In high school, physics and mathematics were speaking clearly to me in a language that helped explain a piece of the world I struggled to understand; I had many unanswered questions. Later at many academic institutions, the choices I made continued to satisfy my ongoing curiosity. Over the course of my training, Johannes Kepler is one of many names whose scientific work made “sense” and provided some “ordered logic” to my (naive and incomplete) perception of “illogic” and “nonsense.”
What I didn’t know is that decades later, I’m interested in discovering and finding the physical traces for those names. I still have questions, but they no longer involve difficult calculations. Instead, it’s about the “math” of how individuals reach their destinations.
I’m on a train heading out from Stuttgart, not to the famous car museums, but to a town where Johannes Kepler was born. There’s no doubt in my mind this has become a kind of pilgrimage.
With S-Bahn Stuttgart S6 train service, Weil der Stadt is a 40-minute trip from Stuttgart.
Kepler-Denkmal (1870) am Marktplatz / Kepler memorial (1870) at the town’s market square.
Inauguration of the Kepler memorial on 24 June 1870. Stadtmuseum (town museum) collection.
In Weil der Stadt, the Kepler-Museum is inside the house where Johannes Kepler was born in 1571. In 1576, the Kepler family moved out from Weil der Stadt and to the nearby town of Leonberg. The museum not only summarizes Kepler’s timeline but also highlights a number of key influences on Kepler, as well as his scientific contributions.
Copernicus view: the heliocentric model of the solar system; idea also attributed to Greek astronomer Aristarch of Samos from 3rd-century BCE.
Aware of Copernicus’ work, Kepler’s own thoughts and ideas were greatly influenced by the Copernicus model of a Sun-centric solar system.
Undoubtedly thanks to the long arduous work by Tycho Brahe, Kepler’s 1627 orbit-data tables for the planets were the most accurate of its time.
With the introduction of the “logarithm” as a mathematical tool by John Napier in 1617, Kepler realized his own calculations became simpler (because, power laws!) and published supplementary data using logarithms.
Celestial mechanics, Kepler’s 1st Law. “Each planet’s orbit is in the shape of an ellipse with the Sun at one of the two foci.”
Celestial mechanics, Kepler’s 2nd Law. “An object in an elliptical orbit around the Sun sweeps out equal areas in equal intervals of time.”Celestial mechanics, Kepler’s 3rd Law. “For an object in an elliptical orbit around the Sun, the time to complete one full orbit is U (T) and the ellipse’s semi-major axis (or average distance) is A. The relationship between U and A is that the square of the period (U^2) is directly proportional to the cube of the average distance (A^3).”
“Keplerstadt: Weil der Stadt.” Inside Weil der Stadt Bahnhof.
I made all photos above with an iPhone15 on 21 Jul 2024. This post composed with Jetpack for iOS appears on Fotoeins Fotografie at fotoeins DOT com.
When I moved to Heidelberg in 2001, I wondered about the origins of the name of the German federal state Baden-Württemberg. I learned about Baden, a strip of land with French roots and bordering the Rhine river. But where was Württemberg?
In Stuttgart today, I went up a hill on which there used to be a family’s ancestral castle. What replaced the castle is a sepulchral memorial chapel, which today masters a grand view of Stuttgart city and the Neckar river valley, as well as vineyards surrounding the hill.
The name Wirtemberg and subsequently Württemberg applied to the area, region, and now, the German federal state. It’s no surprise Stuttgart is the state capital city (Landeshauptstadt).
In Stuttgart’s Rotenberg, the Württemberg family once had their home on the top of this hill. Burg Wirtemberg was first established c. 1080 AD/CE and demolished in 1819 to make way for the chapel seen in the image above.
In 1824, a memorial chapel in the classic architectural style replaced the ancestral castle and home of the Württemberg family.
“Die Liebe höret nimmer auf.” (Love never dies): above the main portal is this message from King Wilhelm I to his deceased wife Queen Katharina.
Chapel interior.
Chapel ceiling.
Crypt below ground.
Final places for King Wilhelm & Queen Katharina.
Outside the chapel, facing west towards the inner city.
Outside the chapel, facing southeast and down towards Uhlbach (centre-right).
I made all photos above with an iPhone15 on 20 Jul 2024. This post composed with Jetpack for iOS appears on Fotoeins Fotografie at fotoeins DOT com.
A tiny church stands proudly in a sub-alpine environment surrounded with meadows, with a winding road below and solid rock pyramids above. Not bad, actually, for a fixed-lens camera and digital zoom.
The hiking paths up to Wamberg are steep, but there is the option of the Eckbauer aerial-way or cable-car to cut some of that time and effort. I’m suitably lazy on the ascent, but the steep descent exacts a cost on wobbly knees and shaky hammies and calves. I’m gettin’ old, and I already recognize these “mountain days” are lookin’ scant for the future.
Ascent on the Eckbauer cable-car; over Olympic ski-jump & Garmisch-Partenkirchen.
Morning light, facing west.
A private house on Eckbauer summit.
Haymaking above Garmisch-Partenkirchen.
I like to think of this as a gateway of sorts.
Wamberg, its church just in view.
A signature snap of Wamberg’s St. Anna, in haymaking season.
Wamberg, first mentioned in 12th-century AD/CE.
St. Anna inaugurated in 1720. Sundial reads “1pm”, at 1336h CEDT.
Facing west, the steep descent on foot begins.
I made all photos above with an iPhone15 on 19 Jul 2024. This post composed with Jetpack for iOS appears on Fotoeins Fotografie at fotoeins DOT com.
Today, I‘m in the midst of Wetterstein mountains in the Northern Limestone Alps to gain new and different perspectives on the tall limestone massif that is the highest mountain in Germany. Here at the border region, it’s easy to get around by train between Germany’s Garmisch-Partenkirchen and Austria’s Lermoos.
Eibsee cable car to Zugspitze: 1st ascent of the day, only for aerialway- & summit-employees.
730am, quiet and chill on the lake; Zugspitze at centre-right.
Grubighütte
Ascent on the Grubig II.
View of Zugspitze massif from the Grubig II mountain station, next to the Grubig lodge.
Thunderhead forming over Zugspitze; next set of photos below are from the area of light green in the valley floor below (between Lermoos and Ehrwald).
Loisachweg
The view from Lermoos: Alps formed by the northerly drift by continental Africa into continental Europe.
Lermooser Moos (Lermoos Marsh): river marsh plains here and graded gravel roads are ideal for hiking and biking.
The grey-white chalky rock that is limestone means that the rock seen elevated today was once sitting at the bottom of an ancient ocean.
I surpassed 700 km of total walking distance on travel day 72. I made all photos above with an iPhone15 on 18 Jul 2024. This post composed with Jetpack for iOS appears on Fotoeins Fotografie at fotoeins DOT com.
Travel day 70, Euro day 69, and Vienna day 36. Morning wake-up in Vienna’s 6., and I’m sleeping tonight among the Wetterstein mountains.
Euro24 in Germany is done and dusted, although I didn’t watch any of the matches because I’d already spent time and energy on the ICC T20 World Cup and that extraordinary up-and-down final between India and South Africa. Time to head back into Germany for the third and final leg: but first, the mountains.
Wien Hauptbahnhof: Südtiroler Platz.
Inside the main (west) entrance, 1211pm.
See ya, Vienna!
RJX62: Budapest – Wien – München.
After departing Salzburg, the train crosses the Saalach river near Freilassing; also, crossing the international border east-to-west, from Austria (left) into Germany (right).
6.5 hours after leaving Vienna, the familiar Waxenstein, Riffelspitze, and Zugspitze peaks come into view (at left), as I arrive finally in Garmisch-Partenkirchen.
Another familiar sight after previous stays: facing north to Kramerspitz (left).
Summertime dusk at 925pm.
I made all photos above with an iPhone15 on 16 Jul 2024. This post composed with Jetpack for iOS appears on Fotoeins Fotografie at fotoeins DOT com.
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