When was johannes kepler born

He took this teaching job even though he wanted to join the ministry. However, because he was pressured to convert to Roman Catholicism, he left Graz and the school and moved with his family to Prague. Some time before these troubles began, he met the Danish astronomer Tycho Brahe. Brahe even supported Kepler and his family financially for a while and made it possible for him to advance in his career through his political connections.

Brahe was the most renowned astronomical observer in Europe at the time and he hired Kepler as his assistant. Kepler conceives of a model with parallel magnetic fibers which links the Sun with the planets in such a way that the rotation of the Sun causes the motion of the planets around it. The planets themselves are polarized, that is, with one pole they are attracted to the Sun, with the other pole they are pushed away from it.

This explains very well the direction of planetary motion: the planets all move in one direction because the Sun rotates in that direction. This phenomenon can be explained by referring to a property of matter, which for Kepler has an axiomatic character: the inclinatio ad quietemthat is, the tendency to rest see especially AN, chap.

As a consequence, the planets are moved when was johannes kepler born the Sun slower than they would be if the power of the Sun were at work alone. At the same time, it should be pointed out that the third law is not necessarily the best point of departure for a dynamical, causal approach to motion, as Kepler intends here; for, in comparison with the previous causal approaches, the question of the location of the cause of power responsible for the production of motion remains relevant.

The spheres, which in the traditional view transported the planets, had been abolished since the time of Tycho. The fact that the orbits are elliptical and not circular, shows that the motions are not caused by a spiritual power but rather by a natural one, which is internal to the composition of matter. The motive power vix motrix comes indeed from the Sun, which sends its rays of light and power in all directions.

These rays are captured by the planets. Kepler, however, tries to explain this behavior of the planets less through astrology and much more through magnetism a physical phenomenon which was by no means clearly understood in his time. Firstly, the Sun rotates and, by so doing, sets in motion the planets around it. Secondly, since the planets are poles of magnets and the Sun itself acts with magnetic power, the planets are, at different parts of their orbits, either attracted or repelled; in this way the elliptical path is causally produced.

Kepler partially gives up the mechanical approach by postulating a soul in the Sun which is responsible for its regular motion of rotation, a motion on which, finally, the entire system depends. In addition to astronomy and cosmology Kepler expanded his causal approach to include the fields of optics see Section 6 below and harmonics Section 7 below.

At least officially, his positions at Graz, Prague, Linz, Ulm and Sagan can be characterized as the typical professional occupations of a mathematician in the broadest sense, i. Besides the field of astronomy and optics, where mathematics is ordinarily applied in different ways, Kepler produced original contributions to the theory of logarithms and above all within his favorite field, geometry especially with his stereometrical investigations.

For the medieval proportions theory as a background for Kepler's logarithms, see Rommevaux-Tani, Thus, on account of his natural predilection and talent and the importance of mathematics, particularly of geometry, for his thought, it is not surprising to find many different passages in his works where he articulated his philosophy of mathematics.

According to Kepler, each branch of knowledge must, in principle, be reducible to geometry if it is to be accepted as knowledge in the strong sense although, in the case of the physics, this condition is, as the AN emphasizes, only a necessary and not a sufficient condition. Thus, the new principles he was elaborating over the years in astrology were geometrical ones.

A similar case occurs with the basic notions of harmony, which, after Kepler, could be reduced to geometry. Of course, not every geometrical statement is equally relevant and equally fundamental. For Kepler, the geometrical entities, principles and propositions which are especially fundamental are those that can be constructed in the classical sense, i.

Once again, Kepler understood this within the framework of his cosmological and theological philosophy: geometry, and especially geometrically constructible entities, have a higher meaning than other kinds of knowledge because God has used them to delineate and to create this perfect harmonic world. From this point of view, it is clear that Kepler defends a Platonist conception of mathematics, that he cannot assume the Aristotelian theory of abstraction and that he is not able to accept algebra, at least in the way he understood it.

The best example of this is perhaps the heptagon.

When was johannes kepler born: Childhood (–)​​ Kepler was born

This figure cannot be described outside of the circle, and in the circle its sides have, of course, a determinate magnitude, but this is not knowable. Kepler himself says that this is important because here he finds the explanation for why God did not use such figures to structure the world. Consequently, he devotes many pages to discussing the issue KGW 6, Prop.

Certainly for a geometer like Kepler, approximations constitute — as mathematical theory—a painful and precarious way to progress. The philosophical background for his rejection of algebra seems to be, at least partially, Aristotelian in some of its basic suppositions: geometrical quantities are continuous quantities which therefore cannot be treated with numbers that are, in the inverse, discrete quantities.

For, despite his mainly theoretical approach in the natural sciences, Kepler often emphasized the significance of experience and, in general, of empirical data. In his correspondence there are many remarks about the significance of observation and experience, as for instance in a letter to Herwart von Hohenburg from KGW 13, let. In MC chapter 18 he quotes a long passage from Rheticus for the sake of rhetorical support when, as was the case here, the data of the tables he used did not fit perfectly with the calculated values from the polyhedral hypothesis.

In this passage, the reader learns that the great Copernicus, whose world system Kepler defends in MC, said one day to Rheticus that it made no sense to insist on absolute agreement with the data, because these themselves were when was johannes kepler born not perfect. In part 2 chap. This hypothesis represents the best result which can be reached within the limits of traditional astronomy.

This works with circular orbits and with the supposition that the motion of a planet appears regular from a point on the lines of apsides. Against the traditional method, here, Kepler does not cut the eccentricity into equal parts but leaves the partition open. To check his hypothesis, he needs observations of Mars in opposition, where Mars, the Earth, and the Sun are at midnight on the same line.

In chapters 17—21, Kepler carries out an observational and computational check of his vicarious hypothesis. On the one hand, he points out that this hypothesis is good enough, since the variations of the calculated positions from the observed positions fall within the limits of acceptability 2 minutes of arc. On the other hand, this hypothesis can be falsified if one takes the observations of the latitudes into consideration.

Further calculations with these observations produce a difference of eight minutes, something that cannot be assumed because the observations of Tycho are reliable enough. Kepler also gave an important place to experience in the field of optics. As a matter of fact, he began his research on optics because of a disagreement between theory and observation, and he made use of scientific instruments he had designed himself see, for instance, KGW For astrology, he uses meteorological data, which he recorded for many years, as confirmation material.

This material shows that the Earth, as a whole living being, reacts to the aspects which occur regularly in the heavens see Bonerpp. In his musical theory Kepler was a modern thinker, especially because of the role he gave to experience. As has been noted Walker,p. Kepler does not accept that this limitation is founded on arithmetical speculations, even if this was already assumed by Plato, whom he often follows, and by the Pythagoreans.

On the basis of his experiments, Kepler found that there are other divisions of the string that the ear perceives as consonant, i. Today Kepler is remembered in the history of sciences above all for his three planetary laws, which he produced in very specific contexts and at different times. Figure 2. The first two laws were published initially in ANalthough it is known that Kepler had arrived at these results much earlier.

His first law establishes that the orbit of a planet is an ellipse with the Sun in one of the foci see Figure 2. The planet P is therefore faster at perihelion, where it is closer to the Sun, and slower at aphelion, where it is farther from the Sun. The first law abolishes the old axiom of the circular orbits of the planets, an axiom which was still valid not only for pre-Copernican astronomy and cosmology but also for Copernicus himself, and for Tycho and Galileo.

The second law breaks with another axiom of traditional astronomy, according to which the motion of the planets is uniform in swiftness. Copernicus, for his own part, insisted on the necessity of the axiom of uniform circular motion.

When was johannes kepler born: Johannes Kepler was born

Kepler, on the contrary, affirms the reality of changes in the velocities of the planetary motions and provides a physical account for them. After struggling strenuously with established ideas which were located not only in the tradition before him but also in his own thinking, Kepler abandoned the circular path of planetary motion and in this way initiated a more empirical approach to cosmology though see Brackenridge In his Epitomehe provided a more systematic approach to all three laws, their grounds and implications see Davis ; Stephenson In Book 5, chapter 3, as point 8 of 13 KGW 6, p.

As a consequence of the third law, the time a planet takes to travel around the Sun will significantly increase the farther away it is or the longer the radius of its orbit. The background for his investigation into optics was undoubtedly the different particular questions of astronomical optics see Straker In this context he concentrated his efforts on an explanation of the phenomena of eclipses, of the apparent size of the Moon and of atmospheric refraction.

Kepler investigated the theory of the camera obscura very early and recorded its general principles see commentary by M. Hammer in KGW 2, pp. Besides these impressive contributions, Kepler expanded his research program to embrace mathematics as well as anatomy, discussing for instance conic sections and explaining the process of vision see Crombie and especially Lindberg b.

Following—but also inverting—the Aristotelian argument for the temporality of motion, he affirms that the motion of light takes place not in time but in an instant in momento. Her father Jobst initially opposed a marriage. Even though Kepler had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. Jobst relented after Kepler completed work on Mysteriumbut the engagement nearly fell apart while Kepler was away tending to the details of publication.

Barbara and Johannes were married on 27 April In the first years of their marriage, the Keplers had two children Heinrich and Susannaboth of whom died in infancy. Inthey had a daughter Susanna ; ina son Friedrich ; and inanother son Ludwig. Following the publication of Mysterium and with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work.

He planned four additional books: one on the stationary aspects of the universe the Sun and the fixed stars ; one on the planets and their motions; one on the physical nature of planets and the formation of geographical features focused especially on Earth ; and one on the effects of the heavens on the Earth, to include atmospheric optics, meteorology, and astrology.

Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over what is now called the Tychonic system with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus.

Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory particularly its theological viability. But without the significantly more accurate data of Tycho's observatory, Kepler had no way to address many of these issues. Instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences.

By assuming the Earth to possess a soul a property he would later invoke to explain how the Sun causes the motion of planetshe established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena. Byhowever, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz.

In December of that year, Tycho invited Kepler to visit him in Prague ; on 1 January before he even received the invitationKepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones. Over the next two months, he stayed as a guest, analyzing some of Tycho's observations of Mars; Tycho guarded his data closely, but was impressed by Kepler's theoretical ideas and soon allowed him more access.

Kepler planned to test his theory from Mysterium Cosmographicum based on the Mars data, but he estimated that the work would take up to two years since he was not allowed to simply copy the data for his own use. With the help of Johannes JesseniusKepler attempted to negotiate a more formal employment arrangement with Tycho, but negotiations broke down in an angry argument and Kepler left for Prague on 6 April.

Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June, Kepler returned home to Graz to collect his family. Political and religious difficulties in Graz dashed his hopes of returning immediately to Brahe; in hopes of continuing his astronomical studies, Kepler sought an appointment as a mathematician to Archduke Ferdinand.

To that end, Kepler composed an essay—dedicated to Ferdinand—in which he proposed a force-based theory of lunar motion: "In Terra inest virtus, quae Lunam ciet" "There is a force in the earth which causes the moon to move". These observations formed the basis of his explorations of the laws of optics that would culminate in Astronomiae Pars Optica.

On 2 Augustafter refusing to convert to Catholicism, Kepler and his family were banished from Graz. Several months later, Kepler returned, now with the rest of his household, to Prague. Through most ofhe was supported directly by Tycho, who assigned him to analyzing planetary observations and writing a tract against Tycho's by then deceased rival, Ursus.

In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: the Rudolphine Tables that should replace the Prutenic Tables of Erasmus Reinhold. Two days after Tycho's unexpected death on 24 OctoberKepler was appointed his successor as the imperial mathematician with the responsibility to complete his unfinished work.

The next 11 years as imperial mathematician would be the most productive of his life. Kepler's primary obligation as imperial mathematician was to provide astrological advice to the emperor. In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble. Rudolf was actively interested in the work of many of his court scholars including numerous alchemists and kept up with Kepler's work in physical astronomy as well.

Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquistbut Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered. The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle.

Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness. In Octobera bright new evening star SN appeared, but Kepler did not believe the rumors until he saw it himself. Astrologically, the end of marked the beginning of a fiery trigonthe start of the about year cycle of great conjunctions ; astrologers associated the two previous such periods with the rise of Charlemagne c.

It was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his De Stella Nova. In it, Kepler addressed the star's astronomical properties while taking a skeptical approach to the many astrological interpretations then circulating. He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens the idea accepted since Aristotle that the celestial spheres were when was johannes kepler born and unchanging.

The birth of a new star implied the variability of the heavens. Kepler also attached an appendix where he discussed the recent chronology work of the Polish historian Laurentius Suslyga ; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem —analogous to the present new star—would have coincided with the first great conjunction of the earlier year cycle.

Over the following years, Kepler attempted unsuccessfully to begin a collaboration with Italian astronomer Giovanni Antonio Maginiand dealt with chronology, especially the dating of events in the life of Jesus. AroundKepler circulated a manuscript of what would eventually be published posthumously as Somnium [The Dream]. Part of the purpose of Somnium was to describe what practicing astronomy would be like from the perspective of another planet, to show the feasibility of a non-geocentric system.

The manuscript, which disappeared after changing hands several times, described a fantastic trip to the Moon; it was part allegory, part autobiography, and part treatise on interplanetary travel and is sometimes described as the first work of science fiction. Years later, a distorted version of the story may have instigated the witchcraft trial against his mother, as the mother of the narrator consults a demon to learn the means of space travel.

Following her eventual acquittal, Kepler composed footnotes to the story—several times longer than the actual text—which explained the allegorical aspects as well as the considerable scientific content particularly regarding lunar geography hidden within the text. Inthe growing political-religious tension in Prague came to a head. Emperor Rudolf—whose health was failing—was forced to abdicate as King of Bohemia by his brother Matthias.

Both sides sought Kepler's astrological advice, an opportunity he used to deliver conciliatory political advice with little reference to the stars, except in general statements to discourage drastic action. However, it was clear that Kepler's future prospects in the court of Matthias were when was johannes kepler born. Also in that year, Barbara Kepler contracted Hungarian spotted feverthen began having seizures.

As Barbara was recovering, Kepler's three children all fell sick with smallpox; Friedrich, 6, died. The University of Padua —on the recommendation of the departing Galileo—sought Kepler to fill the mathematics professorship, but Kepler, preferring to keep his family in German territory, instead travelled to Austria to arrange a position as teacher and district mathematician in Linz.

However, Barbara relapsed into illness and died shortly after Kepler's return. Kepler postponed the move to Linz and remained in Prague until Rudolf's death in earlythough between political upheaval, religious tension, and family tragedy along with the legal dispute over his wife's estateKepler could do no research. Instead, he pieced together a chronology manuscript, Eclogae Chronicaefrom correspondence and earlier work.

Upon succession as Holy Roman Emperor, Matthias re-affirmed Kepler's position and salary as imperial mathematician but allowed him to move to Linz. In Linz, Kepler's primary responsibilities beyond completing the Rudolphine Tables were teaching at the district school and providing astrological and astronomical services. In his first years there, he enjoyed financial security and religious freedom when was johannes kepler born to his life in Prague—though he was excluded from Eucharist by his Lutheran church over his theological scruples.

It was also during his time in Linz that Kepler had to deal with the accusation and ultimate verdict of witchcraft against his mother Katharina in the Protestant town of Leonberg. That blow, happening only a few years after Kepler's excommunicationis not seen as a coincidence but as a symptom of the full-fledged assault waged by the Lutherans against Kepler.

His first publication in Linz was De vero Annoan expanded treatise on the year of Christ's birth. He also participated in deliberations on whether to introduce Pope Gregory 's reformed calendar to Protestant German lands. On 30 OctoberKepler married Susanna Reuttinger. Following the death of his first wife Barbara, Kepler had considered 11 different matches over two years a decision process formalized later as the marriage problem.

Three more survived into adulthood: Cordula born ; Fridmar born ; and Hildebert born According to Kepler's biographers, this was a much happier marriage than his first. On 8 OctoberKepler set out for Regensburg, hoping to collect interest on work he had done previously. A few days after reaching Regensburg, Kepler became sick, and progressively became worse.

On 15 Novemberjust over a month after his arrival, he died. He was buried in a Protestant churchyard in Regensburg that was completely destroyed during the Thirty Years' War. Kepler's belief that God created the cosmos in an orderly fashion caused him to attempt to determine and comprehend the laws that govern the natural world, most profoundly in astronomy.

Those laws [of nature] are within the grasp of the human mind; God wanted us to recognize them by creating us after his own image so that we could share in his own thoughts. Kepler advocated for tolerance among Christian denominations, for example arguing that Catholics and Lutherans should be able to take communion together. Kepler's first major astronomical work, Mysterium Cosmographicum The Cosmographic Mystery, was the first published defense of the Copernican system.

Kepler claimed to have had an epiphany on 19 Julywhile teaching in Grazdemonstrating the periodic conjunction of Saturn and Jupiter in the zodiac : he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations even with extra planets added to the systemKepler began experimenting with 3-dimensional polyhedra.

He found that each of the five Platonic solids could be inscribed and circumscribed by spherical orbs ; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets— MercuryVenusEarthMarsJupiter, and Saturn. By ordering the solids selectively— octahedronicosahedrondodecahedrontetrahedroncube —Kepler found that the spheres could be placed at intervals corresponding to the relative sizes of each planet's path, assuming the planets circle the Sun.

Kepler also found a formula relating the size of each planet's orb to the length of its orbital period : from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius.

When was johannes kepler born: Johannes Kepler was a German astronomer,

Kepler thought the Mysterium had revealed God's geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his when was johannes kepler born convictions about the connection between the physical and the spiritual ; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Sonand the intervening space between them to the Holy Spirit.

His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. Mysterium was published late inand Kepler received his copies and began sending them to prominent astronomers and patrons early in ; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer.

The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system. InKepler published an expanded second edition of Mysteriumhalf as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.

While Copernicus sought to advance a heliocentric system in this book, he resorted to Ptolemaic devices viz. Although he noted that there were discrepancies between the observational data and his model's predictions, he did not think they were large enough to invalidate the theory. The extended line of research that culminated in Astronomia Nova A New Astronomy —including the first two laws of planetary motion —began with the analysis, under Tycho's direction, of the orbit of Mars.

In this work Kepler introduced the revolutionary concept of planetary orbit, a path of a planet in space resulting from the action of physical causes, distinct from previously held notion of planetary orb a spherical shell to which planet is attached. As a result of this breakthrough astronomical phenomena came to be seen as being governed by physical laws.

But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data. In Kepler's religious view of the cosmos, the Sun a symbol of God the Father was the source of motive force in the Solar System.

As a physical basis, Kepler drew by analogy on William Gilbert 's theory of the magnetic soul of the Earth from De Magnete and on his own work on optics. Kepler supposed that the motive power or motive species [ 66 ] radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it. Based on measurements of the aphelion and perihelion of the Earth and Mars, he created a formula in which a planet's rate of motion is inversely proportional to its distance from the Sun.

Verifying this relationship throughout the orbital cycle required very extensive calculation; to simplify this task, by late Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times —his second law of planetary motion. He then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit.

After approximately 40 failed attempts, in late he at last hit upon the idea of an ellipse, [ 70 ] which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Because he employed no calculating assistants, he did not extend the mathematical analysis beyond Mars. By the end of the year, he completed the manuscript for Astronomia novathough it would not be published until due to legal disputes over the use of Tycho's observations, the property of his heirs.

Since completing the Astronomia NovaKepler had intended to compose an astronomy textbook that would cover all the fundamentals of heliocentric astronomy. Despite its title, which merely hints at heliocentrism, the Epitome is less about Copernicus's work and more about Kepler's own astronomical system. Fortunately, wiser heads prevailed, Brahe and Kepler made up, and Kepler returned with his family in tow.

However, inthere was a huge plot twist: After a period of particularly heavy partying, Brahe died. At the time, his death was blamed on a kidney stone, but in the s, it was suggested that Brahe could died from mercury poisoning, with Kepler a suspect in Brahe's death. However, inBrahe's remains were exhumed, and a toxicology report found no evidence of mercury poisoning.

Instead, it is thought that Tycho died from a bacterial infection, prostate cancer or a burst bladder. Kepler died from a fever, possibly the result of a bladder infectionon Nov. However, his name forever lives on, in both his laws of planetary motion and NASA's Kepler space telescopewhich discovered thousands of exoplanets between and On his deathbed, Brahe had permitted Kepler to use his preciously guarded astronomical data, and these data proved vital in the work that Kepler is best known for: his three laws of planetary motion.

InKepler published " Astronomia Nova ," which detailed his year-long study of the motion of Mars in the sky. Remarkably, without knowledge of the force of gravity that governs the orbits of the planets, Kepler had provided the basic mathematics of orbital motion. They were later developed further by Isaac Newtonwho is credited with "discovering" gravity, and Kepler's laws were fundamental to Newton's laws of gravitation.

The laws of planetary motion were not the only valid scientific work conducted by Kepler. Inhe published "Astronomiae Pars Optica" "The Optical Part of Astronomy"which explained why the lunar eclipse he had seen in was red the result of atmospheric refraction of sunlight. Inhe witnessed a supernova in the constellation Ophiuchus, the serpent bearer, which was the when was johannes kepler born supernova seen in the Milky Way.

After the invention of the telescope inKepler experimented with telescopic optics, improving upon the designs of Hans Lippershey and Galileo Galilei to create the Keplerian telescope, which formed the basis of all modern refracting telescopes. The first law of planetary motion states that planets move in slightly elliptical orbits — subtle ovals rather than circles.

Furthermore, it states that the sun is located at one focus of the ellipse. With a circle, there is a center that is equidistant from all points on that circle. In contrast, an ellipse does not have a center that is equidistant. Instead, an ellipse has two foci — one on each side of the center — along the center line linking the two widest parts of the ellipse.

This is called the semimajor axis. The sun is at one of these foci. The second law of planetary motion relates to how a planet orbits more slowly the farther it is from the sun on its elliptical orbit. It states that if you were to draw a line between a planet and the sun, this line would sweep out equal areas during equal amounts of time. To understand this idea, picture an ellipse with the sun at one focus, as described in the first law, and draw an imaginary line from the sun to a planet on that ellipse.

Now, imagine the planet moving along its elliptical orbit for a given amount of time when it is at the opposite side of the ellipse as the sun. Because it is farther from the sun, it's moving more slowly.