Regular readers of my Blog will know that I come more from the data analysis side of astronomy than the pretty pictures side. So this month just for a change, we’ll have some wonderful images as well as data. So, let’s start off with … a pretty picture!
In fact, Figure 1 is far from being ‘just a pretty picture’ – this stunning image shows two galaxies, NGC2788 and NGC2789 which are in collision.
How do we know these galaxies are interacting and that what we are seeing is not just a trick of perspective? If we look at the NASA Extragalactic database, we see the data in Table 1:
The first thing we can see is that both galaxies should be visible in modest sized amateur telescopes. The two galaxies have similar magnitudes, as shown above, although remember that each order of magnitude decreases brightness by approximately 2.5.
The fact that NGC2798 and NGC2799 are close together is revealed by two parameters: their redshifts are similar within two parts in 10,000. And their Hubble distances with respect to the Cosmic Microwave Background (CMB) are approximately only 2.78% different.
Will stars collide?
The NASA/ESA press release that accompanied this picture states “While one might think the merger of two galaxies would be catastrophic for the stellar systems within, the sheer amount of space between stars means that stellar collisions are unlikely”. How can that be established?
As a first approximation, we can model a spiral galaxy such as our Milky Way (MW) as a disk where the radius of the disk, is about 50,000 light-years or 15.33 kpc and the thickness of the disk is about 0.5kpc. The number of stars in the MW is estimated to be N ~ 10¹¹
We are now interested in parameter called the number density of stars - simply, the number of stars divided by the volume of the disk.
However, we can’t work out the volume of the disk simply by calculating the volume of an equivalent cylinder. In reality, the disk of a spiral galaxy is not homogenous – it has been known since the’60s that the spiral arms are density waves (Lin & Shu, 1964). Let's assume 70% of stars are in the spiral arms; there are no stars in the voids between the arms; and that the arms make up 50% of disk. These are of course gross assumptions, good only as a first approximation. The results (calculations are available in Excel® if you are interested) are shown in Table 2 below:
In the ‘Single galaxy’ column the number density of stars is less than one star per cubic parsec; expressed differently: in one cubic parsec of space, there is on average less than one star. In fact, on average we’d need to search 2.63 cubic parsecs of space to find a single star.
In the ‘Two similar colliding galaxies’ column, we imagine two spiral galaxies colliding head on. Here, the number density is doubled as the spiral arms collide. Correspondingly, the volume of space on average we expect to encounter a star is still 1.31 one cubic parsecs.
Let’s just remind ourselves how large a volume of space a cubic parsec is. Imagine a cube of space one parsec on each side. That’s 3.26 light-years on each side or, if you prefer, 3.1*1013 km on each side.
Even a very large star such as the red supergiant Betelgeuse is a very small object in all that space, so even in a galactic collision, as the NASA press release says, the chances of two stars colliding is very small.
How common are galaxy collisions?
The answer is – not uncommon. The next two images show some well-known examples.
The image in Figure 3 shows the distorted disk of NGC4631. This is caused by NGC4631’s interaction with two much smaller galaxies, NGC 4627 and NGC 4656.
The plot in Figure 4 shows the results of radio emissions of NGC4361 reported in Neininger & Dumke (1999). The small dark object above the disk of NGC4631 is the dwarf elliptical galaxy NGC 4627 with which NGC4631 is interacting.
Another source of data about colliding galaxies is Galaxy Zoo, a project that enables citizen scientists to categorise and analyse images of galaxies taken by professional observatories. One of Galaxy Zoo’s initiatives is the Galaxy Merger project (Holinchech 2016). The data collection phase is now complete and comprises 62 colliding galaxy pairs (I have this data as an Excel table for anyone interested).
A good example from the Galaxy Zoo merger table Is ARP148 in Ursa Major (Galaxy Zoo mergers table ID49). This is also called Mayall’s Object, named after American astronomer Nicholas U. Mayall (not John Mayall), who discovered the object in 1940.
Can it happen here?
There is a short answer: ‘Yes’. For example, the Sagittarius Dwarf galaxy has been involved in multiple collisions with our Milky Way galaxy and this is the probable reason for the warped nature of the Milky Way’s disk (Law & Majewski, 2010).
A recent determination of the radial velocity of the Andromeda galaxy, M31 with respect to the Milky Way indicates a velocity of −109.3 ± 4.4 kms per second, the negative sign indicating M31 is moving towards the Milky Way. The same research indicates a low transverse velocity of 17 km per second, indicating the probability of a head-on collision between the two galaxies (van der Marel, 2012)
The end result of this collision will be a very massive elliptical galaxy.
This Blog is not a scientific paper, although it lists various scientific papers as sources in the References section. I am indebted to Hugh Allen for drawing my attention to the paper by Neininger & Dumke (1999).
Data used in Table 1 was obtained from the NASA Extragalactic Database. The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
Holincheck et al (2016).
Galaxy Zoo: Mergers – Dynamical models of interacting galaxies.
MNRAS459,720–745 (2016). doi:10.1093/mnras/stw649
Law, D; Majewski, S (2010). The Sagittarius dwarf galaxy: a model for evolution in a triaxial Milky Way halo.
2010 ApJ 714 1. DOI: 10.1088/0004-637X/714/1/229
Lin, C & Shu, F (1964).
On the Spiral Structure of Disk Galaxies. ApJ, vol. 140, p.646 . DOI: 10.1086/147955
Neininger, N; Dumke, M (1999). Intergalactic cold dust in the NGC 4631 group.
van der Marel, R et al (2012). The M31 Velocity Vector.II. Radial Orbit Towards the Milky Way and Implied Local Group Mass.
ApJ, 753:8 (14pp), 2012 July 1. DOI: 10.1088/0004-637X/753/1/8 https://iopscience.iop.org/article/10.1088/0004-637X/753/1/8/pdf
We haven’t been favoured with particularly good observational weather recently so let’s hope that with darker evenings following the change from BST to GMT we also get clearer skies.
The chart below represents the night sky at 10.00pm on the 8th November and at 9.00pm on the 23rd November. Best viewing of what is discussed will be towards the end of the month and going into December.
If you face south, as usual, and look directly overhead you will easily find the ‘W’ shape of the constellation Cassiopeia which we continue to enjoy on its journey westwards in the evening sky. Look to the west and you should see the bright star Deneb, the tail of the swan in the constellation Cygnus, as it flies to the western horizon. So, as Altair slips below the horizon and out of sight, it’s time to say goodbye to the Summer Triangle, but this month we are looking to the east because as one constellation sets in the western sky another one appears in the east.
This month we will have the arrival of the constellation Orion- The Hunter. It’s my favourite constellation because of its distinctive shape and because it appears to have everything. It doesn’t take much to visualise a hunter from the stars in Orion and what stars they are! Orion’s right shoulder is represented by the star Betelgeuse, a variable red supergiant, varying in magnitude from about 0.3 to 1.2 and the 7th brightest star in the northern hemisphere. If Betegeuse were to replace our sun it would reach out all the way to the orbit of Jupiter. It also has the potential of going supernova but of course we do not know exactly when. Then, representing his left foot, is the blue supergiant Rigel the 5th brightest star in the northern hemisphere with a magnitude of 0.2. Between these stars is a line of three stars going from south east to north west and they represent Orion’s belt and at magnitudes of around 2 they are unmistakable. Less bright but still visible to the unaided eye is Orion’s sword hanging from his belt. The bottom star of the sword should be visible in good conditions and above this is a misty fuzzy patch which is the Orion nebula (aka M42) where star formation takes place. Try to observe it through binoculars or a telescope if you get the chance.
Because it is so easily recognisable, Orion is a good starting point for finding your way about the night sky during the winter months. Follow a line from Orion’s belt to the upper right, underneath the star Bellatrix representing his left shoulder, and you will find the star Aldebaran, a giant red star of magnitude 1 and the 9th brightest star in the northern hemisphere. It is in the constellation Taurus- The Bull, and is said to represent the angry eye of the bull. The ‘V’ shape of stars outlining the bull’s face is an open star cluster called the Hyades. Continue the line beyond Aldebaran and you find the better known star cluster- The Pleiades or Seven Sisters. Remember back in springtime we watched Venus pass close to the Pleiades which catches the unaided eye but much more is revealed if you use a pair of binoculars.
Bright stars are like the proverbial bus, you wait ages to see one then four come along at once. Our fourth star this month is Capella in the constellation Auriga- The Charioteer, lying directly above Taurus. Having followed the line to the Pleiades turn ninety degrees to the north and the bright star you see is Capella. It is the 4th brightest star visible in the northern hemisphere and shines at magnitude 0.1. Auriga is in the shape of a pentagon although the most southerly star is in Taurus.
As mentioned earlier the constellations and stars described above are presently in the east in the evening and will be better viewed later on but are highlighted so that you can enjoy them throughout the winter months.
Something to look out for
Mars continues to be an attraction and it will have a close approach with the Moon on the 25th November and this will visible throughout the evening.
We often say that the planets in the solar system ‘orbit the Sun’; or that the Moon ‘orbits the Earth’. But what exactly is an ‘orbit’?
For many centuries it was believed that the Earth was at the centre of the universe and that all the stars and planets revolved in circular motion around the Earth. It is a curiosity that this theory, usually attributed to Ptolemy, persisted so long. It could only explain the observed pattern of movements of the planets by explaining that they moved in epicycles – effectively circles within circles, but how this movement came about was unexplained.
Copernicus and heliocentric models
The Prussian Nicolaus Copernicus proposed a theory of a heliocentric system, with the Sun at the centre of the universe, in which Earth was one of the six planets known at the time. Copernicus was not the first to espouse this theory, but was the first to extensively document it in his book published shortly before his death in 1543. As in the Ptolemaic system, Copernicus’ orbits were circular, so epicycles still had to be invoked to explain some of the observed motions of the planets. In fact, more epicycles were needed in the Copernican system than the Ptolemaic system, and yet there were still unexplained gaps in explaining astronomical observations.
Johannes Kepler, a prolific German astronomer and mathematician made the key breakthrough in the study of orbital motion by a combination of observation and deductive reasoning empirically deriving three laws which stand in good stead to this day.
Kepler’s key discovery was that planetary orbits are NOT circular, but elliptical. An ellipse is an example of a conic section.
In case you’re not familiar with conics, and with terms such as ‘semi-major axis’, ‘eccentricity’ and ‘focus’, the next section contains a quick primer on the subject. If you are familiar with conics, you could skip this and go to the following section.
Newton’s Laws of Gravitation: formalizing Kepler’s laws
Due to the operation of gravity, two massive objects will move in space-time around their common centre of mass, known as the barycentre. This was established by Sir Isaac Newton who defined his laws of gravitation, our first formal description of gravity. This provides our first definition of what an orbit is.
Newton’s Laws added formal mathematical reasoning to Kepler’s empirically-derived Laws. In his words:
”I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly.”
Kepler’s First Law
Planets orbit on elliptical paths, with the Sun at one focus of the ellipse.
As we’ve seen, an ellipse is an example of a conic section.
More precisely, Newton defined the focus as being at the barycentre of the Sun–planet pair.
So, using Newton’s Laws, how can we determine where the barycentre is? Let’s consider a very theoretical solar system consisting of just the Sun and Jupiter.
With only two objects in a system, it's simple to locate the barycentre of the system around which the two bodies orbit. The Sun’s mass, M⊙=1.99*1030kg. Jupiter’s mass, MJ=1.898*1027kg. Using Newton’s Laws, we have:
Which means the ratio of Jupiter’s mass to the Sun’s mass is about 1/1,000.
In turn that means that the distance from Sun to the system's barycentre approximately 1/1,000 times the distance from Jupiter’s distance to the barycentre.
The mean distance from the Sun to Jupiter is 7.785*1011m; we shall see how to work that out in a moment, using Kepler’s Third Law; please accept it for now. One thousandth of that distance is 7.785*108m. The radius of the Sun is slightly less: 6.96*108m. This means the barycentre of our very simplified two-body solar system is just above the Sun’s surface.
In the real solar system, consisting of the eight major planets, several known minor planets, asteroids etc., the position of the barycentre of the whole system changes all the time. Jupiter is by far the most massive planet and so has the greatest influence on the position of the barycentre. However, the alignment of the other solar system bodies is constantly changing as the planets orbit at different speeds (see Kepler’s Second Law below). So the relative influence of their respective masses changes the position of the barycentre constantly. Technically, this is known as an “n-body problem”, the mathematics of which is very complicated, so we’ll conveniently declare outside the scope of this Blog.
Kepler’s Second Law
Planets sweep out equal areas in equal times.
What this means is that the angular momentum is conserved throughout the course of the orbit.
If the orbit was circular, then the distance of the orbiting body from the primary, r, would be constant. However, since the orbit is elliptical, then r changes. The mass, m is constant, so the velocity, v must change to keep the angular momentum constant.
Kepler’s Third Law
The orbital period squared is directly proportional to the size of the semi-major axis cubed.
Where k is a constant. In his gravitational theory, Newton formalized this constant as:
Where M1 and M2 are the masses of the two bodies. As we have seen, in the solar system even the largest planet, Jupiter, has a mass of only about 1/1,000 solar masses, and this simplifies the equation to become:
However, this can be simplified even further if we pick our units carefully. If the orbital period, P is in Earth years (yr); and the semi-major axis, a is in AU, then by definition k=1. So we don’t even need to know the mass of either the star or the planet to calculate the furthest orbital distance between them.
Let’s again take the case of Jupiter. From observations, we know that the orbital period of Jupiter, PJ=11.86 yr. So:
So the mean distance of Jupiter from the Sun is 5.20AU is approximately 7.78*1011m, just as we assumed when describing Kepler’s First Law above.
Putting it all together
This plot clearly demonstrates the huge effect Jupiter has on the solar system. Jupiter’s mass is greater than the sum of the masses of all the other major planets. Notice that Mercury has by far the greatest orbital eccentricity, despite being closest major planet to the Sun. The huge mass ratio between the Sun and Mercury would mean a near circular orbit were it not for the influence of other large bodies – most notably Jupiter.
The high orbital eccentricity of Mars is due to the high mass ratio between Jupiter and Mars, and Mars mean orbital distance being relatively close to the mean orbital distance of Jupiter.
Saturn, despite being further from the Sun, has a higher orbital eccentricity than Jupiter, due to the more massive planet’s gravitational influence.
Uranus and Neptune, each orbiting further from the Sun than the mean distance at which Jupiter orbits the Sun, are less gravitationally influenced by Jupiter, and so have lower orbital eccentricities.
Less easy to explain is the very low orbital eccentricity of Venus – the lowest of any planetary body in the solar system. This may have something to do with Venus’ retrograde rotation affecting its angular momentum. I’d be very interested in comments on this (NOT a trick question: I don’t have the answer!)
Newton’s Laws were unable to account for the orbital precession of Mercury, yielding values well below the observed movements. GR predicts this to very close accuracy (see my August Blog).
September wasn’t a particularly good month weatherwise but on the 5th, Mars and the Moon were good to see between the rolling clouds. Mars has continued its retrograde motion and is now below the lower arm in Pisces (more about that later) while Jupiter and Saturn have continued westward in the evening sky. Poor weather prevented the viewing of the setting Sun on the equinox so will have to wait till the spring equinox in March to fix due West.
I was rather dismissive of two of the watery zodiacal constellations, Aquarius and Capricornus, in last month’s blog and as a ‘fishy’ constellation features this month it is probably time to say something about stellar magnitudes. It is OK looking at a stick presentation of a constellation in a diagram but they don’t look like that in the sky! Originally the brightness of a star was classified on a scale of 1 to 6, 1 being the brightest and 6 being just visible to the unaided eye. (Note the the bigger the number the dimmer the star. In the modern scientific era measurements have shown that a difference in magnitude of 1 means the brightness differs by a factor of 2.5, ie a magnitude 2 star is two and a half times as bright as a magnitude 3 star and a magnitude 1 star is one hundred times brighter than a magnitude 6 star. Really bright objects have a negative magnitude). But that was over two thousand years ago in the Middle East with clear skies and no light pollution. What can we expect to see today at a latitude of about 50 degrees North with the associated weather that brings and the light pollution from modern towns and cities.
If we face South and look above us just past our zenith we see again the reassuring sight of the ‘W’ shape of Cassiopeia. The three brightest stars Caph, Schedar and Navi are close to magnitude 2 and clearly visible while epsilon Cas on the extreme left is magnitude 3.4 and considerably dimmer but easily visible if conditions are reasonable. (See diagram below).
If we drop down to the horizon towards the right we locate as we did last month the Great Square of Pegasus with the star Alpheratz at magnitude 2.1 and Algenib about half as bright with the other two stars of the square in between. The four stars stand out because they are in a fairly empty part of the sky. Now for the tricky part. Again as we did last month, starting from Alpheratz we look for the two curved strings of stars which make up Andromeda. The lower string isn’t too bad because from Alpheratz; delta Andromeda, Mirach and Almach have magnitudes 3.3, 2.1 and 2.2 respectively so no problem. However the higher curved string of stars from Alpheratz; pi Andromeda, mu Andromeda and 51 Andromeda have magnitudes of 4.3, 3.9 and 3.6 respectively. We are now in a situation where poor atmospherics and light pollution become critical if the stars are to be visible to the unaided eye. For comparison, if you are trying to locate the Andromeda galaxy, M31, it has a magnitude of 3.4.
If you are struggling to see the fainter stars even in a clear sky you need to leave the comforts of your home and find a more rural dark sky site. Sorry!
That’s all my excuses made now so we can return to sky gazing. Below Andromeda and to the south east of the Great Square of Pegasus lies the constellation Pisces- The Fish. Supposedly two fish, one the Circlet and the other the group of stars to the East of Alpheratz, tied together with a ribbon. I use the word ‘lies’ advisedly because unfortunately only two stars in Pisces are brighter that magnitude 4 and even then, only just, so it is unlikely that you will see anything if you are in your back garden! If any readers follow their ‘stars’ in the newspapers or were born under the star sign Pisces perhaps now is the time to consign astrology to the rubbish bin. Why did I bother to mention Pisces? At present the planet Mars is in Pisces and at magnitude -2.3 it is more than a hundred times brighter than a magnitude 3 star and outshines anything nearby. It will have a close approach with the Moon on the 3rd October just three days after the full Moon. It will be at its closest to the Earth on the 6th October and at opposition (on the far side of the Earth from the Sun) on the 14th October so visible all night. Now that is something to look forward to.
The diagram below has more named stars than usual not because they are bright but because I used them in the text to explain the variation we see in stellar magnitudes and again I have omitted some minor star groupings to help with clarity.
With the idea of stellar magnitudes firmly in mind let us look at three further constellations. To the southeast of the lower string of Andromeda and due East of the Great Square of Pegasus is another zodiacal constellation, Aries- The Ram. (Remember you probably cannot see anything in Pisces apart from Mars). Aries contains two brightish stars, Hamal at magnitude 2.0 and Sheratan at magnitude 2.7 which are readily seen but there is not much more. How you make the shape of a ram from that I do not know. However Aries has a claim to fame in that it was the location of the spring equinox about two thousand years ago and that event is still called the ‘first point in Aries’ even though it is now in Pisces.
Between Aries and Andromeda is the constellation Triangulum- The Triangle. It has the great redeeming feature that it is what it says on the tin- a triangle! However it doesn’t have any stars brighter than magnitude 3 but because of its compact nature it is readily recognisable if seen.
Finally to the northeast of Aries and Andromeda and southeast of Cassiopeia is the fairly prominent constellation Perseus- another hero from Greek mythology. It contains the stars Mirfak and Algol both around magnitude 2 and another five stars around magnitude 3 or brighter.
Something to look out for
As mentioned above Mars is going to be the major attraction in the night sky this month so don’t miss it and see if you can follow its retrograde motion to the first week in November. ( I used my binoculars to locate eta Pisces and epsilon Pisces).
If you want to see a ‘falling star’ your best chance will be on the 21st October when the Orionid meteor shower is at its peak.
At the end of the month there are two lunar close approaches to look out for. The Moon and Jupiter on the 22nd and the Moon and Mars on the 29th. Clear skies and happy viewing.
My attempts to see the Perseid meteor shower were thwarted by cloud cover but the close approach of the planets Jupiter and Saturn with the Moon at the beginning of the month was good to see. At the time of writing there has been a lot of cloud cover so I’m not very optimistic about seeing the close approach at the end of August.
I hope you are keeping your eye on Cassiopeia on its journey west because it is approaching its optimal viewing position and with the Plough low in the northern sky, Cassiopeia is better placed to help us find our way among the stars. Also it is just lovely to look at!
The diagram below seems to contain a lot this month but some of it you are already familiar with and I have omitted some minor star groupings to help with clarity.
As usual we start facing south and look up to the zenith and just short of it and to the right hand side we see the bright star, Deneb, the tail of Cygnus the swan and along with Vega and Altair we quickly pick out the Summer Triangle. From the line joining Deneb and Altair turn left by about 45 degrees to look east of south and you will spot the asterism, the Great Square of Pegasus, which stands out not because of the brightness of its stars but because it is away from the Milky Way and there are few stars visible in this area. This asterism is part of the constellation Pegasus (the winged horse in Greek mythology). Again it is difficult to imagine a horse and no obvious signs of wings. Pegasus is quite a large constellation but its other stars do not stand out as much as the square. The square isn’t actually a square and to add insult to injury the star, Alpheratz, at the top of the square isn’t part of Pegasus! However on a positive note, the Great Square of Pegasus is easily picked out and is another good signpost to help us find our way around the skies.
Alpheratz, is part of the constellation Andromeda (the princess, daughter of the mythological Queen Cassiopeia and King Cepheus) and being the brightest star is also referred to as a And (alpha Andromedae). The main features of Andromeda are two curved strings of relatively faint stars meeting at Alpheratz and it is readily found because of its association with Pegasus. The constellation Andromeda is home to one of the most famous objects in the sky- the Andromeda galaxy also known as M31. It is marked on the diagram with a red cross and labelled M31. The Andromeda galaxy is the nearest large galaxy to Earth and is similar in many ways to our Milky Way galaxy and is the only one visible to the unaided eye in the northern hemisphere. To locate it for observing, (your eyesight needs to be pretty good), start at Alpheratz and by star hopping jump to the second pair of stars along the curved strings and the Andromeda galaxy will be to the right hand side at a distance approximately equal to the distance between the two stars. There is no rush as Andromeda will be in a good position right through till November. Now some mind boggling statistics- the distance to Andromeda is about two and a half million light years which means that the light entering your eyes from Andromeda set out two and a half million years ago, about the time the first members of the genus Homo appeared on Earth using stone tools and long before Homo sapiens arrived on the scene! Andromeda is the most distant object you can see with the unaided eye but you will need a dark site with no light pollution and clear skies. Don’t expect to see something like the images shown in the gallery of the WMA website, you will have to settle for something which might be described as a smudge or fuzzy star but that doesn’t detract from the sense of achievement. Good luck!
If we drop down from the Great Square of Pegasus along the diagonal from Alpheratz to the horizon we find another zodiacal constellation, Aquarius (the Water Carrier). Unfortunately to the unaided eye Aquarius has no bright stars and is of an indistinct pattern. Since antiquity it has been seen as a figure pouring water from a jug but I am obviously lacking in imagination.
However I remember a time in the late sixties when any radio channel you switched to was likely to be filling the air with the song ‘Aquarius’ from the musical ‘Hair’ or from a version by an American pop group. It was a song to cheer you up and had the memorable line, ’This is the dawning of the age of Aquarius’. This might lead us in to discussing ‘the precession of the equinoxes’ but luckily this has already been done in a recent blog by Gordon Dennis (Dennis, July 2020).
Now follow the line from Vega through Altair down to the horizon and you will find the right hand edge of another zodiacal constellation, Capricornus (the Sea Goat, associated with many myths from ancient times) just to the south east of Aquarius. This constellation is relatively small and the second faintest zodiac constellation so doesn’t have much to offer the casual observer and I can’t recall a pop song called Capricornus. However, precession is a slow process so there might be one by the year 4750 give or take a few hundred years!
Let’s have a grand tour. Find the Great Square of Pegasus and follow the left hand side of the square upwards past Andromeda on your left till you see Cassiopeia. From the star Navi go across the top of the constellation Cepheus to the pole star, Polaris, in Ursa Minor, and continue in a straight line to the star Alioth in the handle of the Plough, part of Ursa Major. Just as before, follow the arc of the handle down till you find the bright star Arcturus in the constellation Bootes then follow round eastwards to spot the Keystone of Hercules not missing out the small but attractive constellation, Corona Borealis, on the way. One more step eastwards and you are back at the Summer Triangle comprising Vega in Lyra, Deneb in Cygnus and Altair in Aquila from where we found the Great Square of Pegasus at the start. Now give yourself a pat on the back because you have gone round half the visible night sky and identified twelve constellations.
Erratum: In last month’s blog, ’Looking to the Skies August 2020’, the line pointing to the variable star delta Cep should have gone past the first star to the top right hand one of the three stars in the bottom left hand corner of Cepheus. Sorry for the ambiguity.
Something to look out for
This is the month of the autumn equinox when as the Earth revolves around the Sun, the Sun’s apparent path round the ecliptic crosses the celestial equator and the Sun is overhead at the equator and everywhere on earth has almost equal amounts of daylight and darkness. It will happen on the 22nd of September but of course it happens at a specific time which is about a quarter of a day later each year until it is corrected for with the extra day of a leap year and so the date of the autumn equinox can vary by a day or two but it is usually on the 22nd or 23rd. Another feature of an equinox is that the sun rises due east and sets due west so note some landmark on the horizon in line with the sun at sunrise and sunset and you have your east and west directions. As far as astronomers are concerned it means we are into Autumn with more starry evenings.
There are exciting times ahead because the planet Mars is going to be a major attraction in the night sky in the coming months. Try to catch it early in the month because it rises in the east with the Moon on the 5th September at 9.30pm BST. I say catch it early in the month because there is a little project you might enjoy doing- observing the retrograde motion of Mars. By the 10th of September it stops its apparent eastward motion against the background stars of Pisces and then appears to move westwards until November. Use the stars nPsc, mPsc and ePsc on the lower branch of Pisces as your guide. It should pass between the first two of these stars about the 30th September and it will be getting brighter throughout the month. I hope the diagram clarifies the situation. The orange line is the path which Mars will follow during its retrograde motion from 1st September to the first week in November.
Finally there will be a conjunction, I use the term loosely to mean a coming together rather than the more technical definition, of the Moon, Jupiter and Saturn on the 25th September, best viewed to the south just after 8.00pm BST.
In July’s WMA webinar, we looked at Hertzsprung-Russell diagrams. H-R diagrams are one of the most important tools available in stellar physics, since they indicate a great deal about the characteristic of stars. The H-R diagram below, known as a theoretical H-R diagram, is a scatter plot of stars photosphere temperature vs. luminosity.
Brian Davidson’s last couple of Blogs have mentioned the Summer Triangle asterism, consisting of Vega, Deneb, and Altair. Taking a sample of ‘nearby stars’ as shown below we have marked the Summer Triangle stars on the H-R diagram, showing how different these three stars are:
The spectral classes of the stars are indicated by the familiar ‘OBAFGKM’ legend. Before looking at the three stars, look at the track running from Alnitak at the top left to Proxima Centuri at the bottom right. This track is the Main Sequence, where in the stars interior hydrogen is converted into helium by nuclear fusion. Stars leave the main sequence once about 11% of the hydrogen-mass has fused to helium and the core of the star becomes unstable.
About 90% of stars are on the main sequence. It may not appear like this from the diagram, but that’s because of our sample, which is ‘nearby stars’.
Altair is a main sequence star, larger and hotter than the Sun. It will therefore have a shorter main sequence life than the Sun. Altair’s luminosity is 10.6 L⊙. Recall that luminosity is a measure of the power radiated by a star; the unit of luminosity is the Watt.
Vega has a photospheric temperature similar to that of Altair. But Vega’s hydrogen burning phase is now over. The star has entered the main sequence turnoff, on the way to becoming a red giant, before shedding its outer layers to form a planetary nebula. At that time, what will remain of Vega is a hot white dwarf star at the bottom left of the H-R diagram. This sequence of events will also be what happens to the Sun when main sequence turnoff occurs.
Deneb is a super-giant star. Although Deneb’s Photospheric temperature is comparable to both Vega and Altair, its luminosity is very much greater. Deneb has a luminosity of more than 104 L⊙, a mass of 19M⊙ and is destined to end its life in a Type II supernova event. This will leave a supernova remnant perhaps like the Crab Nebula, M1 and a neutron star which is way off scale at the bottom of the H-R diagram.
Open clusters and globular clusters
For this month’s Blog, we’ll consider a question asked at the July WMA webinar, “Can we make H-R diagrams of star clusters to help determine their characteristics?” The answer is yes.
Astronomers are familiar with both open clusters and globular clusters. Their main characteristics are shown in the table below.
How can we conclude that open clusters consist of young stars and globular clusters consist of old stars? The amount of hydrogen that a star has available for fusion is directly proportional to the star’s mass. In simple terms, the greater the mass of hydrogen packed in, the faster the reaction rate, and the higher the luminosity. The star’s luminosity determines how quickly the star will fuse the hydrogen into helium, and hence how long the star lives on the main sequence according to the relation:
Since from the mass-luminosity relation we know that:
The diagram below summarises how stars of different spectral classes leave the main sequence - the “main sequence turnoff” - as they evolve:
Plugging the numbers into the equations, this means that a star of 10M⊙ will have a lifetime of only about 13 million years.
Bear in mind that we know that about 80% of stars are red dwarfs, smaller than the Sun. A low mass star of about 0.6M⊙ has a life of ~34 billion years. That time is much greater than the age of the universe which means that no low mass star has yet completed its main sequence lifetime.
H-R diagram for open cluster M45
So, let’s plot an observational H-R diagram, (also known as a “colour-magnitude diagram”) for open cluster M45, known of course as the Pleiades:
The observational H-R diagram above is a plot of absolute magnitude (VMag) vs. colour index (BMag-VMag). The scale ranges are (x: colour index 0.2 à 1.45; y: absolute magnitude 8 à -2) .
We can see at the top left of the H-R diagram, only a few of the larger, more luminous (which of course implies more massive) stars in the Pleiades have begun their main sequence turnoff. These are the dots at the top left which are turning upward and to the right. The majority of the (less massive) stars in the plot remain very much on the main sequence. They are so young that hydrogen burning has a while to progress.
It is generally thought that open clusters disperse after a short time (in cosmological terms) before the stars in them have commenced main sequence turnoff. It is also thought that then Sun formed in an open cluster which subsequently dispersed and that this accounts for the fact that the Sun is isolated and not part of a multiple star system, although that is far less certain.
H-R diagram for globular cluster M14
Now, let’s look at the H-R diagram for globular cluster M14. This H-R diagram is markedly different to that of M45. The plot is a subset of the total data of over 1,000 stars and is plotted with the same scale ranges as the M45 plot.
In the M14 H-R diagram, just about no main sequence stars are evident. The reason is that most stars in M14 are very old, and have completed hydrogen burning and moved off the main sequence. Low mass stars are either ascending the red giant branch or have already become red giants. Like Altair, Vega, and the Sun, they will end their lives as white dwarfs. A few at the top right of the H-R diagram are supergiants and, like Deneb, will finish their lives in Type II supernova events.
The fact that the majority of stars in this globular cluster are grouped at the red end of the colour index confirms the generally red appearance of the globular cluster.
Contreras Pena, C et al (2013). The globular cluster NGC6402 (M14). A new BV color-magnitude diagram. ApJ, September 2013. DOI: 0.1088/0004-6256/146/3/57 Accessed August 10th 2020
Australia Telescope National Facility
As promised Jupiter and Saturn are now in the late evening sky and they are on the diagram below but with Jupiter shining so brightly in the southern skies it doesn’t need a signpost. The highlight of last month was the appearance of the comet Neowise visible to the unaided eye in the northern sky and Josh Dury gives a description of where to look for it in his recent e-mail, ‘Identify the constellation, Ursa Major, and use the two stars marking the edge of the saucepan to draw a line at about a similar distance until you come across a faint, smudge patch in the sky. This is Comet Neowise’. It is not usually wise to predict when a comet will appear because over the years there have been many disappointments because of unfulfilled promises of a spectacular sight. One comet which did live up to and even exceed expectations was comet Hale-Bopp back in 1997 and I remember it well. I mention it because it was discovered by amateurs.
We talked about the Summer Triangle of Vega, Deneb and Altair last month so we will start from there. From Altair in the Summer Triangle, looking southerly, drop down the Milky Way close to the horizon and to the right is the constellation Sagittarius (the Archer) which lies on the ecliptic to the left of Scorpius. Yet again it is hard to distinguish the archer of mythology but what is easily recognisable is the asterism ‘the Teapot’. The planets Jupiter and Saturn are on the diagram and in fact Jupiter is by far the brightest object in that part of the sky and you cannot miss it. Sagittarius lies in the direction of the centre of our Milky Way. There are dense clouds of gas and dust along the plane of the Milky Way which obscure our view to the centre. See the recent picture of the Milky Way sent back by my granddaughter from New Zealand.
To the right of Sagittarius and also close to the horizon you will see the star Antares which we mentioned last month.
Now let us go to the other end of the Summer Triangle with Vega and Deneb and look at two circumpolar constellations. Face south and look up to find Polaris- the pole star. Obviously it is above your zenith so you need your deckchair again! If you look to the east you should recognise the ‘W’ shape of the constellation Cassiopeia which we found previously from the Plough via Polaris. So do the reverse trip from Navi through Polaris and you come to the Plough. You will see it is almost upside down now. Just as we have watched the Plough change its orientation so we can enjoy watching Cassiopeia continue on its anticlockwise journey around the pole star gradually taking on the proper ‘W’ shape we are accustomed to during the rest of the autumn as it heads south. Just east of Cassiopeia is a group of not very bright stars forming a shape roughly similar to the gable end of a house. This is the constellation Cepheus (King Cepheus of Ethiopia in ancient mythology and husband of Cassiopeia). Perhaps its claim to fame is that it contains the prototype of an important group of variable stars called ‘cepheid variables’ which have been fundamental in establishing a ‘standard candle’ for the measurement of intergalactic distances and the rate of expansion of the universe- a key area of research in cosmology at present. The prototype was delta Cep in the bottom left hand corner of the house shape.
I guarantee you will enjoy seeing Cassiopeia in the southern skies for the rest of the year.
Something to look out for
At the beginning of the month on Saturday 1st there is a close approach of a near full moon and Jupiter with Saturn just to the east. There is another close approach on Friday 28th August. We cannot all be together for the Perseid meteor shower as usual but if you want to see some shooting stars look out on the nights of 11th and 12th August and be prepared to stay up a little longer than usual to give yourself the best chance in spite of a Last Quarter Moon.
Precession is a phenomenon that occurs when massive bodies move, due to angular momentum being affected by other masses in space-time. In the words of John Archibald Wheeler, “mass tells space-time how to curve, space-time tells mass how to move”.
Precession of Earth’s rotational axis
The most familiar example is the precession of a gyroscope; its rotational axis appears to describe a circle under the influence of Earth’s gravity. Exactly the same applies to the rotational axis of the Earth under the influence of the Sun's (and to a lesser extent, the Moon's) gravity:
As most people are aware, Earth’s rotational axis is inclined ~23.5° to the plane of the ecliptic, which accounts for the seasons. Currently, the Earth’s rotational axis points almost exactly at Polaris, which is therefore called the ‘pole star’. However, the precession of Earth’s axis has a period of ~26,000 years, so that in around 13,000 years time, Earth’s axis will point at Vega, which will then be the ‘pole star’. Then, in about 26,000 years time, Polaris will again be the ‘pole star’. This is an example of rotational axis precession.
The precession of Earth’s rotational axis also accounts for the phenomenon of precession of the equinoxes. The First Point of Aries is one of the two points where the plane of the ecliptic intersects the celestial equator (Davidson, 2020). These are called vernal equinoxes. The first point of Aries was recognized in antiquity in the constellation Aries, but due to precession of Earth’s axial rotation is today located in the constellation of Pisces. Exactly 180° around the celestial equator is the first point of Libra, which today lies in the constellation Virgo.
Let’s put that precession cycle into context. The period of precession of Earth’s rotational axis is:
Human civilisations are known to have started ~6,000 years ago. The number of precession cycles during that time is not yet one quarter:
Modern Homo sapiens are believed to have emerged ~200,000 years ago. The number of precession cycles during that time is almost eight:
Earth formed ~4.5 Bn years ago. The number of precession cycles during that time is more than 170,000:
Precession of planetary orbits
As was discovered by Kepler, a planet follows an elliptical path as it orbits the Sun. The point at which the planet makes its closest approach is known as periastron. For many years, it could not be explained by Newtonian theory that the periastron of Mercury does not always occur at the same place in the Mercury’s orbit. This is because the orbit itself is subject to precession, so that over a period of time periastron occurs at a point further around the orbit. This was established by careful observation in the nineteenth century.
Since Mercury is the planet orbiting closest to the Sun, the precession of Mercury’s orbit is higher than any of the other planets.
How orbital precession works is illustrated in the diagram below.
PLEASE NOTE that a) this diagram is looking at the solar system from ABOVE; b) the diagram is emphatically NOT TO SCALE ; c) also, the orbital eccentricities are GREATLY exaggerated; and d) the angular precession angle is GREATLY exaggerated.
Newtonian gravitational theory predicts that the magnitude of the orbital precession of Mercury should be slightly more than half what is actually observed. Although many explanations were produced to account for the observations, none were considered conclusive. Einstein’s General relativity (GR), published in 1917, predicted the rate of orbital precession to be 43 arc-seconds per century. This matched the observations exactly.
In turn, let’s put that into context. How long does it take Mercury’s orbit to precess a full 360 degrees? Based on angular measure (Helps, 2020), the answer is approximately 3 million years:
Or, looked at another way: Mercury is estimated to have formed 4.5Bn years ago. That would imply that Mercury’s orbit has completed
precessions since Mercury’s formation.
This accurate prediction of 43 arc-seconds per century was the first major observational proof that General Relativity is a valid theory. Note that we say a “valid” theory rather than a “true” theory. A scientific theory cannot be proved to be true; it can be showed to accurately account for observations. A scientific theory can only ever be “proved” to be untrue. Later, GR was also able to exactly predict the much smaller orbital precession of Venus (8.6 arc-seconds per century).
The second observational evidence pointing to the validity of GR was that gravity of a large mass would “bend” light rays passing close by it - recall John Archibald Wheeler’s ‘mass tells space-time how to curve’ above. This was verified by an expedition lead by Sir Arthur Eddington to observe a total solar eclipse in 1921. But that’s another story.
John Archibald Wheeler: https://phy.princeton.edu/department/history/faculty-history/john-wheeler
Mathematics of precession: https://en.wikipedia.org/wiki/Precession
Angular size: Helps, L; WMA Blog, May 2020
Celestial equator and plane of the ecliptic: Davidson, B; WMA Blog, May 2020
The summer solstice has passed now so we will gradually get improved lighting conditions for observing. The notes here apply at 11.00pm BST at the end of the first week of the month and at 10.00pm BST at the beginning of the last week in the month. However I find that at present the sky doesn’t really get dark until after midnight and this month you will need a clear view to the southern horizon with no obstructions and free from local light pollution. I did have a look out on the morning of June 19th to see the close approach of Venus and the Moon but I’m afraid the cloudy skies were against me.
Back at the beginning of April if you looked directly above you while facing south, the Plough was directly overhead (at your zenith) and looked like a plough. Now you will notice that it has moved anti-clockwise about the North Pole and is now upright on its handle. Keep checking the orientation of the Plough as the year progresses.
So while facing south, look directly above you and just before your zenith you will see a very bright star. Perhaps this is the time to get your deckchair out and lie flat on your back! This star is easily recognisable due to its brilliance and a grouping of four stars to its bottom left hand side. These stars make up the compact constellation Lyra (the Lyre or Harp) and the bright star is Vega, alpha Lyr, the 3rd brightest star visible from the northern hemisphere. The lighter region of the diagram to the left of Vega represents the Milky Way, the star filled disc of our galaxy, and there you find a giant cross in the sky and this is the constellation Cygnus (the Swan) with the bright star Deneb, alpha Cyg, representing the tail of the swan which is flying down the Milky Way. Deneb is the 14th brightest star visible from the northern hemisphere. At the head of the long neck is the star Alberio, beta Cyg, about which I have heard our chairman, Hugh, wax lyrical on more than one occasion so do look at it through a telescope if you get the chance.
Now face Vega and Deneb and drop down about halfway to the horizon till you find the star Altair in the constellation Aquila (the Eagle). Altair, alpha Aql, is identified by two fainter stars either side of it and together they point to Vega.
I hope you have been keeping count of these bright stars because Altair is the 8th brightest star visible from the northern hemisphere and you have now become acquainted with eight of the eighteen brightest stars. These three stars Vega, Deneb and Altair form what is called the Summer Triangle depicted in yellow in the diagram. The Summer Triangle is something you will be able to enjoy looking at for the rest of the summer into autumn. Like the Plough it is a big help in finding your bearings.
Now let us be a little more subtle because biggest and brightest isn’t always the best. Last month we found Arcturus by following round the arc of the handle of the Plough. Between Vega and Arcturus you find the constellations Hercules (the strong man from Greek mythology) and Corona Borealis (the Northern Crown). Hercules is a fairly faint constellation and looks more like flailing windmill blades than a strong man but the most distinctive feature is the four central stars in the shape of a quadrilateral forming an asterism known as the Keystone. Corona Borealis is small but distinctive, consisting of seven faint stars in a horseshoe shape if you cannot envisage a crown.
We are quite unashamedly going back to bright star ‘bagging’. We are doing this because the object in question is best observed in summertime. Imagine a line from Vega to Arcturus and from its midpoint follow a line to the horizon between Hercules and Corona Borealis until you see a reddish star. Remember you will need a good unobstructed view to your southern horizon. This star is Antares, the brightest star in the constellation Scorpius (the scorpion) and is the sole attraction because most of Scorpius and specifically its fish-hook shaped tail is not visible from our latitude. Antares is the 10th brightest star visible from the northern hemisphere and that is because it is a red supergiant and if it were to replace our sun, its surface would lie between the orbits of Mars and Jupiter. That is big! It is said to represent the heart of the scorpion.
Something to look out for
The major planets, Jupiter and Saturn, return to the late evening sky this month quite close together and visible all night. On July 14th Jupiter will be at opposition, on the opposite side of the Earth from the Sun, so will be at its closest and brightest. A week later on the 20th July, Saturn reaches opposition but unfortunately both planets will be quite low in the southern sky and although bright are not ideally located for good viewing.
This year, we celebrate 30 years of the history of the Hubble Space Telescope Here’s the HST itself, and one of its most famous images, taken in 1995.
The extent of the universe
The HST is named after the American astronomer, Edwin P Hubble, whose observations in the early 20th Century, lead to two, profound discoveries. Looking into these we will also meet several other important characters.
Hubble was physically large and imposing. he was a US Army boxing champion, serving at the closing stages of WW1, although his unit did not go into combat. He affected an English accent despite being very much an American.
For the first twenty or so years of the twentieth Century, there was great scientific debate about the extent of the universe. Many scientists believed at the time that the whole of the universe consisted of our Milky Way galaxy, and that what were then called “spiral nebulae” were some kind of structure within the Milky Way. Following painstaking observations at the 100 inch Hooker telescope at the Mount Wilson Observatory in California, Hubble and his assistant Humasson established in 1924 that spiral nebulae are in fact remote galaxies in their own right; they are now called spiral galaxies.
Hubble’s discovery was made possible by way of an earlier crucial discovery made by Henrietta Swan Leavitt, who worked at the Harvard College Observatory. Leavitt had the task of examining photographic plates to measure and catalog the brightness of stars.
This work led Leavitt to discover the so-called 'period-luminosity relationship' of Cepheid variable stars. Probably the best known Cepheid variable star is Polaris, the current pole star. Leavitt’s discovery was that the rate at which these stars appeared to vary in brightness was directly related to their intrinsic luminosity. This meant that measuring the period of change provided astronomers with the first "standard candle" with which to measure the distance to remote astronomical objects. Hubble used this technique to show that Cepheids in the Andromeda galaxy, M31, was too far distant to be part of the Milky Way Galaxy. It was later discovered that there different types of Cepheid variables, and this meant that M31 is actually twice as far distant as Hubble first calculated.
The expansion of the universe
Hubble’s second observational discovery was to prove equally profound. It was in fact preceded by a theoretical discovery by Georges Lemaître, a Belgian Catholic priest and professor of physics at the Catholic University of Louvain. Lemaître applied Einstein’s general relativity (GR) to cosmology deriving solutions to Einsteins field equations, giving results that implied an expanding universe.
Extrapolating back in time, Lemaître postulated an origin of the universe in what he called a 'primeval atom' – in effect, the “big bang”. This was in 1927, two years before Hubble's publication of his observational findings of expansion of the universe.
An advanced mathematician, Lemaître could hold his corner in intellectual argument with Einstein (no less!). The two met on several occasions, including at the Solvay Conference in 1931.
Albert Einstein of course needs no introduction. Einstein published his theory of General Relativity in 1917. Developed from his theory of Special Relativity (published in 1905), GR included an explanation of the phenomenon of gravity. Among other things, GR successfully accounted for variations in the precession of the orbit of Mercury which Newtonian gravitational theory was unable to explain. Einstein had believed that the universe was static, although others (including Alexander Friedman and Georges Lemaître) provided solutions to his equations that indicated that the universe must be either expanding or contracting.
In January 1931, Einstein visited Hubble at the Mount Wilson Observatory where the 100 inch Hooker telescope is located.
Einstein, perhaps rather reluctantly, conceded that the expansion predicted by general relativity must be real, added a term called the 'cosmological constant' to his field equations. In later life, he said that this was "his biggest blunder", although today the cosmological constant is now thought by many cosmologists to account for the role of dark energy.
Confirming Hubble’s discovery using modern data
Hubble's observations, published in 1929, established that the spectra of majority of galaxies exhibit a redshift, showing they are moving away from us, and that the further away they are, the faster they appear to be receding. This became what is now called Hubble's Law and is a cornerstone of modern cosmology.
The data plot below shows the plot published in Hubble's 1929 paper.
The slope of the trendline indicates the value of what is called the Hubble parameter, H₀, a measure of the velocity of recession of galaxies vs. distance. Hubble's early estimate was that H₀ ~500 km s¯¹ Mpc¯¹ . This was quickly realized to be much too high, as it implied an age of the universe of less than 2 million years, whereas it was known that Earth was much older than this.
The plot below has been constructed from modern data in the NASA Extragalactic Database (NED).
As in Hubble’s work, the plot shows recessional velocities against distances. The red trendline represents H₀. Observations since Hubble's time have refined and reduced the value of H₀ and today the value is thought to be in the range 60-90 km s¯¹ Mpc¯¹ - the exact value is still highly debated in the community. The slope indicates on this plot for this sample of 44 galaxies, H₀ ~64 km s¯¹ Mpc¯¹ .
For Hubble’s confirmation of the extent of the universe and for Hubble’s Law, the Hubble Space Telescope, which has made so many discoveries of its own in its 30 year operation, is named in his honour.