"Schwarze Löcher sind, was Sie in schwarzen Socken bekommen"
Karl Schwarzschild was a gifted and energetic physicist, who had been fascinated by astronomy from an early age. He even saved up his pocket money to buy lenses to make his own telescopes. He was born in 1873 and grew up in Frankfurt, Germany, the eldest of six children in a prosperous Jewish family.
After leaving university, he was appointed to the Von Kuffner Observatory in Vienna, where he spent some time developing techniques to measure the apparent brightness of stars. It was this work that later enabled him to show that different stars are different colours due to their surface temperature, and that some stars have a cyclical change in their temperature.
After moving on to Munich for a time at the university there, he published many more works on the behaviour of stars, and the radiation they emit. All his work ultimately led to him being appointed to director of the Astrophysical Observatory in Potsdam, the most prestigious astronomy job in Germany.
When World War I broke out, Schwarzschild volunteered for military service, even though he was 41 by then, and he saw action in Belgium, France and the cold Russian front. It was whilst here that he developed the ideas that were to ensure his place in science history. Einstein had recently written about general relativity, and Schwarzschild had solved some of the problems associated with it. Most famously, he showed that if a body was massive enough, it would have an escape velocity greater than light - he was the first to hint at the possibility of black holes.
Today the idea of black holes is widely accepted, but at the time it seemed like pure fantasy, and even Schwarzschild thought his proposals were theoretical only. He described a point in space, called a singularity, where all the mass of an object was to be found. That mass would have an influence on the space around it, sucking everything in to the centre, even light. At some distance from the singularity is a boundary, the so-called event horizon, where objects outside that boundary can escape, those inside can’t. It is called an event horizon because events going on inside that horizon are hidden from us, as boats over the horizon are invisible on earth.
The distance from the singularity to the event horizon was later dubbed the Schwarzschild radius, and any body whose mass lies entirely within that radius will become a black hole.
It wasn’t long after Schwarzschild had his major breakthrough that he developed pemphigus, a disease that causes blistering of the skin, and there being no treatment for it at the time, he died some months later, aged only 42.
Now on to the cache…
In the Milky Way galaxy there are hundreds of billions of stars. Around those stars orbit an even greater abundance of planets. On those planets, over the years, civilisations have arisen that have grown to know the pleasure to be derived from geocaching (or its interstellar equivalent, anyway). In order to join together in their celebration of all things caching, these galactic aliens have decided to get together to have the biggest event cache ever. You can forget your UK Mega Events, this party is going to rock. In fact, it will be so big that when the last guest arrives the event cache will be big enough to form its own event horizon, thereby turning into a black hole. No-one is going to be able to leave this party!
This event will have to be in deep space, and guests are only allowed to bring basic life-support gear. They will arrive by teleport and/or time machine as necessary, and make their way to GZ to join the party. It will get pretty crowded, by and by.
Here’s the problem: how many guests must the organisers invite to ensure that the critical mass is reached, and a black hole formed? The answer is A.BC8 x 10DE aliens.
The cache can be found at: N50 3(D-C).(A+C)(B-D)8 W004 0(D+E).CD2
[Assume: G=6.673 x 10-11, c=2.998 x 108, pi= 3.142, the average alien has a density of 1.200kgl-1 and a mass of 90.00kg, work to 4 significant figures]
Check your solution by clicking the image below.
GPS reception at GZ is very poor, so I fine-tuned the co-ordinates using Google maps. It will be obvious when you get there where the cache is hidden.
At the bottom of this cache page is a link to a document which will explain how to solve the puzzle for Great Scientists: Robert Hooke. You can download this document now, but you will not be able to open it without the password, which is printed at the top of the logsheet inside THIS cache.
Alert: You are about to download a file that contains further details you may find helpful to find another geocache. As the cache owner, I represent that this file is safe to download although it has not been checked by Groundspeak or by the reviewer for possible malicious content. Download this file at your own risk. Robert Hooke Solution