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