The weather hasn't been particularly favourable recently but at least we can look forward to earlier sunsets and the chance to see some stars in the evening skies again. Let's hope there are clear skies as well.

Observing
The following charts represent the night sky at 11.59BST on the 8th of August and at 10.59pm on the 23rd of August. To use the chart, face south at the appropriate time with the bottom of the chart towards the southern horizon and you will see the stars in the chart.

Having described the Summer Triangle last month we shall use that as our starting point for navigating the skies. Locate Altair at the bottom of the Summer Triangle and continuing on a line from the two small constellations we introduced last month, Sagitta- The Arrow and Delphinius- The Dolphin, we find the smallest constellation in the northern hemisphere night sky Equuleus- The Little Horse or Foal. It is supposed to represent the head of a young horse. Its brightest star, Kitalpha, is only of magnitude 4 and because it is so small this constellation is easily overlooked.
Between Equuleus and the horizon is the zodiacal constellation Capricornus- The Sea Goat. It is relatively small with stars dimmer than magnitude 4 so it doesn't offer much to the unaided eye. Similarly to the left of Capricornus is another zodiacal constellation Aquarius- The Water Carrier and it is equally faint and indistinct. However this month they are the region of the sky in which we find the two planets Jupiter and Saturn of magnitudes -2.8 and 0.2 respectively and these two will outshine any nearby stars and there are more details about them in the final section.
Now let's go to the other end of the Summer Triangle, locate Vega and Deneb and look at some circumpolar constellations.

Facing Deneb, look above your zenith and find Polaris- the Pole star. To avoid neck strain best to use a deckchair! Between Deneb and Polaris is a group of not very bright stars forming a shape similar to the gable end of a house. This is the constellation Cepheus- King Cepheus of Ethiopia in ancient mythology. To the east of Cepheus is the welcome sight of the constellation Cassiopeia- wife of King Cepheus, its familiar 'W' shape now standing on its end. This is a sight you can enjoy more and more in the coming months as it rises higher in the sky until it is at your zenith in the winter months.
To the west of Cepheus is the large constellation Draco- The Dragon, which wraps otself around Ursa Minor. Unfortunately Draco has no stars brighter than magnitude 2 but it does contain the star Thuban which 5,000 years ago was the pole star in the northern hemisphere. Due to the precession of the Earth's axis, the position of the celestial pole traces out a circle, over a period of about 26,000 years, on the celestial sphere and over the last 5.000 years it has moved from Thuban to Polaris. This is rather fortunate for us because at magnitude 2 Polaris is considerably brighter than Thuban at magnitude 3.7.
Finally between Cassiopeia and Cygnus and straddling the Milky Way is the small and obscure constellation Lacerta- The Lizard. Because of its small size it contains few objects of interest but it is the site of 'Nova' explosions, the subject of Hugh's recent talk

Something to look out for
I think we can allow ourselves to get a little excited becuase this month has the potential for some good observation. The planets Saturn and Jupiter are at opposition on the 2nd August and 20th August respectively so they are on the opposite side of the Earth from the Sun and at their closest approach to the Earth. This means that they appear larger and brighter and compared with last year higher in the sky. They rise as the Sun sets and set as the Sun rises so are visible all night being their highest about midnight. Of course they will continue to be visible for some time to come with Saturn having a close approach with the Moon on the 21st August when the 12 day old Moon will pass 7 Moon diameters to the south of Saturn. Similarly there will be a close approach of the Moon and Jupiter on the 22nd August.
Equally exciting is the prospect of an impressive Perseid meteor shower which, although active from 17th July to the 24th August, will peak on the 12th August. What we call a meteor or 'shooting star' is a grain of dust burning up in the Earth's atmosphere. In the case of the Perseids the grains of dust were left by the comet Swift-Tuttle and each year the Earth passes through that dust trail as it orbits the Sun. The meteors appear to radiate from a point in the sky called the 'radiant' in the constellation Perseus, hence the name, but you don't have to be looking at the radiant to observe the meteors. More important is that you can lie back on a lounger, allow your eyes to become accustomed to the dark and avoid light pollution as much as possible. a blanket and warm drink will help to keep you comfortable. If you are watching with a group then a real party atmosphere as I recall when the group had a meeting in Cheddar a few years back and Ben Sutlieff was recording the meteors indoors with his radio equipment. Let's hope for a return to such times soon. Clear skies.

I’m pleased to report that I had some success with observing the partial solar eclipse at the beginning of June. Although there was a bit of cloud cover it cleared up enough to enable me to see somewhere close to the point of greatest eclipse both through solar eclipse glasses and with a homemade pinhole camera. I was with a group of people at the time and they were quite impressed with the result from the latter. There will be another partial solar eclipse next year so for a bit of fun why not try making a pinhole camera. Easy to make with minimum materials.
 
Observing
The summer solstice is past but we still have long light evenings so the following charts represent the night sky at 11.59pm BST on the 8th of July and at 10.59pm BST on the 23rd July. To use the chart, face south at the appropriate time with the bottom of the chart towards the southern horizon and you will see the stars in the chart.

We shall focus on the jewel of the summer sky this month- The Summer Triangle. It is not a constellation but is an asterism formed by three bright stars from three separate constellations. As usual facing south and looking directly above you just before your zenith you will see a very bright star. It might be easier getting a deckchair out and lying on your back! This star is Vega and you cannot miss it because of its brilliance, it is the 3rd brightest star visible from the northern hemisphere, and it has a grouping of four fairly faint stars in the shape of a parallelogram to its bottom left hand side. Together these stars make up the compact constellation Lyra- The Lyre or Harp. Vega forms a small triangle with the top right hand star of the parallelogram and another star just to its top left. Apparently if you have good eyesight you will observe that this is a double star but closer inspection with a telescope reveals that each of these is a double star. The two pairs of stars are in orbit around each other taking hundreds of years to complete a single orbit and have become known as the celebrated Double Double
            The lighter region of the chart 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. The bright star Deneb represents the tail of the san which is flying down the Milky Way. Cygnus is a lovely summer signpost high in the sky. The star Albireo representing the beak of the swan is another double star, beautiful to see through a telescope.
            Now from a line joining Deneb and Vega, look down about halfway to the horizon and you find another bright star Altair in the constellation Aquila- The Eagle. Altair is identified by two fainter stars either side of it forming a line pointing to Vega. The three stars Vega, Deneb and Altair form what is called the Summer Triangle depicted in red on the chart. You will enjoy looking at it for the rest of the summer and it is a great help in finding your way around the night sky.
            We’ll do that right away to find two small constellations. Contained within the Summer Triangle near the bottom vertex is the constellation Sagitta- The Arrow. It is the third smallest constellation and is somewhat dart shaped but even the brightest star at the point of the arrow is only of magnitude 3.5 so you will need dark sky conditions and a clear sky.
            To the left of Sagitta and outside the Summer Triangle is another small but distinctive constellation Delphinus- The Dolphin. The magnitude of its stars is similar to those of Sagitta so again you will need clear, dark sky conditions.

From Altair, looking southerly, drop down the Milky Way and close to the horizon is another zodiacal constellation Sagittarius- The Archer. It is hard to imagine anything that represents an archer but what is easily recognisable is the asterism- The Teapot, outlined in red in the chart. Lying as it does in the direction of the Milky Way, Sagittarius is an area of the sky rich in star clusters and bright nebulae which hide the very centre of our galaxy where there is believed to be a supermassive black hole some 26,000 light years away.
 
Something to look out for
The planets are not well placed for observing this July so why not enjoy a broad sweep of a starry summer’s evening instead. Start with The Plough and Cassiopeia, which are visible throughout the year, and notice how they have continued on their anti-clockwise journey facing each other across the North Pole with The Plough to your west and Cassiopeia to your east. Now follow the arc of the handle of The Plough down to Arcturus in Bootes as we did in May. Turn slightly east to see The Keystone of the constellation Hercules and continue on to the Summer Triangle discussed above. Take a final look to the east and see if you can pick out The Great Square of Pegasus. Then raise your eyes towards the North Pole and there you see Cassiopeia again. If that doesn’t raise your spirits on a clear summer’s evening I don’t know what will!
Clear skies.

Not that long ago, the phenomenon of cryovolcanism was a regarded as a theoretical possibility on some bodies in the outer part of the solar system.  On Earth, volcanoes consist of an outpouring of molten rock, mainly silicates.  Cryovolcanism is defined as the extrusion of liquids and vapours of materials, mainly water.  It was until recently only a matter of scientific speculation and no such thing had been observed.
At the distance at which the gas giant planets orbit the Sun, surface temperatures on planetary moons are very low.  In the case of Enceladus, the sixth moon of Saturn (see Figure 1), the warmest surface temperature is around just 70K.  At that temperature, water is frozen solid and as hard as granite.  
Enceladus was discovered in 1789, one of many discoveries made by the German-born English astronomer  William Herschel  (1738 –  1822). The moon is very small with a diameter of approximately 500km and little more was known about Enceladus until the late twentieth and early 21st centuries.

The first images of this diminutive moon that showed any surface features were taken by Voyager 1 and Voyager 2.  These were not high resolution and taken at long range (so nothing like as detailed as shown in Figure 1). 
In 2005, the NASA Cassini spacecraft started multiple close flybys of Enceladus, revealing its surface in much greater detail.  We can see that there is very little cratering, suggesting a very young surface.  The very high albedo (loosely speaking, reflectivity) of Enceladus’ surface is due to it being composed of water ice.  The near-linear surface features located particularly near the poles  (Tobie, 2015; Ray et al, 2020) were named “tiger stripes”.  The crucial images taken by Cassini revealed water-rich plumes venting from the south polar region as shown in Figure 2 below.

The important point to remember here is that Figure 2 is NOT an artist’s impression.  This is an actual observation of active and on-going cryovolcanism taking place right now. 
Approximately 93% of the plume material falls back to Enceladus’  The escape velocity  at the surface of Enceladus is only ~240 ms-1, so the rest escapes the moons gravitational attraction, and supplies most of the material making up Saturn's E ring.  Saturn’s atmosphere does have water clouds, but the water can’t reach as high in the planet's atmosphere as the water from Enceladus showering down.  This makes Enceladus the only moon in the solar system known to influence the chemistry of its parent planet.
Evidence from the observed libration of Enceladus plus chemical analysis of the observed plumes using a mass spectrometer instrument aboard the spacecraft  provides evidence with a high degree of certainty that the moon has a global sub surface ocean largely (though not entirely)  of water (Witze, 2014).  Mixed in with water in the plumes are silicates, indicating interaction between the ocean and its underlying rock floor (Choukroun et al, 2021); Tobie, 2015).  This is assumed to be caused by hydrothermal venting in the depths of Enceladus’ oceans, which also happens in Earth’s oceans.  They are made possible by tectonic processes on Earth, giving the strong implication of similar processes occurring on Enceladus.
A hydrothermal vent known as a black smoker near the Galapagos Islands is shown in Figure 3.

Somewhat astonishingly, around these geothermal vents live primitive life forms generally called extremophiles, since they exists under pressures and temperatures which would kill most species.  These extremophiles do not rely on any energy from sunlight and instead receive energy from chemical processes associated with the vent.  Given that over 500 such sites are known on Earth, plus the chemical analysis of Enceladus’ plumes, there is a possibility that similar primitive life forms might exist in Enceladus’ sub-surface ocean.

Habitable zones in planetary systems

As far as we know, all living species need water, including extremophiles mentioned in the previous section which may exist on Enceladus.  The definition of a stars habitable zone has been the range of distances where liquid water can exist on a planetary surface.  Too close to the star, the water will boil off; too far out, the water will freeze.  This concept is shown in Figure 4.
This all sounds very simple, but as with many things, the situation is actually more complex.  For one thing, the fact that a planet orbits the star within that stars habitable zone does not immediately indicate that the planet is inhabited.  Consider for example the case of the Sun.  Within the Sun’s habitable zone there are two planetary-sized objects.  One, which we call Earth, is full of a vast number of living species.  The other, which we call the Moon, is not fare distant from Earth, and within the Suns habitable zone, but is devoid of all life.

The next aspect to consider is the type of star.  Red dwarfs are by far the most common type of star in the Milky Way.  They have surface temperatures of ~2,000K, and so, referring once again to Figure 4, those stars habitable zones will be closer in to the star than as in the case of the Sun, whose surface temperature is just below 6,000K.
One might reasonably assume that in such a system a planet would be as likely as the Earth to harbour life, albeit the planet would need to be orbiting closer in.  For example, the TRAPPIST-1 system in Aquarius, discovered in 2015, has at least 3 earth-sized planets in its habitable zone – see Figure 5.

However, red dwarves are known to produce very intense flares of radiation.  For example, studies by NASA’s Chandra X-ray observatory concluded that about 25% of the time, Barnard's Star, located approximately 6 light years from the solar system, unleashes scorching flares, which may damage the atmospheres of planets closely orbiting it. So once again, while the habitable zones around stars such as Barnard’s or TRAPPIST-1 may be long term theoretically conducive to life, in the short term, life may not even get started due to the intense radiation environment.
So let's get back to icy moons.  As well as Enceladus, evidence of cryovolcanism has been observed on Neptune's moon Triton and is suspected on Jupiter's moon Europa.  And yet, should any of these moons harbour life in their sub-surface oceans, their parent planets - the gas giants Jupiter and Saturn, with the ice-giant Neptune - are well outside the Suns habitable zone.  All of these planets would be well off to the right of the diagram in Figure 5.
From the foregoing, we can see that the “conventional” view of the habitable zone can be somewhat  misleading. We might assume false positives in the case of red dwarf star systems.  Equally we might neglect the cases of life existing in orbits outside of what is conventionally thought of as the habitable zone, such as the possibility of life in the sub-surface ocean of Enceladus.

Conclusions

1. Saturn’s moon Enceladus is a prime target  for life detection.  Plumes containing water, CO2 and sodium chloride, NaCl as well as silicates originating from the ocean floor have been positively identified by the Cassini mission data.
   
2. Sample-return missions to Enceladus have already been proposed (Mackenzie et al, 2021; Neveu et al, 2021)

References

Choukroun, M et al (2021). Sampling Plume Deposits on Enceladus’ Surface to Explore Ocean Materials and Search for Traces of Life or Biosignatures.  The Planetary Science Journal,2:100(7pp), 2021 June.  https://iopscience.iop.org/article/10.3847/PSJ/abf2c5/pdf    Accessed June 6 2021.
Mackenzie, S et al (2021). The Enceladus Orbilander Mission Concept: Balancing Return and Resources in the Search for Life.  The Planetary Science Journal, 2:77(18pp), 2021 April.  https://iopscience.iop.org/article/10.3847/PSJ/abe4da/pdf  Accessed June 10, 2021
Neveu, M et al (2021). Returning Samples from Enceladus for Life Detection.
Ray, C et al (2020). Oxidation processes diversify the metabolic menu on Enceladus.  https://arxiv.org/pdf/2012.08582.pdf  Accessed June 11 2020
Tobie, G (2015).  Enceladus’ hot springs https://www.nature.com/articles/519162a.pdf Accessed June 10 2021
Witze, a (2014). Icy Enceladus hides a watery ocean.  Nature News. https://www.nature.com/articles/nature.2014.14985.pdf   Accessed June 10 2021

I don’t know if any of you had more luck than me but I didn’t achieve my own challenge of seeing Mercury during May. With so much rain and cloud cover, and the usual haze close to the horizon observing has been very difficult but I have managed to see Venus on the odd clear night and I still have two evenings left in May to catch Mercury. Several people have mentioned the ‘super’ moon on the 26th so that always attracts attention especially in those parts of the world where a lunar eclipse was observed.
 
Observing
It is the summer solstice in the northern hemisphere on the 21st June so we have long light evenings and need to do our sky observations later than usual and the following charts represent the night sky at 11.59pm BST on the 8th of June and at 10.59pm BST on the 23rd June. To use the chart, face south at the appropriate time with the bottom of the chart towards the southern horizon and you will see the stars in the chart.

Starting from The Plough like last month we follow the arc of the plough handle down to the bright star Arcturus in the constellation Bootes- The Herdsman. Easily identified by its kite shape. Note that The Plough has continued on its anti-clockwise journey about the Pole star and is now ‘standing on its handle’. Just for interest I’ve named another star in Bootes- Izar, which can be resolved with a small telescope to reveal an orange giant of magnitude 2.7 and a fainter blue star. Something to look out for when we get back to group observing again and the opportunity to make use of a telescope.
Now, while still facing south, look to your left by about 30 degrees (about 3 clenched fists at arm’s length) and you will see a group of four relatively faint stars in the form of a quadrilateral. This is an asterism called The Keystone and is part of the constellation Hercules- the strong man from Greek mythology. Although quite a large constellation, Hercules is relatively faint but The Keystone gives us another signpost in the sky. I can see no likeness to a strong man and in fact Hercules is generally depicted upside down.
Lying halfway between The Keystone and Arcturus is a small but distinctive constellation, Corona Borealis- The Northern Crown. It consists of seven faint stars (but the brightest is of average magnitude 2.2) in a horseshoe shape if you cannot envisage a crown. Corona Borealis forms a very attractive grouping of stars. 

The second diagram shows three constellations and the stars are mostly faint but these constellations deserve a mention because they lie on the zodiac, a region of the sky either side of the ecliptic- the apparent path of the Sun as it traverses the celestial sphere. By definition therefore the Sun passes through all the constellations on the zodiac. Historically the zodiac was divided into twelve equal regions each with its own sign of the zodiac and corresponding approximately to twelve zodiacal constellations. These were mostly used by astrologers about which we shall say no more. In the early part of the 20th century the International Astronomical Union defined boundaries for the constellations by coordinates in the sky and irrespective of the star patterns. The zodiacal constellations were no longer of equal size and there were thirteen rather than twelve. The odd one out is Ophiuchus which is a constellation but not a sign of the zodiac. That might be useful as the answer to a quiz question sometime!
Follow a line from the right side of the Keystone down to the horizon and you will see a bright reddish star with an average magnitude of about 1.4. This star is Antares, the brightest star in the constellation Scorpius- The Scorpion. Most of Scorpius and specifically its fish-hook 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. It is said to represent the heart of the scorpion.
Having located Antares, the small and faint constellation Libra- The Scales lies towards the right.
Between Antares and the Keystone lies the large but faint and indistinct constellation Ophiuchus- The Serpent Bearer. Ophiuchus does not have much to offer the casual observer but its claim to fame is that it is the home of Barnard’s Star, the fastest moving star in the sky and at a distance of only 6 light years is the fourth closest star to the Sun after the three in the Alpha Centauri system.
  
Something to look out for
The big attraction in our skies this month is the solar eclipse which takes place on the 10th June. It will appear as an annular eclipse in some parts of the world but as the Moon passes in front of the Sun we will see a partial eclipse starting about 10.00am and finishing just after 12 noon. At maximum coverage at our location the Moon will extend across almost a quarter of the Sun’s diameter between 11.00am and 11.30am.Remember never to look directly at the Sun as this could result in permanent eye damage. Solar eclipse glasses are available if not locally then definitely online. Don’t risk using any unreliable method. Some of you may wish to try projecting an image of the Sun using a pinhole camera. For an image diameter of 1cm you will need a projection tube more than a metre long. Let’s hope the weather stays good.
            On the 13th June there will be a close approach of the Moon and Mars with the Moon passing just over 5 Moon diameters to the north of Mars. You will be able to observe this from 10.00pm as dusk fades 16 degrees above the western horizon.
Clear skies.

At long last we have been able to enjoy some clear skies and the Moon was prominent high in the sky last month with a close approach to Mars in the middle of April and a super moon on the 27th April.
 
Observing
The following charts represent the night sky at 10.00pm BST on the 8th of May and at 9.00pm BST on the 23rd May. To use the chart, face south at the appropriate time with the bottom of the chart towards the southern horizon and you will see the stars in the chart.

We’ll start from The Plough which we discussed last month and you will notice that it has continued on its anti-clockwise journey round the pole star and is now slightly west of south with the middle of its handle at your zenith. Follow the arc of the handle of the Plough downwards round to the star, Arcturus, which has the distinction of being the second brightest star visible in the northern hemisphere at magnitude -0.05. Also known as alpha Boo (alpha meaning it is the brightest and Boo a short form of Bootes). It is an orange giant nearing the end of its life and relatively close at a distance of 36 light years. It is the brightest star in the constellation Bootes (The Herdsman) and again it is difficult to distinguish such a figure whereas the Kite asterism is easier to see and is what most people recognise as Bootes.
In mythology the constellation Coma Berenices is supposed to represent the locks of Queen Berenice of Egypt but it contains no stars brighter than magnitude 4 so doesn’t present much to observation with the unaided eye. I recall that it was an answer to a quiz question so if it comes up again at least you will have heard of it.  

Carry on following the curve of the arc from Arcturus for about the same distance again until you see another bright star. This is Spica the brightest star in the constellation Virgo- The Maiden. Virgo is of course one of the zodiacal constellations as it lies on the ecliptic. Spica is a blue-white star with an average magnitude of about 1 and is 260 light years from Earth.
 It may be easier to memorise these two star hops using the expression (Arc on to Arcturus and Speed on to Spica).
Now look to your north west and from last month you should recognise Leo- The Lion with Regulus shining brightly. Turn to face Leo then look up and you are back at the Plough.
 
Something to look out for
The challenge this month is to spot the planet Mercury. This is always quite tricky because it is low in the sky and only visible for a short time after sunset in the North West sky. It will be at its brightest early in the month but close to the Sun and it will be at its highest altitude on the 16th May. You will need a clear view to your West/North West horizon and if you have the use of binoculars so much the better. On the 4th May it will be on its easterly journey just below the Pleiades and above and to the left of our old faithful Venus which is significantly brighter. A better opportunity to spot it arises on the 13th May when a crescent Moon, Mercury and Venus form an isosceles triangle about 40 minutes after sunset. I can’t finish without saying how good it is to have Venus back in the evening sky and it will be just above a crescent on the 12th May. Clear skies.

The earliest method of enabling astronomers to determine the distance to remote objects is the parallax method.  As Earth orbits the Sun, we see an apparent shift in the positions of stars relative to much more distant stars, called parallax. For nearby stars, the parallax is larger and for more distant stars the parallax is smaller.
 
The baseline used by the parallax method is fixed by the size of Earth's orbit around the Sun. Recall that like all orbits, that of the Earth is an ellipse rather than a circle. The mean Earth–Sun distance, or Astronomical Unit (AU), is approximately  1.5 * 10 to the power 9 metres. Earth's orbit is so nearly circular that using the mean distance is accurate enough for these purposes.
 
As shown in Figure 1, if we observe a star's position with respect to the distant stellar background between two observations that are six months apart in time we will see the parallax shift in our data. The observation baseline is 2 AU.

At this point, let us to define a unit of distance called the parsec.  This unit of measure is defined as the distance at which 1AU subtends an angle of 1 arcsecond to the observer.

Hence referring to Figure 2, the distance to a remote object is given by:

Some examples are shown in Table 1, where stellar distances are derived from parallax angle using equation (1).

Limitations of the parallax method
Looking at the results above, we can see that distance values for the first two stars agree quite closely with recognized values.  However, the distances for Rigel and Betelgeuse do not agree very well with accepted values.  These stars are both "nearby" in that they are both very much naked-eye objects.  So where does the problem lie?
 
Parallax angles of less than 10 milliarcseconds (mas) are very difficult to measure using Earth based telescopes due to atmospheric effects.
 
Using equation (1) and considering a parallax angle of 10 milliarcseconds:

Hence, distances greater than 100pc pose increasing difficulty for ground based instrumentation. In 2008, researchers using the Very Large Array (VLA) produced a radio solution of 5.07±1.10  mas for the parallax angle of Betelgeuse, corresponding to a distance of 197±45 pc or 643±146 lyr (Harper et al, 2008). In this paper, Harper et al also point out that the angular size of Betelgeuse is greater than it's parallax angle, creating further problems when observing such large stellar objects at this distance range. 
 
The European Space Agency (ESA) Hipparcos satellite mission made it possible to measure the parallax displacements with an accuracy of up to 0.1 mas a big improvement allowing parallax measurements to be theoretically useful up to

The follow-on ESA mission, Gaia can measure parallax angles to an accuracy of  0.01 mas giving useable distance measurements up to:

So we can see that the use of space-based telescopes has extended the range at which the parallax method is of practical use by about 1,000 times.
 
What part does distance measurement play when observing stars?
We'll consider three cases where knowing the distance to a remote object is key in undertanding that object's  properties.  In each case, the reason this is so important is because we can't measure a remote object's luminosity directly.
 
The luminosity of a remote object is observationally determined by measuring its magnitude.  Here we are essentially examining ratios of flux density. Whereas luminosity is independent of distance, flux scales inversely with distance according to Newton's inverse square law, so an accurate determination of luminosity requires an accurate knowledge of distance.

In practical terms, the inverse square law states that if we have two objects of the same luminosity, one twice as distant than the other, then the flux density  of the more distant object will be one quarter of that of the nearer object.
 
Case 1 - the size of a star 
We can estimate stellar radius by using the Stephan-Boltzmann Law:

We can measure the luminosity of the star, L, by photometry. That is, provided we know the distance from us. We can measure and its photospheric temperature, T, by spectrometry. Some simple algebra allows us to determine the star’s radius in terms of the solar radius is:

Those who saw my webinar on the Hertzsprung-Russel diagram last year may recall this equation. Measuring stellar parameters in terms of Solar units is commonplace in astrophysics as it simplifies calculations considerably.  In this case, we don't even need to know the value of the Stephan-Boltzmann constant.  But we do need to know the distance.
 
Case 2 - the size of an exoplanet
When an exoplanet (a planet orbiting a star other than the Sun) crosses the face of the star as seen by an Earthly observer, it causes a dip in the observed magnitude of the remote star.  The characteristic light curve of the star will appear similar to Figure 4, in this case of the star WASP-2A being transited by its planet WASP-2A-b:

HOPS is made available as part of a pro-am collaboration project called Exoclock. The goal of the Exoclock project is to make as many observations of confirmed exoplanet transits as possible.   Amateur participation is valued as there is simply not enough time available on professional telescopes. 
 
Because the cross sectional area of both the star and the planet scale by radius squared, the transit depth, is related to the squares of the ratio of stellar radius and planetary radius:

So, in this case also we can infer the size of the exoplanet in terms of the solar radius, but to know the value of this in metres, as in case 1, we must again know the distance.
 
In the case of WASP2-A-b, it turns out that -according to this light curve- the planetary radius is 1.23*RJ where 1.23*RJ is equal to the radius of Jupiter.  
 
The published value in the  exoplanet.eu/catalog is 1.079 ± 0.033 RJ, so we are reasonably close. Nevertheless we can classify WASP2-A-b as a Jupiter-size exoplanet.
 
Case 3 - the mass of a star 
The mass-luminosity ratio is stated in relation to solar units as:

However, the relation is highly empirical in the sense that both the coefficient a and the exponent b depend on the mass of the star.  Almost as if you have to guess the mass first!
 
For a very small star (e.g. a red dwarf),  a = 0.23 and b = 2.3.
 
For a star comparable to a solar mass,  a = 1 and b = 4. 
 
For a star with a mass comparable to Betelgeuse, a = 1 and b = 3.5.
 
In this case also, to calculate the mass of another star in kilograms (or any other units of mass), we need to know the distance as accurately as possible so that we can calculate its luminosity.
 
The mass of a star also determine its ultimate fate.  There was great excitement in the popular press at the end of 2020 to the effect that "Betelgeuse was about to go supernova".  This was prompted by the fact that Betelgeuse had dimmed considerably.  In fact, this is now believed to be because Betelgeuse had expelled a great deal of its atmosphere as dust, causing the apparent dimming of magnitude (Kidger, 2020).
 
Table 2 is based on much more detailed modeling published in 2015 (Woosley and Heger, 2015 - refer to Table 1, page 3)

Conclusions 
1. The parallax method is earliest method used todetermine the distance to remote objects.  Space-based observatories such as  Gaia have extended the effective usefulness of the  method out to ~10 to the power 5 pc.

 2. In order to calculate parameters such as size and mass, it is necessary to have an accurate value for distance.  Note that we can calculate the mass of a star in abinary system, but we then need the mass of the other star. 

3. Measuring stellar parameters in terms of Solar units is commonplace in astrophysics.  For example we know that M⊙ = 1.99*10 to the power 30  kg.  How we determine soar parameters will be covered in a future blog.

4. Betelgeuse is in many respects an enigmatic object.  Because its distance is not known precisely, so neither is its luminosity.  That also means its mass is not known precisely and hence the ultimate fate of Betelgeuse is uncertain.

 
References
Harper G et al. (2008). A new vla–hipparcos distance to Betelgeuse and its implications  https://iopscience.iop.org/article/10.1088/0004-6256/135/4/1430/pdf, Accessed April 14, 2021.  ApJ, 135:1430–1440, 2008 April.
 
Woosley, S and Heger, A (2015). The remarkable deaths of 9–11 solar mass stars https://iopscience.iop.org/article/10.1088/0004-637X/810/1/34/pdf, Accessed April 14, 2021. ApJ,810:34(20pp), 2015 September 1
 
 
Kidger, M (2020) Supernova Betelgeuse  https://britastro.org/jbaa/pdf_cut/jbaa_25295.pdf , Accessed April 14, 2021.  Journal of the British Astronomical Society, 2020 December.

I am quite surprised that this month’s blog will complete a year of them, meaning that we have been all the way round the night sky. By the nature of the subject there will be a bit of repetition from now on but there is always something new happening and who can ever tire of looking at a lovely starry sky even if you have seen it before. We passed the spring equinox on the 20th March so we are getting more daylight and the clocks went forward an hour on the 28th March so it will be later before the sky darkens. The good news is that we have had some clear nights and seeing Mars, Aldebaran, the Pleiades and a crescent Moon all together just after the middle of the month was particularly pleasing. Since we are making a fresh start I thought that it would be a good idea to repeat the bit about the celestial sphere and how the sky changes in appearance from night to night and month to month. I hope this will prove useful to any newcomers to the subject and any youngsters who are hopefully embarking on observing the skies as a lifetime’s hobby.

The Celestial Sphere
Before we venture outside let us recall some helpful facts. It is useful to think of the sky as a hollow sphere which has the Earth at its centre and to which all the heavenly objects are attached. This sphere is known as the celestial sphere. Just like when you visit a planetarium. The celestial sphere also has north and south poles directly above the corresponding poles on Earth and a celestial equator directly above the Earth’s equator.  Far away objects such as stars and galaxies are in more or less ‘fixed positions’ on the celestial sphere whereas the Sun, Moon and planets continually shift their positions but stay close to a circular path on the sphere’s surface called the ‘ecliptic’ which is tilted to the celestial equator because the Earth’s axis is tilted by 23.5 degrees to the plane of its orbit. In reality of course the Earth revolves round the Sun and the ecliptic is where the plane of the Earth’s orbit cuts the celestial sphere. This makes sense because when we observe the Sun we are looking along the radius of the Earth’s orbit and hence in the plane of its orbit.

The recent equinox marks the point where the path round the ecliptic crosses the celestial equator. This is when the Sun is overhead at the equator and it continues to travel further north until the summer solstice when it is overhead at the Tropic of Cancer. We see from the diagram that the ecliptic is north of the celestial equator during this period of time.
For us in the northern hemisphere we see the stars rotate about the north celestial pole. Don’t worry about some of the additional information on the diagram. The yellow line is the ecliptic and it shows the signs of the zodiac (representing the constellations) and how the Sun appears to pass in front of them as the Earth revolves around the Sun. Remember we are using a model for what we see and this is governed by the movement of the Earth. The Earth spins about its axis from West to East once a day (ie 360 degrees in 24 hours or 15 degrees per hour) and that is why we see the Sun move across the sky daily from East to West. It may not be so obvious that the stars are doing the same thing at night and they move across the sky from East to West at 15 degrees per hour as well. Of course, they also do it during the day, but we cannot see them for the glare of the Sun.
 The Earth also revolves about the Sun once a year (ie 360 degrees in 365 days or about 1 degree per day or 15 degrees in 15 days) which is why the sky at 10.00pm one day will look like the sky at 9.00pm 15 days later. If you wait till 10.00pm again the celestial sphere has moved on by 15 degrees or 1 hour and all the stars have moved that amount further west.

Observing
Okay, it is time to look at the stars. The following charts represent the night sky at 10.00pm BST on the 8th of April and at 9.00pm BST on the 23rd April. To use the chart, face south at the appropriate time with the bottom of the chart towards the southern horizon and you will see the stars in the chart. From ancient times the stars have been put into groups called constellations with names supposedly indicating what they represent but this is seldom clear.

The fact that some stars appear in a group does not indicate that they are close together and their distances can vary by very large amounts. Some groups of stars stand out but may be only part of a constellation and such groupings are called ‘asterisms’.
               So facing south and going up from the horizon you will see the constellation Leo- The Lion. Fortunately it does look like a crouching lion facing towards the right with the brightest star Regulus (the 15th brightest seen from the northern hemisphere) being its front paw and the curve of stars above that representing its head and mane. This latter grouping of stars is an example of an asterism called ‘the Sickle’, looking like a backwards question mark with Regulus being the dot at the bottom.
               Now raise your eyes upward to your zenith (the point directly above where you are standing) and you will see what must be the best known asterism in the night sky- The Plough. It contains seven stars and the chart shows three of them named. The Plough is part of the constellation – Ursa Major- The Great Bear, but it takes a lot of imagination to see a bear and that region is mostly referred to as The Plough. In North America it is called the Big Dipper and perhaps here in the UK a better name in modern times would be ‘The Pan’. We said in the introduction that the stars rotate about the celestial North Pole and stars close to there never set but are visible all year round when the skies are dark. Stars like this are said to be circumpolar and Ursa Major is a circumpolar constellation. But note The Plough’s orientation carefully because as it continues on its circular journey it will appear upside down in six months’ time.
               The constellations are used as signposts in the sky and enable us to engage in a fun activity called ‘star hopping’. Now let’s look at the second chart.

The two stars in the Plough, Merak and Dubhe, are called the pointers and a line from Merak to Dubhe continued onwards leads to Polaris- the Pole Star. The distance is about x5 the distance between Merak and Dubhe. Polaris is very close to the celestial north pole and easily found because although not very bright it is the only star visible in that area. Polaris is in the constellation- Ursa Minor- The Little Bear. Now consider a line from the star Alioth in the Plough, through Polaris and continued onwards for about the same distance again until you see a bright star. It will be the central star of a W formation, an asterism in the constellation Cassiopeia- Queen Cassiopeia in Greek mythology. Most people see the W shape and call it Cassiopeia. The bright star was never given a name in Western or Middle Eastern culture so is referred to as gamma (g) Cas. The convention is to name stars using the letters of the Greek alphabet and an abbreviated form of the constellation. Generally this is done in the order of brightness of the star but it is not a hard and fast rule.However this star has been given the name Navi, allegedly by the American astronaut Virgil (Gus) Ivan Grissom as an anagram of his middle name because it was used for navigation in the early space missions. A fitting tribute to someone who made the ultimate sacrifice for space exploration. The constellation Cassiopeia is also circumpolar and because it is directly opposite the Plough across the North Celestial Pole the two will have exchanged positions in six months so we will see Cassiopeia much better in November. Just imagine the two of them at the ends of a long pole rotating about the North Pole.

Something to look out for
There will be a close approach of a five day old Moon and Mars on Saturday 17th April. They will be separated by about 4 degrees initially but will come within a quarter of a degree of each other at their closest. The pair will be visible after 8.30pm as dusk fades above your western horizon.
 At the end of the month we welcome back Venus to the evening sky and though it is still close to the Sun it will be visible for a short time after sunset above the western horizon. It will have a close approach with Mercury on Sunday the 25th April but you will have to let the dusk sky fade before they become visible. Clear skies.

Fortunately we have had the benefit of a few clear skies and so have had a chance to see a bit more of the winter sky.  Mars continues to provide good viewing even though it is waning in magnitude and it was good to see its close lunar approach in the middle of the month. On the 28th February the Moon was close to Regulus in the constellation Leo- The Lion, but if you watched Ben Sutlieff’s excellent talk on ‘imaging exoplanets’ and his use of a coronagraph you will understand something similar was needed to block out the light from the full Moon. I settled for observing with one eye and using my thumb at arms length  to block out the Moon!


Observing
The chart below represents the south facing night sky at 9.00pm GMT on the 8th March and at 8.00pm GMT on the 23rd March. Remember it is the spring equinox on Saturday 20th March and we move to BST on Sunday 28th March.

This month we are focussing on just one constellation, Leo- The Lion. The chart includes the stars Castor and Pollux in Gemini and the star Procyon in Canis Minor just to give us our bearings. The chart also includes the faint stars in the constellation Cancer- The Crab and part of the constellation Hydra- The Water Snake but we discussed those last month and they are difficult to see.
            Having located the two main stars in Gemini and the star Procyon you need to turn towards the south-east and you will have no trouble in picking out Leo. I think it deserves its name because I can imagine the outline of a lion in a crouching position.The main star is Regulus, the 15th brightest star in the northern hemisphere at magnitude 1.4. Above Regulus is the asterism- The Sickle, which I have outlined in red. The other three stars in Leo which I have named are perhaps not well known but Denebola, Algieba and Zosma have magnitudes of 2.1, 2.2 and 2.6 respectively which explains why Leo stands out so well. Leo is towards the east just now so you will be able to enjoy observing it as it travels westwards over the coming months. Let’s hope we have plenty of clear skies.              
 
Something to look out for
I mentioned Mars in the introduction and am returning to it again because at the beginning of March it passes close to the Pleiades open cluster and on the 3rd/4th March passes within 2.5 degrees of same. Not as eyecatching as Venus when it did something similar last Spring but well worth observing never-the-less. Throuhout the month it travels eastwards through the constellation Taurus, passing north of the red giant star Aldebaran about the middle of the month.We had difficulty tracking its retrograde motion last Autumn because there were no bright stars nearby but this time you can track its movement relative to Aldebaran.It also has a close approach to a six day old Moon on the 19th March so you will see Mars, the Moon and Aldebaran all together.
Last month I mentioned the  open cluster, Praesepe, (marked on the chart with a red cross and also known as ‘the Beehive’) as a difficult target for observation and  perhaps with better conditions it will be possible in March.
Finally with the Spring Equinox on the 20th March we’ll have another chance to to fix directions because on that date the Sun rises due East and sets due West. There is a housing estate being built close to where I live and I’m hoping I don’t have the roof of a house blocking out my horizon to the West!
 Good luck with your observing! 

Cloud cover continues to make observing a bit of a challenge but we have had the odd clear sky recently and what a delight it was to see Orion as beautiful as ever. 
 
Observing
The chart below represents the south facing night sky at 10.00pm on the 8th February and at 9.00pm on the 23rd February. Again Orion and the Winter Triangle (formed by Betelgeuse, Sirius and Procyon) provide all the navigational help required. Last month we were spoilt with all the wonderful bright stars on display but this month you will need to find a dark sky location to observe some dimmer objects. Perhaps you need to have your lockdown exercise walk in the evening to a suitable site free from light pollution. Of course the bright stars are still there but we will be concentrating more on the region to the east of them.

To the north-east of Orion it is easy to pick out the bright stars Castor and Pollux in the constellation Gemini- The Twins, but there is more to the constellation than just those two stars. The bodies of the twins are represented by two lines of faintish stars ending with their feet in the Milky Way. These stars are typically of magnitude 3 to 4 and may be a bit of a challenge depending on light conditions but there is a magnitude 1.9 star, Alhena, representing the feet of Pollux and you should be able to pick it out on a line from Betelgeuse to Pollux.
            Now to three new constellations:- Monoceros- The Unicorn, Cancer- The Crab and Hydra- The Water Snake. The bad news is that they lack an abundance of bright stars. However it is easy to know where to look for Monoceros because it is in the middle of the Winter Triangle, bathed in the brightness of the Milky Way. Its brightest star is barely magnitude 4 so to the unaided eye this constellation doesn’t provide very much so we will move on.
            The constellation of Cancer is one of the zodiacal constellations so needs a mention. It is the faintest of them and is fairly easy to find lying between Gemini and Leo and forming a triangle with the stars Pollux and Procyon. It doesn’t have a particularly distinct pattern but it does have an open cluster, Praesepe, (marked on the chart with a red cross and also known as ‘the Beehive’) which contains about fifty young stars and covers an area the equivalent of three full moons and being in a dark area away from the Milky Way it provides a hazy glow to the unaided eye in good conditions. You will need a pair of binoculars to resolve the individual stars.
            Finally, Hydra- The Water Snake is the longest of the constellations and stretches about one quarter of the way around the sky with its head in the northern hemisphere and its tail in the southern hemisphere. It is difficult to trace out the chain of relatively faint stars but the six stars forming its head are more conspicuous. The brightest star, Alphard, representing the heart of the snake, is of magnitude 2 and lies alone in a blank region of the sky so is easier to spot on a line from Betelgeuse to just below Procyon and extended about the same distance again. Let’s hope for some really clear skies so that some of these dimmer objects stand out.  
 
Something to look out for
There is a New Moon on the 11th February so an opportunity for dark skies in the middle of the month.  You may also care to look out for the waxing crescent Moon on the following days to the WSW just after sunset. Mars is now in Aries and has a close approach with the Moon on the 19th February. The pair will be visible from 6.00pm onwards above your southern horizon with the Moon passing 3.5 degrees (7 Moon diameters) to the south of Mars after 10.00pm. before sinking towards the horizon and setting after midnight. Of course throughout the month you can continue to enjoy Orion, The Winter Hexagon and the Winter Triangle.