Archive for the The Universe and Stuff Category

The Day of Perihelion

Posted in The Universe and Stuff with tags , , , , , , , , on January 2, 2021 by telescoper

Earth’s elliptical orbit viewed at an angle (which makes it look more eccentric than it is – in reality is very nearly circular).

Today (Saturday 2nd January 2021) at approximately 13:50 GMT the Earth reaches at the point on its orbit, which which it is at its closest to the Sun, i.e. at its perihelion. At this time the distance from the Sun’s centre to Earth’s centre will be 147,093,163 km. This year, aphelion (the furthest distance from the Sun) is at 23.57 GMT on July 5th 2021 at which point the centre of the Earth will be 152,100,527 km from the centre of the Sun. You can find a list of times and dates of perihelion and aphelion for future years here.

At perihelion the speed of the Earth in its orbit around the Sun is greater than at aphelion (about 30.287 km/s versus 29.291 km/s). This difference, caused by the Earth’s orbital eccentricity, contributes to the difference between mean time and solar time I blogged about when discussing the Winter Solstice a couple of weeks ago.

It surprises me how many people think that the existence of the seasons has something to do with the variation of the Earth’s distance from the Sun as it moves in its orbit. The fact that perihelion occurs in the depth of winter should convince anyone living in the Northern hemisphere that this just can’t be the case, as should the fact that it’s summer in the Southern hemisphere while it is winter in the North.

The real reason for the existence of seasons is the tilt of the Earth’s axis of rotation. I used to do a little demonstration with a torch (flashlight to American readers) to illustrate this when I taught first-year astrophysics. If you shine a torch horizontally at a piece of card it will illuminate a patch of the card. Keep the torch at the same distance but tilt the card and you will see the illuminated patch increase in size. The torch is radiating the same amount of energy but in the second case that energy is spread over a larger area than in the first. This means that the energy per unit area incident on the card is decreases when the card is tilted. It is that which is responsible for winter being colder than summer. In the summer the sun is higher in the sky (on average) than in winter. From this argument you can infer that the winter solstice not the perihelion, is the relevant astronomical indicator of winter.

That is not to say that the shape of the Earth’s orbit has no effect on temperatures. It may, for example, contribute to the summer in the Southern hemisphere being hotter than in the North, although it is not the only effect. The Earth’s surface possesses a significant North-South asymmetry: there is a much larger fraction of ocean in the Southern hemisphere, for example, which could be responsible for moderating any differences in temperature due to insolation. The climate is a non-linear system that involves circulating air and ocean currents that respond in complicated ways and on different timescales not just to insolation but to many other parameters, including atmospheric composition (especially the amount of water vapour).

The dates when Earth reaches the extreme points on its orbit (apsides) are not fixed because of the variations in its orbital eccentricity so, in the short-term, the dates can vary up to 2 days from one year to another. The perihelion distance varies slightly from year to year too.

There is however a long-term trend for perihelion to occur later in the year. For example, in 1246, the December Solstice (Winter Solstice for the Northern Hemisphere) was on the same day as the Earth’s perihelion. Since then, the perihelion and aphelion dates have drifted by an average of one day every 58 years and this trend will continue. This means that by the year 6430 the timing of the perihelion and the March Equinox will coincide, although I will probably have retired by then…

The Mechanics of Nursery Rhymes

Posted in Cute Problems, The Universe and Stuff with tags , , , , on December 30, 2020 by telescoper

I’ve always been fascinated by Nursery Rhymes. Some people think these are little more than nonsense but in fact they are full of interesting historical insights and offer important advice for the time in which they were written. One such story, for example, delivers a stern warning against the consequences of placing sleeping babies in the upper branches of trees during windy weather.

Another important role for nursery rhymes arises in physics education. Here are some examples that students of elementary mechanics may find useful in preparation for their forthcoming examinations.

1. The Grand Old Duke of York marched 10,000 men up to the top of a hill and marched them down again. The average mass of his men is 65 kg and the height of the hill is 500m.

(a) Estimate the total work done in marching the Duke of York’s men up to the top of the hill.

(b) If, instead of marching down again, the men take turns sliding down a frictionless slide back to where they started, estimate the average speed of a man when he reaches the bottom of the hill.

(You may assume without proof that when they were up they were up, and when they were down they were down and, moreover, when they were only half way up they were neither up nor down.)

2. By calculating the combined rest-mass energy of half a pound of tuppenny rice and half a pound of treacle, and assuming a conversion efficiency of 10%, estimate the energy released when the weasel goes pop. (Give your answer in SI units.)

3. The Moon’s orbit around the Earth can be assumed to be a circle of radius r. A cow of mass m is standing on the Earth (which has mass M, and radius R). Derive a formula in terms of r, R, M, m and Newton’s Gravitational Constant G for the energy the cow needs in order to jump over the Moon.

(The Earth, Moon and cow may be assumed spherical. You may neglect air resistance and udder frictional effects. )

Feel free to contribute similar problems through the Comments Box.

New Publication at the Open Journal of Astrophysics

Posted in Open Access, The Universe and Stuff with tags , , , , , , , , , , , , on December 24, 2020 by telescoper

Just time before Christmas to announce another paper in the Open Journal of Astrophysics. This one was actually published a few days ago but because of holiday delays it took some time to get the metadata and DOI registered so I held off announcing it until that was done.

The latest publication is by my colleague* John Regan (of the Department of Theoretical Physics at Maynooth), John Wise (Georgia Tech), Tyrone Woods (NRC Canada), Turlough Downes (DCU), Brian O’Shea (Michigan State) and Michael Norman (UCSD). It is entitled The Formation of Very Massive Stars in Early Galaxies and Implications for Intermediate Mass Black Holes and appears in the Astrophysics of Galaxies section of the arXiv.

Here is a screen grab of the overlay:

You can click on the image to make it larger should you wish to do so. You can find the arXiv version of the paper here.

I think that will be that for for 2020 at the Open Journal of Astrophysics. We have published 15 papers this year, up 25% on last year. Growth is obviously modest, but there’s obviously a lot of inertia in the academic community. After the end of this year we will have two full consecutive years of publishing.

I’d like to take this opportunity to thank all our authors, readers, referees, and editors for supporting the Open Journal of Astrophysics and wish you all the very best for 2021!

*Obviously, owing to the institutional conflict I recused myself from the editorial process on this paper.

The Great Conjunction

Posted in The Universe and Stuff with tags , , on December 22, 2020 by telescoper

I thought I’d follow the precedent set by many of my fellow astrologists by posting this exciting image of the Great Conjunction of Jupiter and Saturn.

cloudy-night-sky842504659097248730.jpg

It’s hard to believe that it’s been over four hundred years since anyone has seen a sight like this: two planets so close together in the sky that they can both be completely hidden by the same piece of cloud!

Sunrise at the Winter Solstice at Newgrange

Posted in History, The Universe and Stuff with tags , on December 20, 2020 by telescoper

The prehistoric passage tomb at Newgrange in the Boyne Valley North of Dublin is about 1000 years older than Stonehenge. At dawn, around the Winter Solstice, the Sun’s rays penetrate into the inner chamber, as they have done for over 5000 years.

A live stream of this extraordinary sight took place this morning (20th December) and there will be others on Monday 21st and Tuesday 22nd. This is a recording of this morning’s stream.

 

The Winter Solstice 2020

Posted in The Universe and Stuff with tags , , , , , , , on December 20, 2020 by telescoper

The winter solstice in the Northern hemisphere happens tomorrow, Monday 21st December, at 10.02 Irish Time. Among other things, this means that tomorrow is the shortest day of the year in the Northern hemisphere. Days will get steadily longer from then until the Summer Solstice next June.  The longest night – defined by the interval between sunset and sunrise – is tonight and the shortest day – defined by the interval between sunrise and sunset – will be tomorrow. The day tomorrow will be two seconds shorter than today, while the interval between sunrise and sunset on Tuesday 22nd December will be four seconds longer than tomorrow.

This does not, however,  mean that sunrise will happen earlier tomorrow than it did this morning. Actually, sunrise will carry on getting later until the new year, the length of the day nevertheless increasing because sunset occurs later. Sunrise this morning (20th December was at 08.37 Dublin Time while tomorrow it will be at 08.38. Sunset tonight will be at 16.07 and sunset tomorrow will be at 16.08.

These complications arise because there is a difference between mean solar time (measured by clocks) and apparent solar time (defined by the position of the Sun in the sky), so that a solar day does not always last exactly 24 hours. A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767:

Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time.

The discrepancy between mean time and apparent time arises because of the Earth’s axial tilt and the fact that it travels around the Sun in an elliptical orbit in which its orbital speed varies with time of year (being faster at perihelion than at aphelion).

In fact if you plot the position of the Sun in the sky at a fixed time each day from a fixed location on the Earth you get a thing called an analemma, which is a sort of figure-of-eight shape whose shape depends on the observer’s latitude. Here’s a photographic version taken in Edmonton, with photographs of the Sun’s position taken from the same position at the same time on different days over the course of a year:

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The winter solstice is the lowermost point on this curve and the summer solstice is at the top. These two turning points define the time of the solstices much more precisely that the “shortest day” or  “longest night”.

Incidentally, the Tropic of Capricorn is the circle of latitude (about 23.5°, the declination of the Sun at the Winter Solstice) that contains the subsolar point at the December solstice. This is therefore the most southerly latitude on Earth where one can see the Sun directly overhead.

Anyway, the north–south component of the analemma is the Sun’s declination, and the east–west component is the so-called equation of time which quantifies the difference between mean solar time and apparent solar time. This curve can be used to calculate the earliest and/or latest sunrise and/or sunset.

Using a more rapid calculational tool (Google), I found a table of the local mean times of sunrise and sunset for Dublin around the 2020  winter solstice. This shows that tomorrow is indeed the shortest day (with a time between sunrise and sunset of 7 hours 29 minutes and 57 seconds).  The table also shows that sunset already started occurring later in the day from 17th December,  before the winter solstice, and sunrise will continue to happen later  after the solstice, notwithstanding the fact that the interval between sunrise and sunset gets longer from tomorrow onwards.

I hope this clarifies the situation.

New Publication at the Open Journal of Astrophysics

Posted in Open Access, The Universe and Stuff with tags , , , , , , , on December 15, 2020 by telescoper

The Christmas rush is definitely upon us and papers are queuing up to be published in the Open Journal of Astrophysics. The latest publication is by Tom Kitching and Anurag Deshpande of MSSL (University College London) and Peter Taylor of JPL (Caltech). It is entitled Propagating residual biases in masked cosmic shear power spectra. This is another one for the folder marked Cosmology and Nongalactic Astrophysics.

Here is a screen grab of the overlay:

You can click on the image to make it larger should you wish to do so. You can find the arXiv version of the paper here.

When I last posted about a new OJA paper I mentioned that it seemed to be taking authors longer than usual to make revisions. There are signs now that some authors are trying to get papers off their desk before the Christmas break so we may have two or three more to publish before the year is out.

P.S. Last week I received an offer from a commercial organization to buy the Open Journal of Astrophysics. I replied politely that it is not for sale.

New Publication at the Open Journal of Astrophysics!

Posted in Open Access, The Universe and Stuff with tags , , , , , , on December 10, 2020 by telescoper

Time to announce another new paper in the Open Journal of Astrophysics. The latest publication is by Johan Comparat and 27 others – too numerous to list individually here –  and is entitled Full-sky photon simulation of clusters and active galactic nuclei in the soft X-rays for eROSITA. This is another one for the Cosmology and Nongalactic Astrophysics folder.

This paper is closely connected to the eROSITA instrument which is why it involves a considerable number of authors in different institutions – the current record length for an OJAp author list – though this is by no means a large collaboration by the standards of astrophysics and cosmology! It’s good to see some big names in there though!

Here is a screen grab of the overlay:

You can click on the image to make it larger should you wish to do so. You can find the arXiv version of the paper here.

With this paper we have exceeded the number of papers published last year. We do in fact have quite a few in the pipeline but owing to the ongoing pandemic there have been some refereeing delays and in some cases authors are taking more time than expected to do the “revise and resubmit” routine. I think there are plenty of other people around who are just as tired as I am! Perhaps we’ll see a clutch emerging in the New Year!

Lorentz-Fitzgerald or Fitzgerald-Lorentz?

Posted in Beards, History, The Universe and Stuff with tags , , , , on December 9, 2020 by telescoper

I’ve recently moved on to the part about Special Relativity in my module on Mechanics and Special Relativity and this afternoon I’m going to talk about the Lorentz-Fitzgerald contraction or, as it’s properly called here in Ireland, the Fitzgerald-Lorentz contraction.

The first thing to point out is that the physicists George Francis Fitzgerald and Hendrik Lorentz, though of different nationality (the former Irish, the latter Dutch), both had fine beards:

George Francis Fitzgerald (1851-1901)

Hendrik Lorentz (1853-1928)

One of the interesting things you find if you read about the history of physics just before Albert Einstein introduced his theory of special relativity in 1905 was how many people seemed to be on the verge of getting the idea around about the same time. Fitzgerald and Lorentz were two who were almost there; Poincaré was another. It was as if special relativity was `in the air’ at the time. It did, however, take a special genius like Einstein to crystallize all that thinking into a definite theory.

Special relativity is fun to teach, not least because it throws up interesting yet informative paradoxes (i.e. apparent logical contradictions) arising from  that you can use to start a discussion. They’re not really logical contradictions, of course. They just challenge `common sense’ notions, which is a good thing to do to get people thinking.

Anyway, I thought I’d mention one of my favorite such paradoxes arising from a simple Gedankenerfahrung (thought experiment) here.

Imagine you are in a railway carriage moving along a track at constant speed relative to the track. The carriage is dark, but at the centre of the carriage is a flash bulb. At one end (say the front) of the carriage is a portrait of Lorentz and at the other (say the back) a portrait of Fitzgerald; the pictures are equidistant from the bulb and next to each portrait is a clock.The two clocks are synchronized in the rest frame of the carriage.

At a particular time the flash bulb goes off, illuminating both portraits and both clocks for an instant.

It is an essential postulate of special relativity that the speed of light is the same to observers in any inertial frame, so that an observer at rest in the centre of the carriage sees both portraits illuminated simultaneously as indicated by the adjacent clocks. This is because the symmetry of the situation means that light has to travel the same distance to each portrait and back.

Now suppose we view the action from the point of view of a different inertial observer, at rest by the trackside rather than on the train, who is positioned right next to the centre of the carriage as the flash goes off. The flight flash travels with the same speed in the second observer’s frame, but this observer sees* the back of the carriage moving towards the light signal and the front moving away. The result is therefore that this observer sees the two portraits light up at different times. In this case the portrait of Fitzgerald is lit up before the portrait of Lorentz.

Had the train been going in the opposite direction, Lorentz would have appeared before Fitzgerald. That just shows that whether its Lorentz-Fitzgerald contraction or Fitzgerald-Lorentz contraction is just a matter of your frame of reference…

But that’s not the paradoxical thing. The paradox is although the two portraits appear at different times to the trackside observer, the clocks still appear show the same time….

*You have to use your imagination a bit here, as the train has to be travelling at a decent fraction of the speed of light. It’s certainly not an Irish train.

Einstein’s Universe

Posted in The Universe and Stuff with tags , , on December 7, 2020 by telescoper

I’ve just started teaching about special relativity and for some reason I suddenly remembered this blast from the past (in 1979) which I saw when I was still at School. It is now available in fully remastered form on YouTube. It’s a feature-length film (2 hours long) but I think it’s worth sharing in its entirety. Here is the description from YouTube, with a few additions:

Based on Nigel Calder’s book Einstein’s Universe, this fascinating and rare film going by the same title has been re-mastered and digitally enhanced to bring Einstein fans a priceless experience. Narrated by the charismatic Peter Ustinov and hosted by Nigel Calder, the film was first broadcast on the centenary of Albert Einstein’s Birth; March 14th, 1979. Ustinov takes the viewer on a wonderful experience through the McDonald Observatory at the University of Texas-Austin where he is thoroughly enlightened on the great physicist’s theories, especially General Relativity, by a renowned team of scientists including Dennis Sciama, Roger Penrose, John Wheeler, Wallace Sergeant, Irwin Shapiro, Sidney Drell, and Ken Brecher.

Included in Ustinov’s experience at the McDonald Observatory are experiments to help understand gravity, warped space, how light responds to gravity, the “Doppler effect” and how radio waves, as used in police radar, are an unbeatable way of measuring speed. From these simpler experiments much larger concepts are drawn, such as the discovery of a Binary Pulsar, the nature of black holes and how they are created, and the ultimate theory of how the universe was formed. Other demonstrations measure the speed of light, how time passes more slowly for people traveling in an airplane, the incredible accuracy of the Atomic Clock in Washington, DC and how time itself would appear to stop at the surface of a black hole. The conclusion of the program portrays Einstein as a great humanitarian. Although known as the “father of the Atomic Bomb”, his greatest concern was for the potentially devastating effects splitting the atom could have on the future of mankind. His famous letter to President Franklin Roosevelt warned that although the splitting of the atom to detonate an atomic bomb could be used to end World War II, it could also potentially be used for far more deadly ends.

It’s a great chance to see and hear some of the greats of physics as they were over forty years ago, some of whom make remarkably prescient comments about the future (now our present) including about gravitational waves!