A Simple Model of Relativity

I've updated and re-instated this document on the RetroMat website. It goes from Special Relativity to (a special case in) General Relativity using a simple visual model, some reasonable assumptions and minimal maths. Not a tensor in sight!

'Upgrading' a Linux PC

A departure from my usual retro theme...

Until last year, I'd been happily using a laptop bought in 2008! It had been shelved for many years and when I retired was brought back into service, but running Lubuntu, a lightweight distribution of Ubuntu Linux for the desktop. Incredibly, it served me well for about four years.

Last year, my wife replaced her laptop, so that she could run Windows 11. It was a mere(!) 7 years old and had (and still has IMO) a decent spec., but Microsoft had decided they weren't going to support it, so I took it over. Lubuntu were abandoning the lightweight aspect, so I decided that I may as well use another distribution and settled on Linux Mint instead, another Ubuntu variant.

It was OK, but the mouse pointer was often replaced by a spinning icon, indicating the system was a bit too busy to devote itself to my needs. There was the odd glitch and Ubuntu itself is now becoming resource-hungry, with a (crazy, IMO) minimum memory requirement of 6 GB, so I decided to replace it and chose Fedora Workstation.

I started and seemingly made reasonable progress at first. True, it was a faff trying to boot from a USB key with the new OS, but that's BIOS (or UEFI) for you. (A further complication for me is that not all USB ports on my laptop can be used for booting).  The OS seemed to get installed, but I was left with a simple screen, no menu and just (so I thought) the ability to alter some settings by right-clicking the mouse. I rebooted the machine, thinking that would fix it, but was left with the same thing. In desperation I clicked on the top left of the screen which showed a sort of dash and a dot that I'd never seen before. Doing this then revealed the 'apps' with which to use the system - not a menu in sight! (Now, perhaps I should have read the documentation, or been a little more inquisitive, but I genuinely thought there was a problem). What a crazy decision to minimize everything on a new installation, where there is a high chance that the user, like I was, is new to the UI. It seems to be a triumph of aesthetics perhaps over common-sense and what a poor introduction to the UI (Gnome)! After several hours of playing around, I really hated it anyway and installed the KDE UI, which I had been using with Linux Mint. I did so, but couldn't fully get rid of Gnome, so decided to start again and to install Fedora KDE Plasma Desktop instead!

At this point, I discovered the fun was only just beginning! The main problems I encountered with this new OS:

• Whilst I'd been able to write the Fedora Workstation iso file to the USB key OK from Linux Mint and boot from that without too much difficulty, trying to do so for the new OS on Fedora Media Writer was a problem -  I just couldn't boot from the USB key at all. It seemed that Legacy (BIOS) booting was no good and I had to use UEFI instead.
• After that, it booted from UEFI, but then it couldn't see the internal disk on the laptop! So, after much digging around, I found out that I had to change SATA operations to AHCI from RAID in BIOS/UEFI.
• I took the option to overwrite the existing Fedora installation, but that failed, so I chose to write to the entire disk.
• Finally, having installed the OS, I then installed Chrome and encountered a weird error with it. The issue was that while I could log in to my Google account, I couldn't see my bookmarks. Searching the issue came up with lots of helpful advice about synching the bookmarks, but I just couldn't see an option to do that. After, much digging, I had to enter chrome://sync-internals into the browser, then enable something called Sync-The-Feature. I got some pop-up about security and after that, the synch options became available and I was able to finally see my bookmarks! A pure Chrome issue or a combination of Chrome and new OS, I wonder?

I had a career in IT and am a reasonably competent user. Even so, I estimate it took at least 8 hours for me to do the 'upgrade'. The experience puts me in mind of the difficulties I used to encounter decades ago, when nothing was ever simple with PCs and you needed to be a real 'tecchy' to get things working. Since then a lot has changed and we should expect things to work with minimal fuss. Software - OSs, UIs and applications - should be lightweight, intuitive, robust and not require extensive problem-solving.

As to what happened, perhaps part of the problem is that there are too many flavours of Linux and UI out there and they have to work across a wide range of hardware. It's all very fragmented, as indeed was the Unix world before Linux. Maybe things would work better if there was less choice?

(Oh and by the way, simple copy-and-paste doesn't seem to work with the mouse on my new system!)

Scratch dials - a closer look

Updated 11 June 26

This replaces an earlier post.

As noted in the previous post, between the Spring and Autumn equinoxes, such dials, being South-facing, are in shadow nearer sunrise and sunset. Let's use Stellarium for a few examples at 51 degrees North:

- at the Summer solstice, the Sun enters the Southern half of the sky (i.e. lies due East) 3 hours and 40 minutes after sunrise, when its altitude is about 30 degrees and the dial therefore indicates the end of the second hour and the start of the third (no good if we need to know when the second hour starts and similarly for the final hour); the dial is illuminated by the Sun for just over half the daytime,

- about the start of Summer, May 4th say, the Sun enters the Southern half of the sky 2 hours and 20 minutes after sunrise, when its altitude is about 20 degrees and the dial therefore indicates part way through the second hour (again no good if we need to know when the second hour starts, but perhaps ok for the start of the final hour, which can be guessed at); the dial is illuminated by the Sun for just over two thirds of the daytime,

- even in mid-April, less than 4 weeks after the equinox, the Sun enters the Southern half of the sky 90 minutes after sunrise, when its altitude is about 13 degrees and the dial therefore indicates nearly the end of the first hour (and so is likely still usable); the dial is illuminated by the Sun for just over three quarters of the daytime. 

This demonstrates the limited usability of this type of dial when the Sun is North of the celestial equator - surely there were complementary dials for these months? Perhaps something as simple as a North-facing dial of the same type? In this case, it would need marks for the first two and final two hours only of the daytime. In the morning, the shadow cast by the gnomon would be horizontal at sunrise and would rotate until reaching a particular angle at which time the entire dial would go into shadow and the South-facing one would then be illuminated, continuing at the correct angle and hour. Later in the day, the process would be reversed as the South-facing dial went into shadow and the North-facing one became illuminated.

A scratch dial

Updated 11 June 26

Also known as a mass dial, although I seem to recall that strictly speaking there is a distinction. I came across this one by chance at St. Catherine's Church, Montacute, Somerset. It's a vertical sundial that surely pre-dates the Church clock of around A.D. 1400. The hole centre bottom would have held a horizontal gnomon to cast a shadow for telling the time. 

~~~

Originally, I wrote: There are 12 lines radiating from the gnomon hole for indicating the hours from 6 am to 6 pm, albeit inaccurately, as they are spaced regularly (15 degrees) and with no regard for latitude.

However, having read the section Medieval Times and Canonical Hours here on the excellent GAUDIUM SUB SOLE website, I was reminded that centuries ago, day and night were divided into 12 hours each, an hour in the day-time being longer than at night-time in the Summer, for example. 

Then I wrote: There are 12 lines, spaced at 15 degrees, radiating from the gnomon hole for indicating the 12 daytime hours from sunrise to sunset, the length of the hour depending upon the time of year. While perhaps crude in execution, it and similar dials were sufficiently accurate for the needs of the period.

However, on further reflection, this is still only partially correct! These dials show sunrise and sunset only when the Sun is fully in the Southern sky, i.e. between the Autumn and Spring equinoxes. Between the Spring and Autumn equinoxes, for part of the day, after sunrise and before sunset, the Sun is in the Northern sky and such dials are in shadow. More to follow...

~~~

The dial is unusual, being upside down, and hence unusable! Presumably the stone was re-used when the dial was no longer needed. 

More info. on this dial from GAUDIUM SUB SOLE here, along with another dial at the church that I missed!

Note - the design was already ancient when it was made, being the same type as this Ancient Egyptian dial.

Stereo Pairs

There's a new page on the RetroMat website with some stereo pair pictures I've taken, for cross-eyed free-viewing. 

This one, however, is for parallel free-viewing. It's easier on the eye, but by necessity has been reduced in size.

Also, note this is an example of a hyper stereo pair, which exaggerates the depth, the pictures have been taken from points of view that are more widely separated than are human eyes.

Estimating aphelion and perihelion for Mercury and Venus

In an earlier post, I estimated the orbital radii for Mercury and Venus, by taking the sine of the average greatest elongation angles for each, using data for 2014 to 2029 from here.

In fact, I've been treating the orbits as being near-circular, but recently I've been wondering how to find their true shapes (which we know from Kepler and Newton are ellipses). Specifically, can I use the extremes of the greatest elongation angles to find accurate figures for the furthest (aphelion) and closest (perihelion) approaches of these planets to the Sun?

So, here is a summary for the inner planets. I've separated greatest elongation observations by East and West. The sines of the minimum and maximum angles within each set of observations provide estimates of perihelion and aphelion respectively and as can be seen are nearly exactly the same as the true figures, with exceptions to the exact figures highlighted with an *. This surprises me, because I'd assumed that I would have to find and make an allowance for the Earth's orbital eccentricity (loosely, non-circularity) for greater accuracy (which I have not done yet), especially so in the case of Venus, because the Earth's orbit is actually the more eccentric of the two planets.

Notice how eccentric Mercury's orbit is!

Mercury

• Greatest Elongation West
• 50 observations
• min. 17.9 (sine: 0.31)
• max. 27.8 (sine: 0.47)
• Greatest Elongation East 
• 51 observations
• min. 18.1 (sine: 0.31)
• max. 27.4 (sine: 0.46*)
• wikipedia: perihelion 0.31 AUs, aphelion 0.47 AUs

Venus

• Greatest Elongation West
• 10 observations
• min: 45.8 (sine: 0.72)
• max 47 (sine: 0.73)
• Greatest Elongation East
• 10 observations
• min. 45.4 (sine: 0.71*)
• max. 47.2 (sine: 0.73)
• wikipedia: perihelion 0.72 AUs, aphelion 0.73 AUs