essay about how brahe's work help kepler

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Chapter 3 Orbits and Gravity

3.1 The Laws of Planetary Motion – Brahe and Kepler

Learning objectives.

By the end of this section, you will be able to:

• Describe how Tycho Brahe and Johannes Kepler contributed to our understanding of how planets move around the Sun
• Explain Kepler’s three laws of planetary motion

At about the time that Galileo was beginning his experiments with falling bodies, the efforts of two other scientists dramatically advanced our understanding of the motions of the planets. These two astronomers were the observer Tycho Brahe and the mathematician Johannes Kepler. Together, they placed the speculations of Copernicus on a sound mathematical basis and paved the way for the work of Isaac Newton in the next century.

Tycho Brahe’s Observatory

Three years after the publication of Copernicus’ De Revolutionibus , Tycho Brahe was born to a family of Danish nobility. He developed an early interest in astronomy and, as a young man, made significant astronomical observations. Among these was a careful study of what we now know was an exploding star that flared up to great brilliance in the night sky. His growing reputation gained him the patronage of the Danish King Frederick II, and at the age of 30, Brahe was able to establish a fine astronomical observatory on the North Sea island of Hven as shown in Figure 1 . Brahe was the last and greatest of the pre-telescopic observers in Europe.

At Hven, Brahe made a continuous record of the positions of the Sun, Moon, and planets for almost 20 years. His extensive and precise observations enabled him to note that the positions of the planets varied from those given in published tables, which were based on the work of Ptolemy. These data were extremely valuable, but Brahe didn’t have the ability to analyze them and develop a better model than what Ptolemy had published. He was further inhibited because he was an extravagant and cantankerous fellow, and he accumulated enemies among government officials. When his patron, Frederick II, died in 1597, Brahe lost his political base and decided to leave Denmark. He took up residence in Prague, where he became court astronomer to Emperor Rudolf of Bohemia. There, in the year before his death, Brahe found a most able young mathematician, Johannes Kepler, to assist him in analyzing his extensive planetary data.

Johannes Kepler

Johannes Kepler was born into a poor family in the German province of Württemberg and lived much of his life amid the turmoil of the Thirty Years’ War. He is illustrated in Figure 1 . He attended university at Tubingen and studied for a theological career. There, he learned the principles of the Copernican system and became converted to the heliocentric hypothesis. Eventually, Kepler went to Prague to serve as an assistant to Brahe, who set him to work trying to find a satisfactory theory of planetary motion—one that was compatible with the long series of observations made at Hven. Brahe was reluctant to provide Kepler with much material at any one time for fear that Kepler would discover the secrets of the universal motion by himself, thereby robbing Brahe of some of the glory. Only after Brahe’s death in 1601 did Kepler get full possession of the priceless records. Their study occupied most of Kepler’s time for more than 20 years.

Through his analysis of the motions of the planets, Kepler developed a series of principles, now known as Kepler’s three laws, which described the behaviour of planets based on their paths through space. The first two laws of planetary motion were published in 1609 in The New Astronomy . Their discovery was a profound step in the development of modern science.

The First Two Laws of Planetary Motion

The path of an object through space is called its orbit. Kepler initially assumed that the orbits of planets were circles, but doing so did not allow him to find orbits that were consistent with Brahe’s observations. Working with the data for Mars, he eventually discovered that the orbit of that planet had the shape of a somewhat flattened circle, or ellipse. Next to the circle, the ellipse is the simplest kind of closed curve, belonging to a family of curves known as conic sections as shown in Figure 2 .

You might recall from math classes that in a circle, the centre is a special point. The distance from the centre to anywhere on the circle is exactly the same. In an ellipse, the sum of the distance from two special points inside the ellipse to any point on the ellipse is always the same. These two points inside the ellipse are called its foci (singular: focus), a word invented for this purpose by Kepler.

This property suggests a simple way to draw an ellipse as shown in Figure 3 . We wrap the ends of a loop of string around two tacks pushed through a sheet of paper into a drawing board, so that the string is slack. If we push a pencil against the string, making the string taut, and then slide the pencil against the string all around the tacks, the curve that results is an ellipse. At any point where the pencil may be, the sum of the distances from the pencil to the two tacks is a constant length—the length of the string. The tacks are at the two foci of the ellipse.

The widest diameter of the ellipse is called its major axis. Half this distance—that is, the distance from the centre of the ellipse to one end—is the semimajor axis, which is usually used to specify the size of the ellipse. For example, the semimajor axis of the orbit of Mars, which is also the planet’s average distance from the Sun, is 228 million kilometres.

The shape (roundness) of an ellipse depends on how close together the two foci are, compared with the major axis. The ratio of the distance between the foci to the length of the major axis is called the eccentricity of the ellipse.

If the foci (or tacks) are moved to the same location, then the distance between the foci would be zero. This means that the eccentricity is zero and the ellipse is just a circle; thus, a circle can be called an ellipse of zero eccentricity. In a circle, the semimajor axis would be the radius.

Next, we can make ellipses of various elongations (or extended lengths) by varying the spacing of the tacks (as long as they are not farther apart than the length of the string). The greater the eccentricity, the more elongated is the ellipse, up to a maximum eccentricity of 1.0, when the ellipse becomes “flat,” the other extreme from a circle.

The size and shape of an ellipse are completely specified by its semimajor axis and its eccentricity. Using Brahe’s data, Kepler found that Mars has an elliptical orbit, with the Sun at one focus (the other focus is empty). The eccentricity of the orbit of Mars is only about 0.1; its orbit, drawn to scale, would be practically indistinguishable from a circle, but the difference turned out to be critical for understanding planetary motions.

Kepler generalized this result in his first law and said that the orbits of all the planets are ellipses . Here was a decisive moment in the history of human thought: it was not necessary to have only circles in order to have an acceptable cosmos. The universe could be a bit more complex than the Greek philosophers had wanted it to be.

Kepler’s second law deals with the speed with which each planet moves along its ellipse, also known as its orbital speed. Working with Brahe’s observations of Mars, Kepler discovered that the planet speeds up as it comes closer to the Sun and slows down as it pulls away from the Sun. He expressed the precise form of this relationship by imagining that the Sun and Mars are connected by a straight, elastic line. When Mars is closer to the Sun (positions 1 and 2 in Figure 4 ), the elastic line is not stretched as much, and the planet moves rapidly. Farther from the Sun, as in positions 3 and 4, the line is stretched a lot, and the planet does not move so fast. As Mars travels in its elliptical orbit around the Sun, the elastic line sweeps out areas of the ellipse as it moves (the coloured regions in our figure). Kepler found that in equal intervals of time (t), the areas swept out in space by this imaginary line are always equal; that is, the area of the region B from 1 to 2 is the same as that of region A from 3 to 4.

If a planet moves in a circular orbit, the elastic line is always stretched the same amount and the planet moves at a constant speed around its orbit. But, as Kepler discovered, in most orbits that speed of a planet orbiting its star (or moon orbiting its planet) tends to vary because the orbit is elliptical.

Kepler’s Third Law

Kepler’s first two laws of planetary motion describe the shape of a planet’s orbit and allow us to calculate the speed of its motion at any point in the orbit. Kepler was pleased to have discovered such fundamental rules, but they did not satisfy his quest to fully understand planetary motions. He wanted to know why the orbits of the planets were spaced as they are and to find a mathematical pattern in their movements—a “harmony of the spheres” as he called it. For many years he worked to discover mathematical relationships governing planetary spacing and the time each planet took to go around the Sun.

In 1619, Kepler discovered a basic relationship to relate the planets’ orbits to their relative distances from the Sun. We define a planet’s orbital period, ( P ), as the time it takes a planet to travel once around the Sun. Also, recall that a planet’s semimajor axis, a, is equal to its average distance from the Sun. The relationship, now known as Kepler’s third law , says that a planet’s orbital period squared is proportional to the semimajor axis of its orbit cubed, or

When P (the orbital period) is measured in years, and a is expressed in a quantity known as an astronomical unit (AU), the two sides of the formula are not only proportional but equal. One AU is the average distance between Earth and the Sun and is approximately equal to 1.5 × 10 8 kilometers. In these units,

Kepler’s third law applies to all objects orbiting the Sun, including Earth, and provides a means for calculating their relative distances from the Sun from the time they take to orbit. Let’s look at a specific example to illustrate how useful Kepler’s third law is.

For instance, suppose you time how long Mars takes to go around the Sun (in Earth years). Kepler’s third law can then be used to calculate Mars’ average distance from the Sun. Mars’ orbital period (1.88 Earth years) squared, or P 2 , is 1.88 2 = 3.53, and according to the equation for Kepler’s third law, this equals the cube of its semimajor axis, or a 3 . So what number must be cubed to give 3.53? The answer is 1.52 (since 1.52 × 1.52 × 1.52 = 3.53). Thus, Mars’ semimajor axis in astronomical units must be 1.52 AU. In other words, to go around the Sun in a little less than two years, Mars must be about 50% (half again) as far from the Sun as Earth is.

Calculating Periods Imagine an object is traveling around the Sun. What would be the orbital period of the object if its orbit has a semimajor axis of 50 AU?   

Solution From Kepler’s third law, we know that (when we use units of years and AU)

If the object’s orbit has a semimajor axis of 50 AU ( a = 50), we can cube 50 and then take the square root of the result to get P:

Therefore, the orbital period of the object is about 350 years. This would place our hypothetical object beyond the orbit of Pluto.

Check Your Learning What would be the orbital period of an asteroid (a rocky chunk between Mars and Jupiter) with a semimajor axis of 3 AU?

Kepler’s three laws of planetary motion can be summarized as follows:

• Kepler’s first law: Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.
• Kepler’s second law: The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time.
• Kepler’s third law: The square of a planet’s orbital period is directly proportional to the cube of the semimajor axis of its orbit.

Kepler’s three laws provide a precise geometric description of planetary motion within the framework of the Copernican system. With these tools, it was possible to calculate planetary positions with greatly improved precision. Still, Kepler’s laws are purely descriptive: they do not help us understand what forces of nature constrain the planets to follow this particular set of rules. That step was left to Isaac Newton.

Applying Kepler’s Third Law Using the orbital periods and semimajor axes for Venus and Earth that are provided here, calculate P 2 and a 3 , and verify that they obey Kepler’s third law . Venus’ orbital period is 0.62 year, and its semimajor axis is 0.72 AU. Earth’s orbital period is 1.00 year, and its semimajor axis is 1.00 AU.

We can use the equation for Kepler’s third law, P 2 =  a 3 . For Venus, P 2 = 0.62 × 0.62 = 0.38 and a 3 = 0.72 × 0.72 × 0.72 = 0.37 (rounding numbers sometimes causes minor discrepancies like this). The square of the orbital period (0.38) approximates the cube of the semimajor axis (0.37). Therefore, Venus obeys Kepler’s third law. For Earth, P 2 = 1.00 × 1.00 = 1.00 and a 3 = 1.00 × 1.00 × 1.00 = 1.00. The square of the orbital period (1.00) approximates (in this case, equals) the cube of the semimajor axis (1.00). Therefore, Earth obeys Kepler’s third law.

Check Your Learning Using the orbital periods and semimajor axes for Saturn and Jupiter that are provided here, calculate P 2 and a 3 , and verify that they obey Kepler’s third law. Saturn’s orbital period is 29.46 years, and its semimajor axis is 9.54 AU. Jupiter’s orbital period is 11.86 years, and its semimajor axis is 5.20 AU.

For Saturn, P 2 = 29.46 × 29.46 = 867.9 and a 3 = 9.54 × 9.54 × 9.54 = 868.3. The square of the orbital period (867.9) approximates the cube of the semimajor axis (868.3). Therefore, Saturn obeys Kepler’s third law.

Key Concepts and Summary

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion. Kepler’s laws describe the behavior of planets in their orbits as follows: (1) planetary orbits are ellipses with the Sun at one focus; (2) in equal intervals, a planet’s orbit sweeps out equal areas; and (3) the relationship between the orbital period ( P ) and the semimajor axis ( a ) of an orbit is given by P 2 = a 3 (when a is in units of AU and P is in units of Earth years).

Douglas College Astronomy 1105 Copyright © 2017 by Douglas College Department of Physics and Astronomy, Open Stax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

15 Observations of Motion: Brahe, Kepler, and Galilei

Tycho Brahe made numerous measurements of the positions of astronomical objects until his death in 1601. His measurements were accurate to better than 1/100 of a degree.

Johannes Kepler was Tycho’s assistant. Kepler tried to obtain Tycho’s data to fit the Copernican Heliocentric Solar System Model. (Kepler’s and Tycho did not get along.) But Tycho’s data did not exactly work for a Heliocentric Solar System! So Kepler looked for a new model, and from that he developed Kepler’s Laws.

Kepler’s First Law

The planets travel around the Sun in elliptical orbits. Copernicus thought the planets moved in perfect circles, whereas Kepler defined these as ellipses, based on Brahe’s data.

Kepler’s Second Law

As a planet orbits the Sun, it sweeps out equal areas of its ellipse in equal periods of time. The closer the planet to the Sun (or its star), the faster it moves.

Kepler’s Second Law is stated as:

• v  is the orbiting object’s velocity
• a  is the semimajor axis of the object’s orbit
• P  is the sidereal period of revolution
• r  is the distance between the orbiting object and the body being orbited, such as Earth orbiting the Sun, or the Moon orbiting Earth

Kepler’s Third law

A relationship exists between the planet’s period and its distance from the Sun.

Kepler’s Third Law is stated as:

• a  is the orbiting object’s semimajor axis
• P  is the orbiting object’s period to orbit
• r  is a constant, referred to as Kepler’s constant

Introduction to Astronomy Copyright © by Lumen Learning is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

• Follow us on Facebook
• Follow us on Twitter
• Follow us on LinkedIn
• Watch us on Youtube
• Latest Explore all the latest news and information on Physics World
• Research updates Keep track of the most exciting research breakthroughs and technology innovations
• News Stay informed about the latest developments that affect scientists in all parts of the world
• Features Take a deeper look at the emerging trends and key issues within the global scientific community
• Opinion and reviews Find out whether you agree with our expert commentators
• Interviews Discover the views of leading figures in the scientific community
• Analysis Discover the stories behind the headlines
• Blog Enjoy a more personal take on the key events in and around science
• Physics World Live
• Impact Explore the value of scientific research for industry, the economy and society
• Events Plan the meetings and conferences you want to attend with our comprehensive events calendar
• Innovation showcases A round-up of the latest innovation from our corporate partners
• Collections Explore special collections that bring together our best content on trending topics
• Artificial intelligence Explore the ways in which today’s world relies on AI, and ponder how this technology might shape the world of tomorrow
• #BlackInPhysics Celebrating Black physicists and revealing a more complete picture of what a physicist looks like
• Nanotechnology in action The challenges and opportunities of turning advances in nanotechnology into commercial products
• The Nobel Prize for Physics Explore the work of recent Nobel laureates, find out what happens behind the scenes, and discover some who were overlooked for the prize
• Revolutions in computing Find out how scientists are exploiting digital technologies to understand online behaviour and drive research progress
• The science and business of space Explore the latest trends and opportunities associated with designing, building, launching and exploiting space-based technologies
• Supercool physics Experiments that probe the exotic behaviour of matter at ultralow temperatures depend on the latest cryogenics technology
• Women in physics Celebrating women in physics and their contributions to the field
• Audio and video Explore the sights and sounds of the scientific world
• Podcasts Our regular conversations with inspiring figures from the scientific community
• Video Watch our specially filmed videos to get a different slant on the latest science
• Webinars Tune into online presentations that allow expert speakers to explain novel tools and applications
• IOP Publishing
• Enter e-mail address
• Show Enter password
• Remember me Forgot your password?
• Access more than 20 years of online content
• Manage which e-mail newsletters you want to receive
• Read about the big breakthroughs and innovations across 13 scientific topics
• Explore the key issues and trends within the global scientific community
• Choose which e-mail newsletters you want to receive

Reset your password

Please enter the e-mail address you used to register to reset your password

Registration complete

Thank you for registering with Physics World If you'd like to change your details at any time, please visit My account

• Personalities
• Opinion and reviews

Kepler and Tycho Brahe: the odd couple

The Nobleman and His Housedog: Tycho Brahe and Johannes Kepler – The Strange Partnership that Revolutionised Science Kitty Ferguson 2002 Review 372pp £15.99/$31.98hb

Kitty Ferguson presents a double biography with a single theme: the founding of modern astronomy. Johannes Kepler is rightly acclaimed as the father of modern astronomy, but he could not have achieved this distinction without Tycho Brahe’s observational data, which are unanimously considered the most accurate and comprehensive in pre-telescopic astronomy.

Science needs imaginative, daring theorists who can soar high in the world of the almost impossible; Kepler belonged to this tribe. Science also needs accurate observational data to keep this search bound to the ground; Tycho’s data did just this. But this merging of theory and experiment was by no means straightforward or easy.

The Nobleman and His Housedog recounts the strange and intricate way in which this unusual collaboration came about. The story begins with Tycho Brahe – the Danish nobleman of the book’s title – who was 25 years older than Kepler. Breaking with the established traditions of his society, which frowned upon any nobleman engaging in a scientific career, Tycho had been interested in astronomical observations since his youth.

It was from his home observatory at Herrevad that he observed the well known nova of 1572, which challenged the Aristotelian doctrine of the immutability of the celestial world. Later he found lavish favour with King Frederick II of Denmark, who went all out to help him set up an extravagant state-of-the-art observatory at Uraniborg and the subterranean observatory of Stjerneborg on the island of Hven.

However, Tycho fell badly out of grace with King Christian IV – Frederick’s successor – and was forced to leave Denmark in disgrace in 1597. Soon Emperor Rudolph II of the Holy Roman Empire welcomed him in Prague and extended generous support to set up an observatory at nearby Benatky. Unfortunately, Tycho’s life and activities at Benatky were cut short by his rather untimely death in 1601, although he left a priceless legacy in the form of the most accurate astronomical observations – the fruit of 38 years of tireless, ingenious labour.

Physics World Careers

Providing valuable careers advice and a comprehensive employer directory

• Everyday science

Doughnuts reveal life's secrets

• Culture, history and society

European best-sellers in 2002

Discover more from physics world.

• Quantum mechanics

Entangled entities: Bohr, Einstein and the battle over quantum fundamentals

• Particle and nuclear

Peter Higgs: Nobel-prize-winning particle theorist dies aged 94

• Stars and solar physics

Dispatches from the Great North American eclipse of 2024

Related jobs, msc courses in nuclear science and technology, engineering manager, senior aerospace engineer, related events.

• Mathematics and computation | Conference World Robotics Conference 2024 15—17 April 2024 | Berlin, Germany
• Biophysics and bioengineering | Workshop Information Processing, Noise, and Adaptation in Living Systems 15—19 April 2024 | Dresden, Germany
• Biophysics and bioengineering | Workshop Interdisciplinary challenges in non-equilibrium physics: from soft to active, biological and complex matter (IntCha24) 22—26 April 2024 | Dresden, Germany

• Studierende/Studierendenportal
• Beschäftigte/Dienstleistungsportal
• Stellenbewerber
• Forschungsdatenbank
• Vorlesungsverzeichnis
• Mitarbeitendensuche
• Studierendensuche
• Stellenangebote
• Vermietung und Verpachtung

• Anniversary of the University 2019
• Tycho Brahe - Exhibition
• Brahe and Kepler
• World models
• The island Hven
• Tycho Brahe as poet
• Rudolphine Tables
• The legacy of Tycho Brahe

Tycho Brahe and Johannes Kepler

Brahe was so enthusiastic „Mysterium Cosmographicum“ [„Secret of the World“], Kepler’s debut work, that he invited him to for a visit to Prague. Brahe hoped to create a new world model with the help of Kepler’s ideas and mathematical skills, which is why he appointed Kepler assistant at the Prague court. Still this cooperation turned out to be difficult. Kepler, the theorist, and Brahe, the practitioner, were unable to agree on a common world model. Brahe considered the earth as the centre orbited by the sun, which, again, is orbited by the planets. Kepler, on the contrary, supported the Copernican system that considers the sun as the centre, which is orbited by all planets. Brahe’s sudden death in 1601 also abruptly ended his project of compiling planetary position prediction tables and rules prediction, known as Rudolphine Plates today. It was Kepler who finally completed his master’s work.

Brahe’s Exhumation

Theories have kept on weaving themselves around Brahe’s sudden death. And it was Johannes Kepler who was in the focus of the accusations. He was accused of having poisoned his master to get access to his precious recordings.

In 2012, Professor Ludwig Jonas, who had worked for 40 years at the University of Rostock after finalizing his biology studies here, was able to refute these accusations by means of a facial hair analysis. According to this, mercury was found in the hair only, but not in hair shaft and hair roots. These investigation results indicate long-term poisoning resulting from many years of handling chemicals. The study published by Ludwig Jonas, acquitted Johannes Kepler of assassination, centuries after his death.

Kepler completed Brahe’s work

Johannes Kepler used Brahe’s recordings for studying the planetary motions of Mars. With these investigations, he intended to plausibly explain the apparent loop movements and to achieve a more precise predictability of planetary positions in a next step. The laws developed by him have remained valid until today.

Kepler’s laws

• The planetary orbits are ellipses with the sun as focal point.
• The connection line planet – sun underlines covers same surfaces in the same time.
• The squares of the planet’s orbital periods are like the cube of their average distance from the sun.

In remembrance of Brahe and Kepler In the Prague district Hradcany, a bronze sculpture reminds of the achievements of Tycho Brahe and Johannes Kepler.

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

3.1: Observations of Motion- Brahe, Kepler, and Galilei

• Last updated
• Save as PDF
• Page ID 64077

Tycho Brahe made numerous measurements of the positions of astronomical objects until his death in 1601. His measurements were accurate to better than 1/100 of a degree.

Johannes Kepler was Tycho’s assistant. Kepler tried to obtain Tycho’s data to fit the Copernican Heliocentric Solar System Model. (Kepler’s and Tycho did not get along.) But Tycho’s data did not exactly work for a Heliocentric Solar System! So Kepler looked for a new model, and from that he developed Kepler’s Laws.

Kepler’s First Law

The planets travel around the Sun in elliptical orbits. Copernicus thought the planets moved in perfect circles, whereas Kepler defined these as ellipses, based on Brahe’s data.

Kepler’s Second Law

As a planet orbits the Sun, it sweeps out equal areas of its ellipse in equal periods of time. The closer the planet to the Sun (or its star), the faster it moves.

Kepler’s Second Law is stated as:

• v is the orbiting object’s velocity
• a is the semimajor axis of the object’s orbit
• P is the sidereal period of revolution
• r is the distance between the orbiting object and the body being orbited, such as Earth orbiting the Sun, or the Moon orbiting Earth

Kepler’s Third law

A relationship exists between the planet’s period and its distance from the Sun.

Kepler’s Third Law is stated as:

• a is the orbiting object’s semimajor axis
• P is the orbiting object’s period to orbit
• r is a constant, referred to as Kepler’s constant
• Provided by : Florida State College at Jacksonville. License : CC BY: Attribution

previous    index    next

Tycho Brahe and Johannes Kepler

(Condensed Version: see below for links to fuller version)

Michael Fowler, University of Virginia

These two colorful characters made crucial contributions to our understanding of the universe: Tycho's observations were accurate enough for Kepler to discover that the planets moved in elliptic orbits, and his other laws, which gave Newton the clues he needed to establish universal inverse-square gravitation.

What you should know:

Tycho Brahe (1546-1601), from a rich Danish noble family, was fascinated by astronomy, but disappointed with the accuracy of tables of planetary motion at the time. He decided to dedicate his life and considerable resources to recording planetary positions ten times more accurately than the best previous work. After some early successes, and in gratitude for having his life saved by Tycho's uncle, the king of Denmark gave Tycho tremendous resources: an island with many families on it, and money to build an observatory. (One estimate is that this was 10% of the gross national product at the time!) Tycho built vast instruments to set accurate sights on the stars, and used multiple clocks and timekeepers.

He achieved his goal of measuring to one minute of arc. This was a tremendous feat before the invention of the telescope. His aim was to confirm his own picture of the universe, which was that the Earth was at rest, the sun went around the Earth and the planets all went around the sun - an intermediate picture between Ptolemy and Copernicus.

Johannes Kepler (1571-1630) believed in Copernicus' picture. Having been raised in the Greek geometric tradition, he believed God must have had some geometric reason for placing the six planets at the particular distances from the sun that they occupied. He thought of their orbits as being on spheres, one inside the other. One day, he suddenly remembered that there were just five perfect Platonic solids, and this gave a reason for there being six planets - the orbit spheres were maybe just such that between two successive ones a perfect solid would just fit. He convinced himself that, given the uncertainties of observation at the time, this picture might be the right one. However, that was before Tycho's results were used. Kepler realized that Tycho's work could settle the question one way or the other, so he went to work with Tycho in 1600. Tycho died the next year, Kepler stole the data, and worked with it for nine years.

He reluctantly concluded that his geometric scheme was wrong. In its place, he found his three laws of planetary motion :

I The planets move in elliptical orbits with the sun at a focus.

II In their orbits around the sun, the planets sweep out equal areas in equal times .

III The squares of the times to complete one orbit are proportional to the cubes of the average distances from the sun .

These are the laws that Newton was able to use to establish universal gravitation.

Kepler was the first to state clearly that the way to understand the motion of the planets was in terms of some kind of force from the sun. However, in contrast to Galileo, Kepler thought that a continuous force was necessary to maintain motion, so he visualized the force from the sun like a rotating spoke pushing the planet around its orbit.

On the other hand, Kepler did get right that the tides were caused by the Moon's gravity. Galileo mocked him for this suggestion.

A much fuller treatment of Tycho Brahe and Johannes Kepler can be found in my 1995 notes:

Links to: Tycho Brahe ,    Kepler ,   More Kepler

• Up to about this time people that studied science tended to be rich, bored, upper class that did it as a hobby.
• More and more people were starting to study science as a career.
• They also started setting up what we would today think of as basic research labs.
• In this section we look at two people that were doing there work during these changing times, and neither of them fit perfectly into these two categories, but both of them had elements of this change in them.

Tycho Brahe (1546 – 1601)

Born in modern day Sweden, Tycho Brahe was not satisfied with the imperfections he saw in the measurements of stars and planets.

• Most where in fact from a book written by an ancient Greek named Ptolemy about 1400 years earlier!
• Brahe was sure that he could do better calculations.
• To finance an observatory Brahe became buddy-buddy with Frederick II, King of Denmark!
• Frederick II liked Brahe’s ideas so much that he gave him an entire island called Hven off the coast of Denmark. That way Brahe would be away from all the bright city lights.
• He also gave Brahe the money to build the observatory on the island, which was named Uraniborg ("Fortress of the Heavens").

Brahe spent the next twenty years making observations from this location that were more precise and detailed than any that had ever been done before.

• Finally, Frederick II died and Brahe couldn’t convince the new king to support his work. Uranienborg was shut down and Brahe moved away to live near Prague.
• Before he could finish building a new observatory Brahe died.

Brahe was one of the new types of careful, professional scientists that were starting to appear.

• Unfortunately, he wasn’t very good at coming up with theories.
• He was basically a careful observer with books of collected data that he didn’t know what to do with.

He also had a rather interesting life…

• They had a duel and part of Brahe’s nose was cut off (ouch!)
• For the rest of his life he wore an artificial nose made out of copper (yuck!)
• Because his hostess kept talking, he couldn't leave the table to go to the bathroom (this would have been very rude in that society).
• He ruptured his bladder and died several days later.

Johannes Kepler (1571 – 1630)

Johannes Kepler came from a very poor family (his dad was a common soldier).

• He was part of the new breed of scientists, people who made it their career to study science.
• Although he still had patrons (rich people that give you money so you’ll do stuff like write “Dedicated to…” in the cover of your next book), he also made money directly from using his knowledge.

Kepler was known for being a little odd.

• According to some accounts he once walked into a lake, and once walked clear over to a neighboring town.
• He also had a theory about the planets being attached to crystal spheres and that if you listened carefully you could hear them hum as they moved.

Kepler was also known for his way of coming up with scientific theories… come up with a whole bunch, even wacky ones, and eventually you should stumble on the correct one.

• In 1600 he became Brahe’s assistant (just one year before Brahe’s death).
• This was a very fortunate partnership, since Brahe had a lifetime worth of data, and Kepler was good at coming up with theories.
• Although Brahe died a short time later, Kepler still used a great deal of his data to form the basis of his later work.

• EO Explorer

• Global Maps

The Science: Orbital Mechanics

Kepler’s laws of planetary motion.

While Copernicus rightly observed that the planets revolve around the Sun, it was Kepler who correctly defined their orbits. At the age of 27, Kepler became the assistant of a wealthy astronomer, Tycho Brahe, who asked him to define the orbit of Mars. Brahe had collected a lifetime of astronomical observations, which, on his death, passed into Kepler’s hands. (Brahe, who had his own Earth-centered model of the Universe, withheld the bulk of his observations from Kepler at least in part because he did not want Kepler to use them to prove Copernican theory correct.) Using these observations, Kepler found that the orbits of the planets followed three laws.

Like many philosophers of his era, Kepler had a mystical belief that the circle was the Universe’s perfect shape, and that as a manifestation of Divine order, the planets’ orbits must be circular. For many years, he struggled to make Brahe’s observations of the motions of Mars match up with a circular orbit.

Eventually, however, Kepler noticed that an imaginary line drawn from a planet to the Sun swept out an equal area of space in equal times, regardless of where the planet was in its orbit. If you draw a triangle out from the Sun to a planet’s position at one point in time and its position at a fixed time later—say, 5 hours, or 2 days—the area of that triangle is always the same, anywhere in the orbit. For all these triangles to have the same area, the planet must move more quickly when it is near the Sun, but more slowly when it is farthest from the Sun.

This discovery (which became Kepler’s second law of orbital motion) led to the realization of what became Kepler’s first law: that the planets move in an ellipse (a squashed circle) with the Sun at one focus point, offset from the center.

Kepler’s third law shows that there is a precise mathematical relationship between a planet’s distance from the Sun and the amount of time it takes revolve around the Sun. It was this law that inspired Newton, who came up with three laws of his own to explain why the planets move as they do.

Newton’s Laws of Motion

If Kepler’s laws define the motion of the planets, Newton’s laws define motion. Thinking on Kepler’s laws, Newton realized that all motion, whether it was the orbit of the Moon around the Earth or an apple falling from a tree, followed the same basic principles. “To the same natural effects,” he wrote, “we must, as far as possible, assign the same causes.” Previous Aristotelian thinking, physicist Stephen Hawking has written, assigned different causes to different types of motion. By unifying all motion, Newton shifted the scientific perspective to a search for large, unifying patterns in nature. Newton outlined his laws in Philosophiae Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy,”) published in 1687.

Law I. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed theron.

In essence, a moving object won’t change speed or direction, nor will a still object start moving, unless some outside force acts on it. The law is regularly summed up in one word: inertia.

Law II. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Newton’s second law is most recognizable in its mathematical form, the iconic equation: F=ma. The strength of the force (F) is defined by how much it changes the motion (acceleration, a) of an object with some mass (m).

Law III. To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

As Newton himself described: “If you press a stone with your finger, the finger is also pressed by the stone.”

Within the pages of Principia, Newton also presented his law of universal gravitation as a case study of his laws of motion. All matter exerts a force, which he called gravity, that pulls all other matter towards its center. The strength of the force depends on the mass of the object: the Sun has more gravity than Earth, which in turn has more gravity than an apple. Also, the force weakens with distance. Objects far from the Sun won’t be influenced by its gravity.

Newton’s laws of motion and gravity explained Earth’s annual journey around the Sun. Earth would move straight forward through the universe, but the Sun exerts a constant pull on our planet. This force bends Earth’s path toward the Sun, pulling the planet into an elliptical (almost circular) orbit. His theories also made it possible to explain and predict the tides. The rise and fall of ocean water levels are created by the gravitational pull of the Moon as it orbits Earth.

Einstein and Relativity

The ideas outlined in Newton’s laws of motion and universal gravitation stood unchallenged for nearly 220 years until Albert Einstein presented his theory of special relativity in 1905. Newton’s theory depended on the assumption that mass, time, and distance are constant regardless of where you measure them.

The theory of relativity treats time, space, and mass as fluid things, defined by an observer’s frame of reference. All of us moving through the universe on the Earth are in a single frame of reference, but an astronaut in a fast-moving spaceship would be in a different reference frame.

Within a single frame of reference, the laws of classical physics, including Newton’s laws, hold true. But Newton’s laws can’t explain the differences in motion, mass, distance, and time that result when objects are observed from two very different frames of reference. To describe motion in these situations, scientists must rely on Einstein’s theory of relativity.

At slow speeds and at large scales, however, the differences in time, length, and mass predicted by relativity are small enough that they appear to be constant, and Newton’s laws still work. In general, few things are moving at speeds fast enough for us to notice relativity. For large, slow-moving satellites, Newton’s laws still define orbits. We can still use them to launch Earth-observing satellites and predict their motion. We can use them to reach the Moon, Mars, and other places beyond Earth. For this reason, many scientists see Einstein’s laws of general and special relativity not as a replacement of Newton’s laws of motion and universal gravitation, but as the full culmination of his idea.

• Air University. (2003, August). Orbital Mechanics. Space Primer. Accessed May 22, 2009.
• Blitzer, L. (1971, August). Satellite orbit paradox: A general view. American Journal of Physics, 39, 882-886.
• Gleick, J. (2003). Isaac Newton. New York: Vintage Books.
• Gribbon, J. (2008). The Scientists: A History of Science Told Through the Lives of Its Greatest Inventors. New York: Random House.
• Hawking, S. (2004). The Illustrated on the Shoulders of Giants. Philadelphia: Running Press.
• Iannotta, B., and Malik, T. (2009, February 11). U.S. satellite destroyed in space collision. Accessed May 22, 2009.
• Komoma. GPS Satellite Orbits. Accessed May 22, 2009.
• Wolfe, J., and Hatsidimitris, G. (2005). Einstein Light. University of New South Wales. Accessed June 11, 2009.
• About Orbits
• Planetary Motion
• Flying Steady

• No category

Brahe’s Observations and Kepler’s Laws of Planetary Motion

Related documents

Add this document to collection(s)

You can add this document to your study collection(s)

Add this document to saved

You can add this document to your saved list

Suggest us how to improve StudyLib

(For complaints, use another form )

Input it if you want to receive answer

Disclaimer: The following material is being kept online for archival purposes.

Although accurate at the time of publication, it is no longer being updated. the page may contain broken links or outdated information, and parts may not function in current web browsers., (10)  kepler and his laws  .

Author and Curator:   Dr. David P. Stern      Mail to Dr.Stern:   stargaze ("at" symbol) phy6.org . Last updated: 12.17.2001

Above is background material for archival reference only.

• Anatomy & Physiology
• Astrophysics
• Earth Science
• Environmental Science
• Organic Chemistry
• Precalculus
• Trigonometry
• English Grammar
• U.S. History
• World History

... and beyond

• Socratic Meta
• Featured Answers

How did Tycho Brahe and Kepler employ the scientific method?

How did Tycho Brahes work help Kepler develop his laws of planetary motion?

Kepler was Brahe's assistant. He continued to analyze Brahe's data after Brahe's died. Kepler determine that the planets revolve around the sun in elliptical, or ovalshaped, orbits. He also developed three laws that describe planetary motion. These laws are still used today. Hope I explained this clearly(:

Lydia Schulist ∙

Add your answer:

How many laws of planetary motion did Johannes Kepler discover?

3 laws' of planetary motion

How are Brahe and Kepler related?

They were both early observational astronomers. Some people believe that after Brahe's death, Kepler 'stole' his data and used it to develop Kepler's three laws of planetary motion.

How did Brahe's work help Kepler develop his laws of planetary motion?

Kepler was Brahe's assistant. He continued to analyze Brahe's data after Brahe's died. Kepler determine that the planets revolve around the sun in elliptical, or ovalshaped, orbits. He also developed three laws that describe planetary motion. These laws are still used today. Hope I explained this clearly(:

Who is responsible for developing the three laws of planetary motion?

I'm pretty sure you're thinking of Johannes Kepler.

What is German astronomer who devised three laws of planetary motion in the seventeenth century?

Johannes Kepler

How did Kepler us tycho brahe's data?

Kepler used Tycho Brahe's data by developing his Laws of planetary motion and by analyzing his observations about planet's orbit.! :D

Who formuleted the laws of planetary motion?

The laws of planetary motion are attributed to Kepler.

Who was the brilliant student of Tycho Brache that formulated the three laws of planetary motion?

No. Kepler discovered the laws using Tycho Brahe's data.

What did Kepler formulate?

His laws of planetary motion.

Who discovered the planetary motion?

What are the eponymous laws of planetary motion.

"Eponymous" means "Same name". The laws of planetary motion were devised by Johannes Kepler, and are generally called "Kepler's Laws".

What was Kepler's major area of study?

Planetary motion.

Who discovered laws of planetary motion?

Who discovered the idea of planetary motion, what developed the three law of planetary motion.

Top Categories