[The original written text sheets for the talk had no title].     

 

    Prehistoric societies noted the seasons, the Sun, Moon and the visible planets and  their movements, and incorporated their basic knowledge into ceremony, in life and death.. It is evident in both the simple and complex monuments they constructed, and which we now attempt to explain.

    The ancient Greeks, were guided by a consensus of belief, given by Pythagoras (570 - 475 BC) which stated :-

  • The Sun, Moon, planets and fixed stars move in perfectly circular orbits.
  • The speeds of all these is uniform.
  • The Earth is at the exact centre.

        Plato (427 - 347 BC) set his students a tough question, namely, as a planet goes into retrograde motion why does it brighten ?:

        Aristotle (384 - 322 BC), had been a student of Plato. He could not answer the last question but took a realistic view that only one theory or model can be correct. Obvious today, less so then.

        Another follower, Exodus, produced the imaginative theory that the sky was a series of clear concentric spheres, centred by the Earth. The fixed stars were on the largest, outer sphere, the other bodies on smaller ones, closer in, and all moving at appropriate speeds. This still fitted with Pythagoras’s three principles.

 

      To explain actual observations astronomers brought in the famous ‘epicycles’ to deal with retrograde motion and the increase in brightness. These anti-clockwise epicycles allowed variation in Earth - planet distance, an important step forward, but the complex epicycles were more ‘wheels within wheels’.

      Meanwhile, important advances were being made in practical astronomy.

 

      Aristarchus (310 - 230 BC) made the experiment to find the relative distance of Earth to Moon compared with Earth to Sun by measuring the Moon - Earth - Sun angle, when both Moon and Sun were visible, the Moon being at exactly first or last quarter, ie. an exact  half Moon.

      To do this accurately needs the following :-

  • Knowledge of the precise point when the Moon is half lit ; not easy to decide with accuracy.
  • The  precise measurement from the exact centre of the Moon (easy) and the Sun (hard). To view the Sun some form of smoked glass should be used.

Both the Moon and the Sun should be well above the horizon at the time of the measurement. If the Sun is setting refraction by the atmosphere will make it appear higher than it really is, although easier to see. But did the Greeks know about refraction ?   

      Doubtless there were many attempts by Aristarchus, before he produced the angle of 87 degrees, which gave the Sun 19 times the Moon distance. He was in the right direction, but today we know the angle is 89 degrees 51 minutes, giving the Sun - Moon distance 400 to 1. However accurate the angular measurement, the half Moon point timing must be within a very few minutes since in 10 minutes the Moon moves one sixth of a degree round its orbit (12 degrees in 24 hours).                                                                                                

     Having found his Moon / Sun distance ratio Aristarchus then worked out the Earth / Moon size ratio, using lunar eclipses. He noted that the time taken for the umbria to touch the edge of the Moon to the start of totality, and vice versa, end of totality to end of umbria’s appearance, was equal to the period of totality in the best eclipses. He did not realise that the umbria was a cone extending behind the Earth, but thought it was a cylinder. Thus he concluded that the Moon was half the diameter of the Earth instead of one quarter.

     Because the Moon and Sun subtend equal angular diameters he considered that the Sun was 19 times the diameter of the Moon. With the then best estimate of the size of the Earth he could give sizes and distances to the Moon and Sun.

    Aristarchus was way ahead of his time.

   

    Pythagoras himself noticed the curve of the umbria, and assuming that only a sphere could give this curve every time, correctly considered that it was the Earth’s shadow across the Moon. From this he deduced the size of the Moon. The idea was right but not the size, because the umbria gets smaller with distance.

    The exact start of the penumbria ( first contact for a lunar astronaut watching the Earth eclipse the Sun ) is very hard to see from Earth.

 

   I will digress for a few minutes to the legendary Library and Museum of Alexandria, started in the 3rd century BC. The first librarian, Zenodotus, worked here about 250 BC. His successor, Callimarchus, catalogued some 120,000 scrolls by subject, and had another 400,000 mixed scrolls kept on racks and in pigeon holes. Subjects included mathematics, astronomy, geometry, mechanics, medicine and philosophy, along with stories and poetry. Besides the donated collections the library would also borrow volumes, which might come in by sea, copy them and return the original. Volumes in book form appeared in Roman times. For a long while there were at least 3 coexisting libraries. The destruction by fire in the 1st century BC is well attested by legend but with scant details, though associated with Caesar’s defeat of Cleopatra’s brother. 

 

    Eratothenes ( 276 - 196 BC ) was the Greek 3rd chief librarian at Alexandria. He experimented in Earth measurement, and noticed that on the summer solstice the midday Sun shone directly down a well at Syrene ( Aswan ). So at noon the Sun was at 90 degrees, directly overhead. But at Alexandria, on the summer solstice the Sun was never directly overhead, even at noon, so he measured the angle off verticle, 7.2 degrees. Now he needed to know the distance Syrene was south of Alexandria. It seems astronomers had more influence then, for soldiers were sent to march the distance and determine it. Reported to be about 5000 ‘stadia’, 787 kms, or around 500 miles.

    From this he calculated the circumference of Earth as the equivalent of 24,440 miles, and the diameter 7785 miles.. Eratothenes also amassed a catalogue of 44 constellations and listed475 fixed stars, possibly using Egyotian and Near East observations. He deduced that a year was of 365.25 days, and was the first to suggest an extra day every 4 years. 

     Not recorded in antiquity, but a feasible method of obtaining the Earth / Moon distance would be a combination of Erosthanes two simultaneous observations, hundreds of miles apart, and a ‘good’ partial (say 80% covered) solar eclipse, using parallax.

    When such an eclipse occurs, note the time of its maximum, ideally close to midday, and as accurately as possible do a drawing or cut out of the remaining crescent. (Smoked glass needed). When it has finished send soldiers to the north or south as appropriate, and to keep going until they reach an area where the locals saw a Total Eclipse. Then measure the distance from here to home base. The distance between the two sites should equal the widest part of the visible crescent sun at eclipse maximum at home base, and therefore the real distance to that part of the Moon.

 

  Hipparchus ( 180 - 125 BC) made observations from Rhodes. He imported the 360 degree system from Babylonia, worked out a year to within 6 minutes, and speculated that stars could have births and deaths. He made a catalogue of 850 stars, giving positions in celestial latitude and longitude which remained of primary importance until the 17th century.

  

   Ptolemy ( 85 - 165 AD) will be our last Greek astronomer. He refined or forced the epicycle theory closer to known observations and geometry by introducing for each crystal sphere an eccentric or the ‘True’ centre of motion. This was at some distance from the Earth, and an ‘equant’, another point in space, was chosen so that the Earth was mid way between the ‘eccentric’ point  and the conveniently chosen ‘equant’. This still allowed the Earth to be at the centre of the action, as it were.

   Even so, while robbing the Earth of its true central position gave a better fit for the theory it was sailing a bit too close to the wind. All these epicycles would soon smash the crystal spheres - shooting 2 of the 3 Pythagorian principles out of the sky. So Ptolemy, in a final stroke of genius, said that his model was not an ‘official’ theory but merely a useful mathematical tool for predicting orbits and events. Something of a cop-out but it lasted for 1500 years. 

   Not recorded in antiquity, but a feasible method of getting the Earth - Moon distance could have been a combination of Eranothenes two simultaneous observations, hundreds of miles apart, and a ‘good ‘ partial (say 80 % covered) solar eclipse, using parallax.

  When such an eclipse occurs, note the time of its maximum, ideally close to midday, and as accurately as possible do a drawing or cut-out of the crescent remaining. (More smoked glasses needed). Then send soldiers out to north and south, as appropriate, to keep going until they reach an area where the locals saw a Total eclipse, and measure the distance from here to base, going north or south.

   The distance between the two sites should equal the widest part of the visible crescent Sun at eclipse maximum back home, and therefore the real distance of that part of the Moon.

 

   Coming closer to our times, in the mid 1300’s an English philosopher, William of Occam, stated that in any theory the simplest model that fits is the best, ie. One requiring the fewest assumptions and modifications to fit observations. This principle is still used when adopting one of two competing theories, and is known as Occams razor.  Guided in part by this principle, Renaissance scientists and astronomers had real doubts about the 1500 years old complex and contrived Ptolemy system. These included Galileo, Copernicus, Kepler, Newton, Tycho Brahe, etc.

  

   Before I finish - All I’ve described is fairly well known stuff, but perhaps not often gathered together in the form of a talk. Less well known and more bizarre are early views on elements of space travel. Between classical times (when it was in the hands of the gods) and the 1600’s ideas about space travel were sparse, even in fiction. But with the Galilean discoveries of Jupiter’s moons,  and craters on our own Moon, stories became commonplace. The Moon and planets were now seen as actual worlds, to be visited, even inhabited.

 

    Johannes Kepler (1571 - 1630). Published in 1634, after his death, was “Sommium”, a demon powered trip to the moon, with concerns about gravity, temperature extremes, and the availability of air.

                                                          

    Ben Jonson (1572 - 1637) wrote in  “News from a New World” - There are but three ways of going thither. First, Endymions way - by rapture, sleep, or a dream. Second, Menippus’s way - by wing, which the poet took. Third, old Empedocles way. He leapt intoAetna, having a dry sear body, and light, and the smoke took him and whift him up to the moon.

 

   John Wilkins (1614 - 72), English  churchman and scientist, who wrote “Discovery of a New World in the Moon” in 1638. He tried to look forward to a scientific future, with ways we could be flying, all singularly imaginative and most very unscientific.

  A. By our own strength.

  B. By the strength of others.

  C. By spirits or angels

  D. By the help of fowls.

  E.  By wings fastened to the body.

  F.  By a flying chariot.

 

  Cyrano de Bergerac (1619 - 55). A year after his death was published “The Comical History of the States and Empires of the Worlds of the Moon and Sun”. Flights of fancy involved the following :- 

  A. Strapping vials of dew to the body. Since the Sun sucked up dew, so he would be sucked up into space. (He had to break a lot of vials to stop himself overshooting the Moon).

  B. Using fireworks. (The first fictional space rocket).

  C. The use of a huge magnifying glass to create a massive up-current of air to lift him. (The first solar power ?).

 

 Domingo Gonzales ( About 1640 ). Apparently Domingo trained his swans to carry him about on terrestrial flights., but being a careful chap he used a lamb as the first passenger. When that worked he used the swans for personal airborne transport. What he did not know was that swans flew to the Moon in autumn, taking a surprised Domingo on a trip with them.

       

               And with that particular piece of nonsense, I’ll end my talk.