Where is the Andromeda Galaxy right now?

When I watched the BBC’s The Sky at Night: Guide to the Galaxy (aired on 12 Jan 2017) the description of which stated “we discover that the Milky Way may already be colliding with our neighbouring galaxy, Andromeda” I thought that the presenters might discuss an issue with astrophysics that has been on my mind for a few years now.  But they stated that what is defined as the edge of a galaxy had been redefined / defined more accurately leading them to the conclusion that the newly defined edges were beginning to overlap.
The issue that I have had in my mind is about distances, velocity and time.  These factors mean that things we observe in space are not now where we observe them to be.  Let me explain.  We observe distant objects in space via the electromagnetic spectrum (light, radio, ultra violet, infra red etc) (we can now add gravitational waves to our repertoire).  Waves in the EM spectrum travel at a finite velocity, 3.0 × 108 m s-1.  If the objects we observe are very distant from the Earth then the time required for the EM radiation emitted by those objects to reach us on Earth can be very large – millions of years.  Whilst the radiation is travelling toward us the objects will continue to move.  This means that by the time the radiation has reached us the objects will no longer be at the location they appear to be according to what the radiation communicates to us.
A simple example: If an object is 2 million light years away and moving at 100 m s-1 then by the time the light from the object reaches Earth, 2 million years later, the object will have moved 6.3 × 1015 m from the location where it emitted the light we observe.  We observe the past locations of objects in space.
In most cases the difference will be proportionately small compared to the distance from the star / galaxy concerned but it may affect data significantly enough to require some revisions to how we understand the universe to be developing.  The difficulty here is that in order to do any calculations one has to assume that the object concerned has continued to behave exactly as it was when the radiation that we observe was emitted.  That wouldn’t have been an altogether terrible assumption were it not for the accelerating expansion of the universe.
Notwithstanding the problematic assumption I have just outlined here is an example calculation for the Andromeda galaxy.

Data for Andromeda obtained from Wolfram Alpha.
Distance from Andromeda to Earth = 2.571 million light years
Redshift, z = −9.907 × 10-4  (the negative indicating it is actually blue shifted).
Equation for redshift: z = v/c
⇒ velocity of Andromeda, v = zc = (–) 9.907 × 10-4 × 3.0 × 108 = 297,210 m s-1
Time taken for light to reach Earth from Andromeda (in seconds):
t = 2.571 million years = 2.571 × 106 × 31.536 × 106 = 8.10791 × 1013 s
Distance travelled by Andromeda during transit of light from there to Earth:
d = vt = 8.10791 × 1013 × 297210 = 2.40975 × 1019 m
Distance conversion to light years, 1 ly = 9.4607 × 1015 m
⇒ d = 2547 ly
As a percentage of total Andromeda–Earth distance: 0.0991 %
Actual present day distance to Andromeda should be 2.568 million light years.  Value is changed at the fourth significant figure.

Do you think that this issue does make a significant difference to our data or not really?  Does anyone know if this effect is already factored into the distances in our data books?

“Old People Messed Up the Referendum” Or did they?

Before I begin.  I voted to remain.  I did not vote to leave.  Got that?  So let’s not write me off as a bigoted¹, racist Brexiter.
So what’s the problem?



Blaming older generations is disingenuous, possibly hypocritical, definitely not valid.  There were problems with the General Election, I said so myself at the time, it was not representative.²   But the referendum was on the Conservative manifesto and the Tories got voted in.  Remain mourners need to take a long look at themselves, they did not mobilise for the General Election. We all knew the referendum was coming if the Conservatives were given the government.  If the people didn’t want a referendum the General Election was the time to make that known.  The turnout of 66% shows that people were complacent.
There is always a threshold for the voting age and so voters inevitably make choices that affect younger generations.  I believe that 16 or 17 year olds should be given the vote (despite 16 and 17 year old students not being able to articulate concrete reasons for their choice).  But even so they would be casting a vote that decides something profound for those younger than them.  And those younger than whatever the threshold will have to live with the consequences for longer than the voters.  The point is that drawing the line so that the votes of older generations is discredited is entirely arbitrary.  You may not like the way they voted but that is merely your opinion on the matter.
A genuine democracy treats all people as equal regardless of gender, age, race, or socioeconomic background, etc.  Their votes are therefore equally significant.  Don’t praise young people for voting in line with their beliefs and criticise older people for doing exactly the same thing.  Just maybe older generations have something valuable to offer as a result of their life experience.
Older people always have a higher turnout than younger generations.  So if their votes therefore make up a higher proportion of the total votes they are not to blame for that.  A graphic published by the BBC shows that a proportionately lower voter turnout correlated remarkably well with a proportionately higher fraction of younger voters (those in the 18–24 year old bracket).
In fact, given the turnout statistics blaming older generations for how they voted fundamentally undermines the argument that the choice of younger generations was more important.  If the choice of younger generations was more important then they should have turned out to vote in a higher proportion.  Don’t blame older people for valuing their role in a democracy more than younger people.
The facts do show, I believe, that blaming older generations for how this referendum turned out is not in line with evidence or rational argument.
Update 24/6/16
One more point. Let’s not forget that both the original decision to join the EU and the subsequent decision to stay in the EU were the choice of the older generations when they were young.  Those decisions were forced on the present younger generations too.  But no one is complaining about that today. 

¹ By the way, being obstinately attached to a belief works both ways.  Plenty of remain supporters held that position out of some kind of blind loyalty to an irrational metaphysical inclination.  Conversely some Brexit supporters had very rational reasons for their choice.  There were both rational and irrational supporters on both sides.
² Although the misrepresentation did not disadvantage the left.  A representative vote would have seen UKIP wield significant power in Parliament.

Astro–photography with an iPhone

Got the college’s telescope out and I wanted to take some photographs with my iPhone…

The Occasional Tech Blog

The past couple of weeks I’ve been learning how to set up and use the telescope my physics department recently bought.  During one session I wanted to get a photograph of the Moon but it was too difficult to hold my iPhone camera steadily over the eyepiece.  So I began thinking about how to set up a rig to hold the phone over the eyepiece.

At first I looked for an object as tall as the telescope’s eyepiece, which happened to be a speaker with a thin book underneath it.  I then used my Joby tripod to (awkwardly) position the phone’s camera lens over the eyepiece.  This worked but it was incredibly tricky to work with.  In order to line up the camera and eyepiece I had to manoeuvre the speaker at floor level, which meant that I couldn’t look into the screen to know that it was correctly lined up.  So I had to use trial and error to…

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Factoring proportional representation into General Election 2015 results

Imagine that proportional representation was factored into our existing (archaic) election system. I tinkered with the results data for the General Election 2015 to give each party’s MPs a weighted vote.  The percentage of seats that each party won and the percentage of the total votes that each party received were calculated.  Then their percentage of votes was divided by their percentage of seats to give a relative weighting.*

This model shows that if proportional representation was factored into MP voting parties with a lot of seats, but who did not have a large share of votes (like the SNP) their MPs would receive a fraction of a vote.  Conversely parties with a few seats or one seat, but who did have a large share of votes (like the Greens and UKIP) their MPs would receive a multiplied vote – in UKIP’s case a dramatically multiplied vote!

Take a look and see how much collaboration should actually exist in UK politics and how much less relevant the SNP should actually be.

The parties listed are only those who had an MP elected.  The raw data is from the BBC : http://www.bbc.co.uk/news/election/2015/results.

Reference Data

Electorate 46,425,386
Turnout %


Total Votes 


Election Results by Party



Seats %

Vote %

Votes / Seat

Votes % / Seats % Weighting

Total Weighted Votes

















Scottish National Party








Liberal Democrat








Democratic Unionist Party








Sinn Fein








Plaid Cymru








Social Democratic & Labour Party








Ulster Unionist Party 
















Green Party





















Each elected MP’s vote has been weighted according to their party’s proportion of votes by using the percentage of seats the party won and the percentage of votes for the party.    So if a party received a proportion of votes equal to their proportion of total seats they would receive a weighting of 1.0.  E.g. The Conservative weighting is 36.94/50.92 = 0.73.

I’ve then multiplied each party’s number of seats by their weighting to calculate their total voting power.  Values have been rounded up so that the total votes is 650.  E.g. The Conservative total voting power is 331 × 0.73 = 240.

Visualisations of weighted votes for each political party.

Visualisations of weighted votes for each political party.

There were other party candidates who could have potentially had a higher weighting than some of the lower weighted parties if they had won one seat.  If Alliance had retained their seat would have had 61,556 votes per seat and a weighting of 1.31.  If TUSC had got a candidate elected they would have had 36,327 votes per seat and a weighting of 0.77.  Of course in the instance that they had won a seat the overall percentages would have shifted and the weightings also shifted slightly across the board.

One significant issue with this analysis is that of the weighting given to the seat categorised under ‘Others’.  As the votes categorised here appear not to have been for the one candidate who was elected, the corresponding weighting will have been exaggerated.  Therefore his/her vote weighting should be lower and the others would increase slightly. However as I had to round up the total weighted votes to make 650, so those values would probably not change much.

*There are probably more complex and accurate methods but this is only a matter of interest.


Solar Eclipse 20 March 2015

A total solar eclipse is due to occur on Friday 20 March 2015 over much of the Northern Hemisphere – are you ready for it?

Total solar eclipses* are very rare astronomical events so the opportunity to view one shouldn’t be passed up too quickly – the next major solar eclipse in the UK is due to happen in 2090!  This eclipse is also special because the path of the total eclipse will end at the North Pole on the spring equinox.  That is not due to happen again for thousands of years.  The shadow of this total eclipse (i.e. the umbra) will cross the Faroe Islands and Svalbard.

The UK will experience a partial eclipse ranging from about 86% coverage in the south to about 98% in northern Scotland.  If the weather is clear we should observe the Sun’s light be reduced by the same amount as if a very thick cloud had covered the Sun.

Solar Eclipse 2015 poster.003

*Don’t get your eclipses muddled up: solar eclipses are when the Moon comes between the Sun and Earth; lunar eclipses are when the Earth comes between the Sun and Moon.  During a lunar eclipse the Moon appears red/orange because only some of the long wavelength end of the visible light spectrum is refracted around the Earth enough to reach the Moon.

Be Safe When Observing the Eclipse

Viewing the Sun without proper eye protection is always dangerous, even during an eclipse!  The fact that the retina has no pain receptors and any damage caused is not immediately noticeable only adds to the risk.  Even with solar filters the Sun should not be observed for too long, always check the instructions supplied with solar filters.  For example our filters, which reduce light intensity by approx. 100,000 times, have a maximum viewing time of 3 minutes.  The reason for this time limit is that there is still a lot of potentially harmful infrared radiation that gets through the filters.

A Great Astronomy App

Last week I scouted out a location for viewing the eclipse with the help of a great astronomy app called Skyview made by Terminal Eleven.  The app is available on iOS and Android – details on their website.


Eclipse Geometry and Factors

Solar eclipses are possible because the Sun is 400 times larger than the Moon and also 400 times further from the Earth than the Moon is.  But there are several factors that affect whether the Moon will actually move exactly between the Earth and Sun and where the shadow will fall on the Earth’s surface.

  1. The Earth’s orbit around the Sun.
  2. The Earth’s rotation.
  3. The tilt of Earth’s axis of rotation.
  4. The Moon’s orbit around the Earth.
  5. The inclination of the plane of the Moon’s orbit to the plane of the Earth’s orbit.

Why are Solar Eclipses Possible- poster.003

Scientific Observations During Eclipses

Solar eclipses are wonderful events to witness and yet they are also events of significant scientific interest.  Total solar eclipses enable important scientific observations to take place. Below are two observations that are enabled by total eclipses.

1. The Sun’s corona. 


The aura of plasma that surrounds the Sun and extends millions of kilometres is the corona.  It is not possible to observe the corona ordinarily as the glare from the main body of the Sun is too intense.  Coronagraphs have been designed which block out the main part of the Sun to allow for observation of the corona.  However, the Moon during a total eclipse is a vastly superior coronagraph!  Total eclipses allow for observation of the lowest parts of the corona, this is something not currently achievable by artificial coronagraphs.  The corona is of great interest to scientists because it is much, much, hotter than the surface of the Sun and the method by which it is heated is still the subject of debate.

See more amazing photography of solar eclipses by Miloslav here.

2. Gravitational lensing.
Gravitational Lensing Diagram.001
Objects with mass curve the space-time continuum, and the space-time continuum defines the passage of light.  Therefore, the presence of objects with mass can alter the passage of light compared to the absence of such objects.  Gravitational lensing is only visible near objects with very large masses and of objects very far behind the massive object.  The Sun is a suitable candidate for causing gravitational lensing of distant stars behind it.  However, the Sun emits a lot of light which obscures the lower intensity light from distant stars.  But during a total eclipse virtually all of its light is obscured.  That gives a small window of opportunity for astronomers in the umbra (i.e. in the Moon’s total shadow) to observe distant stars to see if their apparent position shifted due to the presence of the Sun.  The position during the eclipse is compared with the position as measured approximately six months earlier / later which is when the Sun is not have been between Earth and the star(s) in question.

Physics A-Level revision guides going on sale until the end of January

Have you or has someone you know made a New Year’s resolution to work harder at A-level physics?  If so my physics iBooks textbooks will be on sale from Monday until the end of January.

2015/01/img_0446.jpgFor less than the price of a coffee you will be able get all this:

  1. Essential content for the OCR AS-Level Physics A course.
  2. Built in glossary of key terms with links embedded into the content overviews to enhance the usefulness of the overview.
  3. Instant study cards based on the pre built glossary – plus any further notes you make.
  4. Annotated graphs that you need to be familiar with.
  5. Annotated diagrams of practical applications of physics relevant to each unit.
  6. Links to interesting physics websites and videos to stretch your learning.
  7. Hyperlinks between relevant content.
  8. Help section for key mathematical concepts.
  9. Review questions to check your understanding.
  10. A brief history of physics – find out about some of the big names in physics and their historical context.
    Interested?  Click to find out more about the AS Physics book or the A2 Physics book.

Only available on iBooks, up to date iPad or Mac required.


Embed your Twitter Feed into a Virtual Learning Environment (VLE)

If you are a teacher who uses Twitter for teaching and whose institution has a virtual learning environment (VLE), such as Moodle or Blackboard, you may want to embed the feed into the VLE to give your students easier access to it if they themselves do not have a Twitter account. I do this also so that there is one place to which I can direct my students to access all my electronic resources without needing to be very familiar with all of them. If you would like to do this I have some instructions below, they are specifically for Moodle. However, if you know your way around another VLE the same principles can be applied to it.

You can save this to Evernote if you find it helpful: http://bit.ly/11ZEn8L

At twitter.com

  1. Log into Twitter in a web browser.
  2. Click on Profile / Settings button.
    Choose “Settings” from the drop down menu.
  3. Click on “Widgets” in the menu (bottom left).
  4. Click “Create New”.
  5. Adjust settings for your new widget.
    I recommend the following for Moodle: Exclude replies, and 700 height.
  6. “Save changes”. Then copy the html code.

Switch over to Moodle

  1. Login to Moodle, navigate to the course where you want the timeline embedded and click the “Turn editing on” button.
  2. Scroll to the section where you want to add the link for the timeline in the Moodle page.
  3. Click “+ Add activity or resource” and choose “Page” from the menu.
  4. Give the Page a name, e.g. Twitter Feed.
  5. Click the “html” button under “Page content”.
  6. Paste the html for the Twitter widget into this field.
  7. Click “Update” and then save the Page by scrolling to the bottom of the page and clicking “Save and return to course”.
  8. Mission Accomplished!


Evernote : A Teacher’s Best Friend

Evernote is a useful and powerful note taking application. Millions of people around the world rely on it for activities as diverse as ticking items off a shopping list to collaborating on extensive projects.  For many Evernote is so invaluable it is like an extension of their brain!

Several core features make Evernote hard to beat for most people: it is easy to use, it is reliable, apps exist for just about every platform (desktop, mobile and web) and it is quick to perform detailed searches.  In addition to its wide appeal, Evernote is a fantastic tool for teachers and students.  Below are the main ways in which Evernote aids my day to day planning and teaching.

A large part of my work consists of thinking up new ideas and new resources, Evernote’s biggest strength is capturing information.  It is great at capturing ideas typed up, scribbled on an envelope, doodled, sketched – you name it Evernote can capture it!  Type directly into Evernote if you are able to or write / sketch onto paper and use the excellent document scanner which is built into the mobile apps.

There are three main ways to organise stuff in Evernote: stacks, notebooks and tags.  Stacks and notebooks provide the overarching structure.  I use Stacks to broadly differentiate between personal and work notes, each area has with a few / several sub categories provided by notebooks.  My work area consists of a general archive, a resources archive, notes from meetings, notes for tracking student performance, and an archive of physics / teaching related articles.

Notebooks are useful for imposing order upon Evernote content but the most useful aspect of organisation is the use of tags.

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Whereas a note can only be in one notebook at a time, a single note may have several tags.  It is also possible to nest tags in order to keep them organised too.  Tags make searching through thousands of notes much easier.

It is also sometimes useful to be able create a checklist for lessons and tick them off as the lesson progresses.  Checklists are easy to create and tick off in Evernote mobile apps.  Managing tasks in the office and classroom is straightforward and effective.

In one form or another Evernote is nearly always at hand, whether I’m commuting or at my desk I have a way of collecting and shaping ideas.  The mobile apps are very capable so refining ideas for a lesson on the go is possible.  The desktop apps are even more powerful so my work accelerates when I’m at my desk.  I much prefer to have my ideas and plans in a custom made application rather than as separate documents in folders on a computer.  In Evernote I can click / tap on a note and instantly start reading it, but documents have a time delay before I can start reading through them.  That difference is accentuated on mobile platforms.  And as mentioned above, organising notes in Evernote with tags makes finding what I need a heck of a lot quicker.

Planning on paper has the big advantage of being able to sketch or doodle ideas as you go.  But paper is messy when it comes to archiving – I am hopeless at paper based filing!  It is also incredibly slow to search.  Digital platforms are excellent at search.  Evernote brings paper and digital together wonderfully.  It has a document scanner built it – it’s the camera function I use most.  After planning something on paper I scan it into Evernote.  Once it’s uploaded to Evernote’s servers even the handwritten text will become searchable!  I have terrible handwriting so it’s usually hit and miss for me but it does get it right sometimes.  Nonetheless good use of note titles and tags makes searching much more efficient anyway.

Evernote searching is very useful, it can be narrowed down by notebook, tag, and attachment type.  If you find yourself searching with the same terms regularly then you can save the search too.  Notes can also be tagged with locations if you like.  That can create a whole new approach to browsing your note history, especially if you travel a lot.

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I’ve often created notes in Evernote that I think my students will find useful.  With a few taps any note can be made public with its own link.  Share that link with a class and they have access immediately via the link.  If I make something in advance of a class I can insert the link into Moodle (our VLE, the same can be done with Blackboard etc) so students can login and tap / click on the link.  I usually make a QR code for the link too and add it to the note / presentation so that the students can scan the code and navigate straight to the note on their phones / tablets.

Often my students and I may produce something worth keeping on the whiteboard in a class.  The document scanner works very well on whiteboards too, so I’ll often scan it and then share it with the class.  The above method of sharing is useful for sharing resources or ideas with other members of staff too.

If you want to take sharing to the next level, then share a whole notebook with students or staff.  Then collaborate on projects in the notebook.  Anyone who has an Evernote account and to whom give editing rights in a notebook can add new notes or collaborate with you on existing notes.  In order to give editing rights to someone else in a shared notebook you will need a Premium Evernote account.

Make an Evernote account here: http://bit.ly/1brRE7T, download the app, then get more productive.