For me personally the ‘great conjunction’ of Jupiter and Saturn in December was a big disappointment because whenever I tried to make an observation the cloud to the SW horizon thwarted me. I hope some of you had better luck. However 2020 wasn’t all bad from an astronomical point of view as witnessed by the reminiscing at our online Christmas party of what had been observed throughout the year so let’s look forward to what this year will bring.  
 
Observing
            We had a broad look at the sky last month so we will focus in more detail on the winter sky facing south this month.The chart below represents the south facing night sky at 10.00pm on the 8th January and at 9.00pm on the 23rd January. No need for navigational help this month because Orion is so obvious but facing south and looking up you will find the bright star  Capella just short of your zenith.

With clear skies we are in for a treat because we have seven of the twelve brightest stars visible from the northern hemisphere. You will be familiar with the chart above but I’ll fill in some details for completeness sake. We have already come across four of the constellations- Orion- The Hunter, Taurus- The Bull, Auriga- The Charioteer and Gemini- The Twins. The two new constellations are Canis Major- The Great Dog and Canis Minor- The Little Dog. In mythology they are the dogs of the hunter Orion but from an observational point of view these constellations are small with little to offer apart from their main stars, Sirius (alpha Canis Major, the brightest star visible from the northern hemisphere) and Procyon (alpha Canis Minor, the 6th brightest star). Incidentally they are two of our Sun’s closest neighbours, Sirius being 8.6 light years distant and Procyon 11.4 light years. These two stars along with Betelgeuse in Orion form an asterism known as the Winter Triangle depicted in yellow in the diagram.
But Betelgeuse is roughly in the middle of another asterism- the Winter Hexagon comprising the stars Sirius, Rigel, Aldebaran, Capella, Pollux and Procyon and depicted by the red outline in the diagram. It is obvious with the unaided eye that these stars are different and within that grouping, including Betelgeuse, you will find a yellow giant (binary twin), a red supergiant, a blue supergiant, a red giant, a yellow star and two stars which are part of a binary system with a white dwarf (not visible to the unaided eye). And allowing for variability they all have a magnitude of about 1 or brighter.If that doesn’t make you reflect on what you are looking at in the winter night sky I don’t know what will. Now that we are in lockdown again if you are not sure which star fits into which category why not do a little research to fill in your time of an evening!
You may be thinking I’ve said nothing about Castor, the second bright star in Gemini, because it’s not as bright as the others but in fact it is an amazing star in its own right.To the unaided eye, the star Castor appears as a bright pinpoint of light but it’s actually three pairs of binary stars – six stars in all – in a complex dance about a common centre of mass. Even a fairly small telescope will show Castor as two stars and perhaps a glimpse of a much fainter star nearby, also part of the Castor system. Each of these three stars is also double but they cannot be resolved in a telescope and have to be inferred from spectroscopic data.
           
Something to look out for
            Although the ‘great conjunction’ is now in the past, Jupiter and Saturn continue to be of interest as they have a close approach with the planet Mercury between the 9th and 14th of January, visible above the south-west horizon from around 4.30pm as darkness falls, and you need to be quick as they are visible for only a short time. On the final day they are joined by a crescent Moon. We will be saying ‘Goodbye’ to Saturn and Jupiter as they are lost to view behind the Sun but Mercury continues to its greatest elongation and highest altitude above the horizon on the 27th January. Let’s hope for some clear skies to show off the winter night sky to its best.   

We have been struggling a bit recently with observations  but the close approach of the Moon and Mars produced the goods on the 25th November.  It was good to see. Let’s hope ‘the great conjunction’ lives up to expectations but more on that later.
 
Observing
            December is the last month in the year and the winter solstice takes place on the 21st so I thought it was time to take a look at the bigger picture rather than focussing on the detail and where better to start than the winter night sky.The charts below represent the whole night sky at 10.00pm on the 8th December and at 9.00pm on the 23rd December. The first chart is the night sky facing north.

Most people believe that it is a good idea that we all know some basic first aid. How to deal with cuts, bruises, stings and nose bleeds. More serious problems can be left to the professionals. By the same token I think everyone should know something about observing the night sky and I’ve come up with my list of five objects in the winter night sky which I think everyone should recognise. (Yes, I did have a job limiting it to five!). Obviously this is my personal list and some of you may come up with your own different selection. These are the things which I think you should be pointing out to your children and grandchildren on a crisp clear winter’s evening. It might just get them hooked on astronomy.
 

1. The Plough    Everyone in the northern hemisphere should be able to recognise The Plough. As an asterism it has a large clear distinctive shape- no need to worry about the fact that it is part of a constellation much of which is indistinct. Of course it is even more interesting when you point out that the ‘pointer stars’ of the plough lead you to the pole star, Polaris, and most children know that it gives the direction of north. The distance to Polaris is about four times the distance between the ‘pointer stars’.
2. Cassiopeia      I’ve chosen Cassiopeia both because it’s worthwhile in its own right, easily recognisable for its ‘W’ or ‘M’ shape and because of its link to Polaris and The Plough. A line from the third star in from the end of the plough handle through Polaris and extended about the same distance beyond leads to Cassiopeia. No need to get too technical but it is worth saying that The Plough and Cassiopeia are always in the night sky and rotate about Polaris during the year as if connected by a pole with Polaris at the centre. Of course the other stars do likewise but many dip below the horizon at certain times of the year and cannot be seen. This explanation might just help people understand why the night sky changes from month to month as it does.
   

This second chart is the night sky facing south.
 
3. Orion   As I said last month, Orion has everything and I would defy anyone not to have it on their list of things to see in the winter’s evening sky. It is a brilliant object in the sky and attracts everyone’s attention. Its bright stars and distinctive belt are likely to produce questions so you might want to be able to name Betelgeuse and Rigel if asked. Like The Plough, Orion also leads you on to other objects like my next choice.
4. The Pleiades ( or Seven Sisters)    The Pleiades doesn’t form a large object in the sky but it does catch the eye when looking at the sky hence on the list. Found by extending a line from Orion’s belt through the red star Aldebaran. Use a pair of binoculars to enhance the view.
5. Sirius Simply a star but it does happen to be the brightest star in the night sky when it is present so it should be up there with the tallest mountain and longest river as an item of general knowledge. It is also of historical interest because its appearance was used by the early Egyptians to tell that the river Nile was about to flood. Again easily located to the bottom left hand side of Orion.
 
I’m sure many of you will have your own favourites and might be wondering why I have not included them but I wanted to restrict the list to five. Remember this is just a starting point.            
 
Something to look out for
            Mars continues to be easily observed during the evening but this month it will have to take second place to ‘the great conjunction’. First though, there is a close approach of a three day old Moon with Jupiter and Saturn on the 17th December. Visible above the south-west horizon from around 4.30pm as darkness falls, this will provide an opportunity to get your bearings right for the ‘great conjunction’ four days later.   On the evening of the winter solstice, 21st December, the planets Jupiter and Saturn will be within about a tenth of a degree of each other. Remember that the Moon has an angular width of about half a degree so these two planets will be separated by about one fifth of the Moon’s diameter. Jupiter is much brighter than Saturn so they might be difficult to resolve. Of course these planets are widely separated in space and this optical effect comes about because Jupiter revolves around the Sun in just under 12 years whereas the orbital period of Saturn is over 29 years and so Jupiter laps Saturn every twenty years. This is the closest they have appeared since 1623 and won’t appear as close again until 2083 so definitely a once in a lifetime event.

I’ve included the chart just to show that Jupiter and Saturn will be close to the horizon and will set at 6.30pm. The Sun will set at 4.03pm so you will need to be outside during twilight to be ready to observe either side of 5.30pm. and you will need an unobstructed view to the south-west/west horizon. Let’s hope the skies are clear. The planets will still be within a degree of each other the weeks either side of the winter solstice so try to catch them whenever you can. The diagram below shows their separation over a two week period.

As 2020 draws to a close we can look forward to a once in 20 year astronomical event, the conjunction of Jupiter and Saturn, on the 21st of December.

What is a Conjunction?
Occasionally two or more objects meet up with each other in our sky. Astronomers use the word conjunction to describe these meetings. Technically speaking, objects are said to be in conjunction in that instant when they have the same right ascension on our sky’s dome. Practically speaking, objects in conjunction will likely be visible near each other for some days.

The word conjunction comes from Latin, meaning to join together. In language, conjunctions relate to clauses brought together in sentences with words like and. In astronomy, conjunctions relate to two or more objects brought together in the sky as we see them.
​
An inferior conjunction is when an object passes between us and the sun. Any object in space that orbits the sun closer than Earth’s orbit might pass through inferior conjunction from time to time, assuming its orbit lies more or less close to the ecliptic. Usually, though, when you hear the words inferior conjunction, astronomers are speaking of the planets Venus and Mercury, which orbit the sun inside Earth’s orbit. Astronomers sometimes refer to Venus and Mercury as inferior planets. When they’re at or near inferior conjunction, we can’t see them. They’re hidden in the sun’s glare. Occasionally, though, Venus or Mercury can be seen to transit across the sun’s disk at inferior conjunction. Consider also the moon. It passes between the Earth and sun at new moon once each month. Therefore you could say that the Moon is at inferior conjunction when it’s a New Moon.

A superior conjunction is when an object passes behind the sun from our point of view. Think of Venus or Mercury again. Half of their conjunctions with the sun – when they are brought together with the sun on our sky’s dome – are inferior conjunctions, and half are superior conjunctions. It’s kind of fun to imagine them on an endless cycle of passing in front of the sun, as seen from Earth, then behind it, and back again, like watching squirrels running around a tree. Meanwhile, the superior planets – or planets farther from the sun than Earth such as Mars, Jupiter, Saturn, Uranus and Neptune – can never be at inferior conjunction.

However there are many more conjunctions that occur which fall into neither of these categories. They occur when planets, or a planet and the moon, appear close together in the sky. The conjunction between Jupiter and Saturn is one of these and is often called a Great Conjunction.

How often do they happen?
As a result of their long orbits, Jupiter and Saturn meet in the sky only once every 20 years. In this period of time, Saturn completes two-thirds of its 30-year orbit (since 20 is two-thirds of 30). In the same period, Jupiter completes one 12-year orbit, plus, in the remaining 8 years, two-thirds of its next orbit (since 8 is two-thirds of 12). In other words, 20 years is the time it takes Jupiter to catch up and pass Saturn again as they circle the Sun.
 
The last conjunction of Jupiter and Saturn occurred on 28 May 2000, but was almost impossible to view because it occurred while the two planets were just 14.9° west of the Sun from our point of view. So the spectacle was largely lost in the Sun’s glare.

After 2020, the next great conjunctions will occur on November 2, 2040 and April 7, 2060. On both these occasions, the minimum separation of Jupiter and Saturn will be 1.1 degrees—which means they will appear 11 times further apart from each other than on December 21, 2020.

In fact, the 2020 great conjunction of Jupiter and Saturn is exceptionally close. Over a period of one thousand years, from 1600 to 2599, there are only six great conjunctions where the minimum separation between Jupiter and Saturn is less than 0.2 degrees: 1623, 1683, 2020, 2080, 2417, and 2477.

Though each successive ‘great conjunction’ takes place around 117º apart in the sky, the planets’ orbital resonance is such that each conjunction returns to the same part of the sky roughly every 800 years.

How and when to see it
The conjunction actually occurs at 13:30 GMT – that’s when the right ascension of the two planets will be the same, but the Sun will still be high in the sky at that point. When the Sun sets at 16:05 (according to Heavens Above website) the two planets will only be 14 degrees above the south-western horizon and set less than 2hrs 30mins later.

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.
 
 
Acknowledgements 
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.

References 
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.
DOI: 10.1073/pnas.96.10.5360
 
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 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’?

Geocentric theories
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.

Kepler’s breakthrough
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.

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.
In practice,

• Near perihelion: planet is closer to the Sun > r is smaller >  v is proportionally greater.
• Near Aphelion: planet is farther from the Sun > r is larger > v is proportionally less.

 
 
Kepler’s Third Law
The orbital period squared is directly proportional to the size of the semi-major axis cubed.

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

1. In a gravitationally bound system, as in the cases of the major and minor planets in the solar system, orbits are elliptical.
   

The eccentricities of the orbits of the major solar system planets are shown here:

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!)

1. Our current best description of gravity is general relativity (GR), announced by Einstein in 1915.  However for many purposes (e.g. getting a spacecraft to the Moon or any of the major planets), Newton’s Laws of Gravity are sufficiently accurate.

The greatest success of Newton's gravitational theory was when it was successfully used by others to predict the existence of Neptune based on observed perturbations in the orbit of Uranus.
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).

1. If the bodies in the system are gravitationally unbound, the orbits will still be conics, but in this case, they will both follow either parabolic or hyperbolic paths.   

Examples of this behaviour are ‘visitors from outside the solar system’ such as Oumuamua, the first known interstellar object detected passing through the Solar System, discovered on 19 October 2017.