FEATURE: Keplers laws

Kepler’s laws

Nature uses as little as possible of anything

Johannes Kepler
 

I measured the skies, now the shadows I measure, sky bound was the mind, earth-bound the body rests

Kepler’s epitaph

Johannes Kepler’s three laws of planetary motion are a cornerstone of modern physics they describe the elliptical paths taken by planets around the sun, the time it takes to complete one orbit and how distant planets more slowly than nearby ones. These laws are applied today in the detection of dark matter and can also be applied to planets orbiting distant stars. Kepler 1571-1630 grew up in Germany with his mother living at his grandfather’s inn.  He became interested in astronomy as a child and by the time he was ten he had recorded a comet and a lunar eclipse in his diary.  Kepler studied at the university of Tubingen and went on to teach mathematics at Graz.  Kepler thought that god had created the universe according to a mathematical plan.  His theory of cosmology was published in ‘the sacred mystery of the cosmos’ he later assisted Tycho Brahe at his observatory outside Prague inheriting his position as imperial mathematician in 1601.  There Kepler prepared horoscopes and analysed Tycho’s astronomical tables publishing his theories of non-circular orbits and the first and second laws of planetary motion in ‘New Astronomy’ the third law of planetary motion was published in ‘harmony of the worlds’

                Modern astronomy began in 1609 with the publication of his masterwork ‘Astronomia nova’ Kepler had derived equations to describe the orbits of the planets based on careful records of the motions of mars taken by Tycho Brahe a Danish astronomer and aristocrat for whom Kepler worked as an instrument builder.  Kepler’s measurements of mars where much more accurate than had been achieved before.

Kepler’s first law

Kepler’s first law states that planets trace out an elliptical path with the sun at one focus of the ellipse. Until this radical theory was put forward everyone believed the orbits of planets to be perfect circles, it was thought that nature loved perfection and abhorred deviation from it Kepler inherited this belief at first imagining that planets were arranged about the sun in a nested series of crystal spheres spaced according to mathematical ratios derived from polygons.  But Tycho’s data caused him to change his mind.  When viewed from earth Mars's speed seems to seems to vary considerably it also seems to take backward steps drawing out loops in the sky.  Before Kepler many had tried to explain away the retrograde movements by adding small extra circles known as epicycles to large circular orbits.  In fact these days the phrase adding epicycles is a byword for bad science.  Kepler spotted that an ellipse did a much better job of explain Mars’s motion and to realize that it is because we are viewing the solar system from a moving platform that the other planets seem to back track.

Kepler’s second law

In his second law Kepler details how quickly a planet moves around its orbit; as it progresses along its elliptical path, it sweeps out a segment of equal area in an equal time. The segment like a slice of pie is measured by drawing a line from the planet to the sun and again at a given period.  When the planet is close to the sun it moves quickly and it draws out a broad pie slice; when it is further from the sun it travels more slowly subtending a smaller angle in the same amount of time. But states Kepler’s second law, the area of this long thin pie slice is the same as that of the short fat one.  Kepler figured this out by noting how fast mars moved around its orbit

Kepler’s third law

Kepler’s third law goes one step further and tells us how the orbital periods scale up for different sized ellipses at a range of distances from the sun.  It states that the squares of the orbital periods are proportional to the cube power of the longest axis of the elliptical orbit.  The larger the elliptical orbit, the slower the period of time taken to complete an orbit, So planets further from the sun orbit more slowly than nearby planets.  Mars takes nearly two Earth years to go around the Sun, Saturn 29 years and Neptune 165 years mercury circles the sun in just 80 earth days.  If Jupiter travelled at the same speed it would take 3.5 Earth years to complete an orbit when in fact it takes 12.

Modern man

Kepler’s laws have stood the test of time. They apply equally to anybody in orbit around another from comets asteroids and moons in our solar system to planets around other stars and even artificial satellites whizzing around the Earth.  Kepler succeeded in unifying the principles into geometric patterns of nature.  It took Newton to unify these laws into a universal theory of gravity

580 BC	Pythagoras suggests that planets orbit on the surface of perfect spheres
150	Ptolemy explains retrograde motions with epicycles
1543	Copernicus proposes that planets orbit the Sun
1576	Tycho Brahe maps planets positions
1609	Kepler publishes first and second laws
1619	Kepler publishes his third law
1687	Newton proposes theory of gravity
2009	Kepler satellite launched by NASA to find planets around distant stars