Johannes-Kepler

“We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way.”
-Johannes Kepler, 1619.

Image credit: Kevin Shearer (instagram: k.d.s.photography)

How Do the Planets Stay in Orbit?

The manner in which stars and planets form is not well understood, but according to the most popular hypothesis (nebular) of cosmic evolution; all planetary and stellar systems are born from the gravitational collapse of giant interstellar clouds.

Solar system formation happens when part of a molecular cloud begins to contract under its own gravitational force. As gravity forces the dense core to become smaller, it spins faster and faster –due to the conservation of angular momentum. The collisions between particles in the molecular cloud gradually reduce random motions, only circular orbits remain and as a result the contracting cloud flattens into a spinning pancake shape (protoplanetary disk) with a bulge at the center (protostar). All orbital motion of the planets – including the spin, is due to this original angular momentum.

The reason why the planets stay in their orbits is because the force of gravity between the planet and the Sun provides a centripetal force: the Sun pulls the planets in orbit around it with the force of gravity that is strong enough to divert the planets from a straight line path. At the same time, the angular momentum of the planets gives them a tangential velocity that prevents the Sun from pulling them in. Isaac Newton’s law of universal gravitation states that everything with mass generates gravity, and like all objects with mass, planets have a tendency to resist changes to their speed and direction. This tendency is called inertia.The combination of the centripetal acceleration that gravity provides and the tangential velocity that inertia provides is what keeps the planets in stable orbit.

Newton’s laws of motion and law of gravity explain Kepler’s three laws of orbital motion which govern the orbits of planets, satellites, comets, asteroids, stars and even galaxies. Kepler’s laws apply to any object, orbiting another object, under the influence of gravity. So, what are these universal laws?

Kepler’s first of three laws states that each planet moves in an elliptical orbit, with the Sun at one focus (The Law of Ellipses):

Kepler’s second law: the orbital speed changes regularly as the distance from the Sun changes, meaning that when the planet is far away from the Sun, it does not move as fast as when it is close to the Sun (The Law of Areas). This implied that whatever force was moving the planet weakened with distance, and this led to the realization of what became Kepler’s first law: that the planets move in an ellipse:

Kepler’s third law (The Law of Harmonies) can be derived from Newton’s laws of motion and the universal law of gravitation. The third law shows that orbital period increases with orbital radius:

Kepler’s laws clearly show the effects of gravity on orbital motion. Using these laws and calculus (which Newton invented), Newton was able to prove that the planets orbit the Sun because they are influenced by its gravity.

Harmonices Mundi (Harmony of the World) by Johannes Kepler, 1619

In Harmonices Mundi (1619), Kepler attempted to explain the harmony of the world and contained what is known today as his third law. The work was founded on geometry, from which Kepler derived first a theory of musical harmony and then a cosmology of the heavens and the earth. Kepler attempted to find common rules between music and movement in the solar system. His music of the spheres is based on the relative maximum and minimum angular velocities of the planet measured from the sun. Using his theories, Kepler allotted to the planets musical intervals and musical motion.

The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway” -Kepler.

Johannes Kepler (1571-1630) was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his laws of planetary motion based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton’s theory of universal gravitation.

Prints of Harmonices Mundi are available here. Does anyone know what “Hiclocum haber eriam” means?

3

Astronomer Johannes Kepler was born 442 years ago today (27 December) and is commemorated by Google

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer and a key figure in the 17th century scientific revolution. His major contribution to science was the discovery that the earth and other planets travel around the sun in an elliptical orbit. He was also the inventor of the Keplerian Telescope, an upgraded version of the refracting telescope.

The dance of Venus as illustrated by its discoverer Johannes Kepler

The Dance of Venus. An accurate scientific drawing of Venus amazing pattern around the Earth Did you know that Venus, our closest planetary neighbour, draws a beautiful fivefold pattern around Earth? She does this every eight years.

Interesting article on the topic Venus, the Heart and the Rose

theparisreview.org
Signed, Sealed, O’Connored, and Other News
Charlotte Strick’s concept for Flannery O’Connor postage stamps. Image via Work in ProgressThe USPS, in its infinite wisdom, has finally put Flannery O’Connor on a postage stamp, but it’s kind of an ugly one. (Peacock feathers have never more resembled dune grasses.) Our art editor Charlotte Strick took a stab at a redesign: “I thought... Read More »
By Dan Piepenbring

Flannery O’Connor gets a postage stamp, Max Beerbohm knows his way around a sentence, and Johannes Kepler’s “Somnium” gets illustrated. Read more of today’s arts and culture news.

2

On the 15 November 1630, German astronomer Johannes Kepler died aged 58.

Kepler formulated three major laws of planetary motion which enabled Isaac Newton to devise his  3rd Law - For every action, there is an equal and opposite reaction.

Working form the carefully measured positions of the planets, Kepler mathematically deduced three relationships from the data: 1) the plants move in elliptical orbits with the Sun at one focus; 2) the radius vector sweeps out equal areas in equal times; and 3) for two planets the squares of their periods are proportional to the cubes of their mean distances from the Sun.

We are lucky enough to have a first edition of Kepler’s ‘Astronomia Nova’ (1609) within the Rare Book Collection of the Ri & thought that we would give it a little outing in the Faraday Theatre to celebrate the life of this amazing individual.

Johannes Kepler - Geometrical Harmonies in the Perfect Solids, “Harmonices Mundi”, 1619.

Kepler was convinced “that the geometrical things have provided the Creator with the model for decorating the whole world”. In Harmony, he attempted to explain the proportions of the natural world - particularly the astronomical and astrological aspects - in terms of music. The central set of “harmonies” was the Musica Universalis or “Music of the Spheres”.

Kepler began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler’s solids.
Harmony resulted from the tones made by the souls of heavenly bodies - and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work, Kepler dealt with planetary motions, especially relationships between orbital velocity and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler treated them much more precisely and attached new physical significance to them.