghong', and 'Tianyuan'. 'Mingxing' is the 'root' of the Dao, the stage before Taisu where the original substance of heaven and earth was in a formless void; the second stage is 'Panghong', the 'trunk' of the Dao's development, where substance transitions from formless to form, with unified qi and color, chaotic and indistinct; finally, 'Tianyuan' is the 'fruit' of the Dao, where all things gradually take form, the original qi separates, and hardness, softness, clarity, and turbidity differentiate, leading to the formation of heaven and earth and the nurturing of all things.

Lingxian is Zhang Heng's monumental astronomical work, the result of years of practical and theoretical research, and an immortal masterpiece in the history of world astronomy. The book comprehensively elaborates on the generation of heaven and earth, the evolution of the universe, the structure of heaven and earth, the nature and movement of the sun, moon, and stars, and many other significant topics, elevating the level of ancient Chinese astronomy to an unprecedented new stage, placing China's astronomical research at the forefront of the world at that time, and having a profound impact on later generations.

The astronomical achievements of Lingxian:

First, it discusses the origin and structure of the universe. Regarding the generation of heaven and earth, Lingxian posits that all things in heaven and earth developed from the original undifferentiated qi. Initially, the original qi was chaotic and undifferentiated, later separating into clarity and turbidity, with the interaction of clear and turbid qi forming the universe. The clear qi formed the heavens outside, and the turbid qi formed the earth inside. This idea of celestial evolution explains the formation of the universe through the movement of matter itself, suggesting that the structure of the universe is not eternal but constantly evolving. These views are fundamentally aligned with modern theories of cosmic evolution.

Second, the cause of lunar eclipses. Based on the Hun Tian theory, it scientifically explains the reason for lunar eclipses. Zhang Heng wrote in Lingxian: "The light of the moon is born from the illumination of the sun; the shadow is born from the obstruction of the sun. When facing the sun, the light is full; when turning away from the sun, the light disappears." (The general idea is: the moon itself does not emit light, but when the light of Taiyang (EX-HN5) shines on the moon, the moon reflects the light. The part not illuminated by Taiyang (EX-HN5) appears deficient, which is the so-called "the moon has its phases of waxing and waning." If the moon enters the earth's shadow?Zhang Heng named the earth's shadow "dark void"?a "lunar eclipse" occurs.) It can be seen that Lingxian's explanation of the cause of lunar eclipses is very scientific.

Third, the finiteness and infinity of the universe. Although Zhang Heng compared the sky to an eggshell and the earth to the yolk within the shell, he did not consider the hard shell as the boundary of the universe. The debate over the finiteness and infinity of the universe has been a long-standing issue in the field of astronomy, both ancient and modern, Chinese and foreign. Zhang Heng was influenced by some astronomical views in Yang Xiong's "Tai Xuan Jing" when writing "Lingxian," but he did not follow Yang Xiong's views on the infinity of the universe, instead holding his own opinions. Zhang Heng believed that the universe visible to the human eye is finite, but beyond what the human eye can see, it is "unknown. What is unknown is called the universe. The surface of the universe is boundless, and the end of the universe is infinite."

Fourth, the measurement of the average angular diameter of the sun and moon. Zhang Heng measured the angular diameter of the sun and moon to be 1/736 of the entire celestial sphere, which converts to 29 degrees and 21 minutes in the modern 360-degree system. Compared to the modern astronomical measurements of the average angular diameter of the sun and moon, which are 31'59" and 31'5" respectively, the absolute error is only 2'. Given the scientific and observational conditions over two thousand years ago, this value can be considered quite accurate.

Fifth, the creation of a new star catalog with three thousand stars. Zhang Heng, based on careful observation of celestial bodies, compiled and summarized several star catalogs passed down from predecessors, creating a new star catalog with as many as three thousand stars. According to "Lingxian," among them, "there are 124 constant bright stars in the inner and outer regions, 320 nameable stars, and 2,500 stars, with the divinations of the sea people not included." Zhang Heng's star catalog not far surpassed those of his predecessors but was also deficient for later generations. During the turmoil at the end of the Han Dynasty, Zhang Heng's star catalog was lost. The star catalog established by Chen Zhuo at the beginning of the Jin Dynasty contained 1,464 stars, only half of Zhang Heng's. It was not until the Kangxi period of the Qing Dynasty, using telescopes, that the number exceeded three thousand. Thus, the loss of Zhang Heng's star catalog is a significant loss in the history of Chinese astronomy.

Sixth, the motion of the five planets. Regarding the motion of the five planets, Zhang Heng proposed that the sun, moon, and five planets move between heaven and earth, not on the celestial sphere. Moreover, the speeds of these seven celestial bodies vary, "closer to heaven, slower; farther from heaven, faster." By "heaven," he meant the hypothetical celestial sphere, meaning that closer to the earth, the speed is faster, and farther from the earth, the speed is slower. Based on the distance of the five planets from the earth and their speed of motion, he divided the five planets into two categories: Mercury and Venus, close to the earth, moving fast, attached to the moon, belonging to yin; Mars, Jupiter, and Saturn, far from the earth, moving slowly, attached to the sun, belonging to yang. He inherited the tradition of dividing the direction of planetary motion into direct motion, stationary, and retrograde motion. Although this view is incorrect, his attempt to explore the mechanical causes of celestial motion was undoubtedly correct. Zhang Heng did not yet know that planets, including the earth, revolve around the sun (EX-HN5), but he did discover that the speed of planetary motion is related to the distance from the central body. Unfortunately, this correct idea did not receive sufficient attention from later generations, greatly limiting the development of Chinese astronomy. It was not until the 17th century that Kepler, based on Copernicus's heliocentric theory, pointed out the three laws of planetary motion, one of which is that the speed and orbital period of a planet are determined by its distance from the central body, the sun (EX-HN5).

Lingxian is one of the most outstanding astronomical works in the history of ancient Chinese astronomy, and it also marks a milestone in the development of Chinese astronomy reaching a new height. Although there are still some errors and shortcomings, its significance in the history of astronomy is not diminished by this.