Showing posts with label Interests. Show all posts
Showing posts with label Interests. Show all posts

Monday, August 31, 2009

MODELLING THE SUN’S ALTITUDE FROM SUNRISE TO NOON

A note by Eamon Henry, 5 August 2009


Foreword:This note follows the Henry note of 27 July 2009 “How warm is the summer sun!”, now available on http://www.asits.blogspot.com/. The trigonometric model which gives results presented below uses two formulae appearing in a 14-page document “Spherical Trigonometry” available on the web at www.krysstal.com/sphertrig.html. This interesting article even gives 2 pages of (in effect) a “do it you yourself kit” for building your own sundial (just what we all need!!).The Henry Excel 97-2003 worksheet “Sunrise to Noon Sun Altitudes­_rev1”(3 July 2009) gives model results for midsummer day and midwinter day, at 15-minute intervals, computed by him. At present the ASITS blogspot is not able to carry an Excel worksheet as such. Table 1 following gives summary results for 30-minute (0.5- hour) intervals.
Results:
Table 1: Model estimates of Sun’s altitude at Dublin from Sunrise to Noon, Midsummer and Midwinter
Time, local, hours
Midsummer altitude, degrees
Midwinter altitude, degrees
12.00
60.0
13.0
11.30
59.8
12.7
11.00
59.3
11.8
10.30
58.5
10.2
10.00
57.3
8.0
9.30
55.7
5.1
9.00
53.6
1.5
8.48

0.0
8.30
51.1

8.00
48.0

7.30
44.3

7.00
40.0

6.30
35.1

6.00
29.7

5.30
24.0

5.00
18.3

4.30
12.7

4.00
7.4

3.30
2.6

3.12
0.0

“Local time” means calibration so that noon (Sun due south) is 12.00 hours, and thus for Dublin some 25 minutes later than Greenwich Mean Time (GMT) noon, because Dublin is about 6.25 degrees West (longitude); Sun due east will be at 6.00 hours local time, for Earth’s rotation 15 degrees per hour. Thus, in “Azimuth” terms, direction East is 90 degrees away from South, and direction West is 90 degrees away in the opposite direction, as for “Azimuth” angles to be used for model applications described below. “AZIMUTH is the angular distance from the north or south point of the horizon to the intersection with the horizon of a vertical circle passing through a given celestial body” (page 97 of the Oxford Encyclopedic English Dictionary, 1991 edition).

How the Model differs from the Real-World Situation:The model gives 21 June Sunrise as occurring at 3h 12m a.m. The actual Dublin sunrise time is about 3h31m local time, some 19 minutes later. For 21 December, the model gives Sunrise as at 8h48m local time, compared with actual 8h15m local time, some 33 minutes earlier. On page 11 of “Spherical Trigonometry” a calculation is made for Sunrise times at London. The azimuth angles are 39.62 degrees north of east (3h21.2m am local time) and 39.62 degrees south of east (8h38.5m am local time). My Diary 2009 gives London 20 June sunrise as 3h43m, about 22 minutes later, and London 19 December sunrise as 8h03m a.m., some 35 minutes earlier. So the model is wrong in a consistent way, it seems.
One reason for these differences is that the model implicitly assumes that the Earth’s orbit is a circle about the Sun, and thus completely regular. But in fact the orbit is an ellipse with the Sun at one focus, and our distance from the Sun ranges from 147 million kilometers in December to 152 million in June (page 9 of Patrick Moore: “Exploring the Night Sky with Binoculars”). However, the model gives no discrepancy for the Spring and Autumn equinoxes, 21 March and 23 September, with sunrise at 6.00 hours local time everywhere. Altitudes are not calculated for one of these, in the attached Excel sheet, but can be readily derived by changing a few parameters of the model, as will be indicated below.
Note that the model gives exactly 12 hours as the sum of the times from sunrise to noon, 8h48m midsummer plus 3h12m midwinter. The actual sum is about 12h15m, meaning that the Northern Hemisphere does in fact get more Sun-time than the Southern Hemisphere.
Because of these model discrepancies, I am re-calculating (in the Postscript section below) the relative per-hour intensities of the Sunshine for midsummer versus midwinter, as given in my previous note of 27 July 2009. For the summer sunrise situation, one might estimate actual Sun’s altitudes (angles of elevation) by going to the model altitude at least 15 minutes earlier: take the 5.45 hours altitude 26.9 degrees as estimating actual altitude at 6.00 hours, and take model 8.45 hours altitude 52.4 degrees as estimating actual altitude at 9.00 hours. My own estimates (for these times) used in my note of 27 July were 23 degrees and 47 degrees, respectively.Of course, both model and actual altitudes coincide at local noon, so they must gradually come closer as the morning progresses.
Technical description of the Model:The main equation I use is on page 8 of “Spherical Trigonometry” as follows:
sin(D) = sin(L)*cos(Z) – cos(L)*sin(Z)*cos(A)………………………………….. (1)
The sign * means “multiplied by”.I use latin letters where the text uses greek letters. D is the angle of declination (latitude on the Celestial Sphere) of some star, in our case the Sun, at 0 degrees for the equinoxes, 23.5 for summer solstice and -23.5 degrees for winter solstice. L is the Latitude of the point of observation, for Dublin about 53.5 degrees North, for Oxford about 51.6 degrees North. Z is the “Zenith distance”, given as 90 degrees less the Altitude(angle of elevation) of a star (in our case the Sun). A is the Azimuth, measured in degrees from direction South (e.g. direction East has azimuth value “minus 90 degrees”). Here a comment on the Celestial Sphere is in order. At Greenwich at noon on 21st March (spring equinox), the Sun is at location (0,0) on the Celestial Sphere, whose equator coincides with the imaginary circle where the plane of Earth’s equator cuts this visual sphere of stars etc. around the Earth. Longitude is called “Right Ascension” and latitude is called “Declination”. The north pole of the Celestial Sphere is directly above Earth’s north pole, its axis of rotation coinciding with that of Earth.
Let us get the Sunrise equation from equation (1) above. For altitude zero degrees, Z has value 90 degrees, Cos (Z) is zero and sin (Z) has value 1. Thus equation (1) reduces to:
Sin(D) = -cos(L)* cos(A), which can be written cos(A) = - sin(D) / cos(L),………..(2)
And we can write it as cos (A)= sin(D)/cos (L), if we measure A from North direction clockwise, i.e. East is 90 degrees. So, for D and L given we have A, measured from North direction. A gives the Sunrise azimuth angle, as each 15 degrees equal to one hour of time, measured from midnight onwards. For example, find the summer sunrise direction and time for Dublin:
cos(A) =sin 23.5/cos 53.5 (in degrees) = 0.398749/0.594823 =0.670366.A has value 47.90 degrees X 4 = 191.62 minutes of time after midnight (North direction) =3h11.6m a.m.
To use equation (1), see the column headings and function expressions on the Excel worksheet. D has value 23.5 for midsummer (Dublin). All trig calculations must have radian measure of angles, hence the columns of radian values. L has value 53.5 degrees. Angle A (azimuth) is progressed backwards in degrees negative from noon of value 0 degrees. Find Z from this equation for each specified value of azimuth A. In column I you put in estimated altitude values from noon known value 60 degrees back to 0 at time of sunrise. (At equinoxes, Sun’s noon altitude is given by 90-latitude 53.5=36.5; add 23.5 more for Sun coming up by 23.5 degrees (declination) so as to have noon altitude 60 degrees at midsummer).
Now calculate value of right-hand-side (RHS) of (1), and subtract it from left-hand-side to give error. Calculate value of Z-differential of RHS, which is –sin(L)*sin(z) – cos (L)*cos(Z)*cos (A), and divide the error by the latter, to give a Z correction, added on to first Z estimate. (This approach is called Newton’s Method of solving equations.) Re-calculate the RHS of (1) and again find error. These resulting errors are so small (see column R) that a second iteration (to find a further Z increment) is not warranted. So the amended Z is our solution in each row; subtract it (in degrees) from 90, and this is the required altitude (angle of elevation) of the Sun given by the model for that time of morning (as A expressed in time before noon) and shown in column X.
Obviously, Sun’s altitude calculations could be made for other times of year, for any specified Sun declination value D. The Sun’s declination throughout the year is shown on the “Ecliptic” curve on star maps. Just now (early August) it has an approximate value of 12.5 degrees, well below the 23.5 degrees of 21 June.
Postscript (21 August 2009)The right-hand columns Z to AI of the Henry Excel worksheet give detailed calculations of the average per-hour Sun intensity, midsummer and midwinter. In the note “How warm is the summer sun!” rough estimates of per-hour average square- metre areas were given as 3.39 for midsummer and 11.35 for midwinter. Revised figures are 3.419 and 8.587, respectively, as shown on the Excel worksheet. The midwinter area is considerably reduced, due to the Sun’s apparent curve (as given by the model) being well above the previous assumed straight-line movement from sunrise to noon, thus giving larger sine values with matching smaller 1/sine values and thus smaller areas.
These new results are calibrated to match 15-minute intervals from sunrise to noon, but again omitting first 1 degree altitude (elevation) of the Sun after sunrise. The time-factor multiplier is taken to be (for each 15-minute interval) the average time per 1 extra degree of the Sun’s altitude, based on the model results. The relative per-hour midsummer/midwinter intensity is now 2.512, given by 8.587/3.419.

Thursday, July 24, 2008

REFERENDUM RESULTS, ACTUAL AND POSSIBLE
A note by Eamon Henry. 22 July 2008

This short discussion offers a statistical (regression) analysis of the Irish (12 June 2008) Referendum results, of voting on the Lisbon Treaty. For a turnout of 53.1 percent, there was a NO vote of 53.4 percent, implying a YES vote of 46.6 percent.
Readers not familiar with statistical analysis are asked to accept “on faith” the results presented below via “Simple Regression” analysis of YES percentage as depending on TURNOUT percentage across all 43 constituencies. The next paragraph gives results in technical format. There follows a non-technical discussion. The actual Yes and Turnout percentages, by constituency, are given as an appendix table below, having been extracted by me from the Irish Times of 17 June 2008. The “Data Desk” software package has been used by me to give the regression results shown below.
I first present some simple results. Of all 43 constituencies, only 9 gave a Yes result above 50 percent. Of these 9, five were in the Dublin-Dun Laoghaire area, including Dublin South East constituency, which had a 61.6 percent Yes for a 49.6 percent Turnout. The regression results are as follows (and rather technical). For a fairly loose-fitting Rsquared of 15 percent, a highly significant (99 percent probable) positive coefficient emerged, namely an average 0.779 percent Yes extra for every 1 percent extra Turnout. This coefficient has a “standard error” of 0.289. Based on an assumed “Normal distribution” background, we can have about 95 percent probability that in repeated referenda of similar voter behavior, a lower limit Yes connecting coefficient is given by the average coefficient 0.779 stated above less twice the standard error value 0.289, that is a value 0.201 (given by 0.779 less twice 0.289). What this means in practice will be explained in what follows, as illustrating how to project or estimate results for non-voters supposedly voting.
We first apply the regression average coefficient to the non-voters supposedly going out to vote, as per each extra 1 percent of the electorate (across all constituencies). Call this the “naïve” assumption. A connecting coefficient of 0.779 rounded to be 0.8 indicates that an extra 5 percent turnout would give an extra 4 percent Yes. In other words, 58.1 percent turnout (actual 53.1 plus 5.0) would yield 50.6 percent Yes (actual 46.6 plus 4.0), namely a Yes majority.
By contrast, let us apply a “lower-limit pessimistic” connecting coefficient of value 0.201, as derived above. To obtain an extra 4 percent Yes would now require an extra 20 percent Turnout , via connecting coefficient now only about 0.2. In other words, a 73.1 percent turnout (actual 53.1 plus 20.0) would yield 50.6 percent Yes (actual 46.6 plus 4.0), namely a Yes majority.
It is clear that a larger (than 0.2) assumed connecting coefficient would require a smaller (than 73 percent) turnout to obtain a Yes result larger than 50 percent. These results are interesting, in providing some “parameters” regarding possible voter behavior in a repeat performance.

Appendix: Lisbon Treaty Irish Referendum (12 June 2008) Results by Constituency.

Constituency Yes Percent Turnout Percent
Meath East 50.9 50.7
Laois Offaly 56.0 54.3
Kildare North 54.6 51.5
Clare 51.8 52.5
Dublin North 50.6 55.3
Dublin NorthCentr 50.6 61.1
Dublin SouthEast 61.7 49.6
Dublin South 62.9 58.4
Dun Laoghaire 63.5 58.8
Dublin West 47.9 54.5
Dublin NorthWest 36.4 52.9
Dublin NorthEast 43.2 57.2
Dublin Central 43.8 48.8
Dublin MidWest 39.6 51.7
Dublin SouthCentr 39.0 51.6
Dublin SouthWest 34.9 53.6
Donegal NorthEast 35.3 45.7
Donegal SouthWest 36.6 46.5
Sligo Leitrim 43.3 52.6
Cavan Monaghan 45.2 53.4
Louth 51.9 53.4
Mayo 38.3 51.3
Roscommon.Sth. Leitr 45.6 56.9
Longford West Mth 46.3 51.4
Meath West 44.5 51.9
Galway west 46.1 50.00
Galway East 46.9 49.8
Wicklow 49.8 60.8
Tipperary North 49.8 58.5
Limerick East 46.00 51.4
Carlow Kilkenny 50.0 50.9
Kildare South 48.5 48.7
Limerick West 44.6 51.8
Wexford 44.0 52.8
Kerry North 40.4 51.3
Tipperary South 46.8 55.4
Waterford 45.7 53.4
Kerry South 42.6 53.1
Cork North West 46.1 55.6
Cork East 43.0 50.6
Cork South West 44.4 55.3
Cork South Central 44.9 55.0
Cork North Central 35.6 53.4

Friday, July 18, 2008

THE EVOLUTION DEBATE: TWO UNPUBLISHD LETTERS
Author: Eamon Henry. Date: 17 July 2008

Preface:The two letters of mine given below were not published by the Irish Catholic weekly newspaper. As preface, I quote a comment on the more recent one by my son Manus aged 45, a member of staff of the Department of Engineering Research at Oxford University: “The whole Science/Religion debate is one I have followed over many years. On the one hand, pretty bizarre religious/educational practices do occur in the US, but on the other hand there are serious attempts to debate the issues, whereas the establishment in Europe blocks any serious, populist critiques of science’s over-stretched claims. I wish you luck with your letter, but I’m not holding my breath.”The two letters follow, in chronological order.

Rooney on Dawkins (28 January 2007)
Dear Editor,
The letter from Professor John Rooney in your issue of 25 January 2007 raises several points on which I strongly disagree with his views as stated. Given that his expertise is in Physical Chemistry and mine relates to Mathematical Economics, we each can hold similar or different convictions on matters outside our areas of competence, namely aspects of Philosophy and Theology. My approach below is to comment briefly on each paragraph of Dr. Rooney’s letter, which implies that readers need to have his letter to hand, as well as mine.
I would wish the name “Science” to be qualified by descriptive adjectives, such as “Physical”, “Geological”, etc., in the context of the letter’s first paragraph. I agree that proximate causes (Occam’s Razor most narrow view) might neither prove nor disprove the existence of deeper causes. These are what the “Meta” (meaning “After”) part of the word “Metaphysics” signifies. As soon as we know our Physics well, we can move on to a deeper level of human thought about causes, whether primal or final.
His second paragraph rules out “Intelligent Design” views, thus directly contradicting the “Five Ways” (meant to be taken together) of St. Thomas Aquinas, which point towards a reasonable “First Cause”. Pages 57-70 of Peter Kreeft’s 1990 book Summa of the Summa give the actual discussion of St. Thomas in English translation, with copious notes by the author. “Whether it can be demonstrated that God exists” is the descriptive heading of this part of the Summa Theologica. St. Thomas finds the answer “Yes” to this question of Cosmology.
My comment on his third paragraph is covered by my last paragraph above. In the next paragraph we find “Evolution” presented as a fact, with Homo Sapiens emerging from it. Many educated people have regarded “Evolution” as a totally unproven theory – a wishful-thinking view without a shred of supporting evidence – right from its beginning about 1860. A. N. Field’s book The Evolution Hoax Exposed (TAN Books 1971 issue) gives numerous grounds for rejecting this theory. Christian views on the problem of evil have a long history, through St. Augustine to C. S. Lewis. A brief summary is that God can draw greater good out of the evil due to the exercise of Free Will by some of his creatures, which is why God gave them rational Free Will, and not merely irrational instincts.
Regarding “Orthodox doctrine”, which for Christians ought to mean “God’s Truth” on the sin of Adam and Eve and its consequences, clear statements appear in the Catechism of the Catholic Church (VERITAS 1994, paragraphs 355-400). I offer no apologies on this score.
The final two paragraphs comprise an imaginative but tentative view of what it all might (or might not) amount to. A “transcendental” possibility would seem to offer a new approach, not covered at this point in time by Philosophy, Theology, or the Physical Sciences. However, an “ice and water” mix of Pantheism and Dualism might come within an asses’ roar of what Dr. Rooney seems to be dreaming about. We must allow both concepts as wide a range of metaphysical meanings as possible. Thus, perhaps, everybody might feel happy!Yours truly, Eamon Henry

Communications Science Analysis of “Intelligent Design” (6 July 2008)
Dear Editor,
In your issue of 3 July 2008, you published an article by Professor William Reville, of title “Intelligent Design”. In its summary section, various claims for “Evolution” producing “Design” are made. Two such claims are as follows: 1.The argument for intelligent design of living organisms fails to stand up against the theory of evolution by natural selection, just as Paley’s argument failed 150 years ago.2. Science shows us that the design we find in the biological world was produced naturally and unconsciously over deep time by the natural forces of natural selection.
A few definitions of terms are needed, to help us to be clearer on what we think we are talking about, as follows. I use the most relevant definition, as given in the Oxford Encyclopedic English Dictionary (1991 edition):Evolution: a process by which species develop from earlier forms, not by special creation, as an explanation of their origins;Design: a preliminary plan or sketch for the making or production of a building, machine, etc.;Intellect or Intelligence: the faculty of reasoning, knowing and thinking, as distinct from feeling;Life: the condition which distinguishes active animals and plants form inorganic matter, including the capacity for growth, functional activity and continuous change, preceding death;Cybernetics: the science of communications and automatic control systems in both machines and living things.
The two claims stated in the first paragraph above are totally rejected in a book by A. E. Wilder-Smith, of title “The Creation of Life: a Cybernetic Approach to Evolution”, first published in 1970 by Harold Shaw Publishers, Wheaton, Illinois. The author’s academic qualifications as such are quite impressive: D.Sc., Ph.D., Dr.es Sc., F.R.I.C. His varied career as a researcher and recognized expert in Organic Chemistry and Pharmacology is summarized at the back of his book, and need not be detailed here. What all this amounts to is that we may take his findings seriously.
Technical detail must necessarily be limited in a letter like this. The book’s Chapter 12: Quantitative Considerations and Prospects (pages 239-255) presents the core of his argument. The following is a summary of a few of his findings. The Darwinians (like Professor Reville) insist that information stored on genes (or DNA spirals) arose originally by spontaneous random processes. Such an assumption, per information theory, is mathematically unsound. The Second Law of Thermodynamics states that entropy (i.e. disorder) increases with time in any closed system. In other word, codes and order will decrease with time, if left to themselves. Genes are chemical structures of a highly ordered non-random nature.
The vast amount of information which all living creatures bring into the closed system of the universe has been pre-coded upon the genes of their first parents. Evolution, said to begin without any such pre-programming, runs counter to the findings of every thermodynamicist and communications engineer. Information theory requires a programmer to account for the increasing complexity of the whole program of evolution. The evolution theory as it stands provides for no information source to account for this increasing complexity.
I trust that these few thoughts will help the quest for truth.Yours sincerely, Eamon Henry

Monday, July 14, 2008

LOCAL ASTRONOMY – A FEW QUESTIONS AND ANSWERS
A note by Eamon Henry. Date: 23 September 2002.

Introduction:
Recently I asked myself a few questions on astronomical matters within the Solar System. Not only did I not know the answers, but I could find no answers within easy reach, either. So I decided to do my own sums. I share with you the answers. I hope you enjoy them!

A few constants etc. are needed. Force = mass * acceleration, where * means “multiplied by”. Powers of 10 such as 10 to the 7th power (meaning 7 tens multiplied together) will be written below as 10(7). One divided by 10(7) will be written 10(-7) . The constant “pye” (3.141592654) will be written pye. R to the power of 2 will be written Rsquared or R*R. (This unusual notation is to fit blog text conditions, which do not accept superscripts for powers of numbers or of symbols.)
The unit of force is the “Newton”, which gives to a mass of one kilogram (kg) an acceleration of one metre (m) per second, per second. So all units will be expressed in kg and m, with lots of powers of 10 as well.
At a long distance, massive bodies act with gravitational force upon each other as if all the mass were concentrated at the centre of gravity of each such body.
We need G, the universal constant of gravitation, of value 6.67259*10(-11)

The basic fact is that a body in orbit has a centrifugal force on it per kg mass (to make it fly away) given by V*V /R, where R is its distance from the “centre of force”, and V is its velocity in metres per second. It is kept from flying away by the force of gravity between it and the body it is orbiting, given by G* M1* M2 /( R*R) , here R being the distance in metres between the centers of the two bodies and M1 and M2 their masses in kg. So we have two formulae to calculate what we want, which is a useful check, as will appear below. We keep life simple by assuming circular orbits, of length 2*pye* R, which is alright because many planetary orbits are ellipses nearly circular (a circle is an ellipse with its two foci together).

Given values of mass and distance for Sun, Earth, Moon, Mars, Venus, and Jupiter (mostly in Britannica 2002 but some in Patrick Moore’s “Exploring the Night Sky with Binoculars”), we can now ask and answer a few questions:

What gravitational force does the Sun exert on the Earth, on average?
What gravitational force does the Earth exert on the Moon, on average?
How do these forces compare?
What gravitational forces of Sun and Moon affect the sea tides on Earth (diameter 12756 kilometres, same as 7926 miles)?
What force of gravity do Venus, Mars, Jupiter exert on the Earth, when they are at their nearest, approximately? How does this compare with the Moon-Earth force?
Calculate the parameters of a typical artificial satellite orbiting the Earth only a few hundred kilometers up.
Calculate the parameters for a satellite to rotate at same speed as Earth, so as to stay above a fixed point of the Equator (not to complicate our problem unduly).



Masses and Distances and Velocities:

SUN: mass: 1.99* 10(30) kg; mean distance 149.59285* 10(9) metres from centre of Earth

EARTH: mass 5.976* 10(24) kg; equatorial radius 6378,000 metres.

MOON: mass 73.506* 10(21) kg ( 1/ 81.3 of Earth); mean distance 386.0637* 10(6)
metres from centre of Earth.
VENUS: mass 4.87* 10(24) kg; shortest dist. from Earth’s centre 42* 10(9) metres

MARS: mass 6.418* 10(23) kg; shortest dist from Earth’s centre 78.4036*10(9) metres

JUPITER: mass 18.99* 10(26) kg; shortest dist from Earth’s centre 628.4036* 10(9) metres

Shortest distances have been generally approximated as the difference between their average distances from the Sun, as their orbital planes are fairly close together. Venus: mean distance from Sun 108* 10(9) metres.
Mars: mean distance from Sun 228* 10(9) metres
Jupiter: mean distance from Sun: 778* 10(9) metres.
Average velocity of Earth 29784 metres / second on assumed circular orbit of radius average distance from Sun and for 365.25 days period (of one complete circuit)
Average velocity of Moon 1036 metres / second on assumed circular orbit, of period 27.1 days (during which Moon completes 360 degrees of rotation around Earth).

Gravitational Force Results:

Sun on Earth : 35.44* 10(21) newtons ,using V*V /d formula (centrifugal formula)
35.14* 10(21) newtons, using G*M1*M2/(R*R) formula (gravity formula)

Earth on Moon: 20.44*10(19) newtons, using centrifugal formula
19.66*10(19) newtons, using gravity formula.
Thus, the Sun-Earth force is about 179 times (3514 / 19.66) as great as the
Earth-Moon force. A value of about 173 is given by 3544/20.44.

For the other three planets, I have used the ratio of their gravity formulas to that of
Sun-Earth to obtain as follows for approximate shortest distance effect:
Venus 0.56 ( about ½ ) of 1 percent of Earth-Moon force
Mars 0.02 ( about 1/50) of 1 percent of Earth-Moon force
Jupiter almost (0.98 of) 1 percent of Earth-Moon force.
We may notice how relatively small these last three planetary forces are, with Jupiter’s largest being hardly 1 percent of the Earth-Moon force. If these three planets vanished overnight, we would suffer no noticeable changes in our present orbital behavior.


Ocean Tides on Earth:

The Moon pulls on the Earth with an equal and opposite force to that estimated above,
19.66*10(19) newtons, per gravity formula. We may divide this by Earth’s mass 5.976*10(24) kg, and obtain 3.290*10(-5) equal to 0.0000329 newtons as average Moon gravity-force on each kg of Earth’s material.

Ocean tides on Earth are due to variation in the forces of gravity of both Sun and Moon across the diameter of Earth, to be calculated by the inverse distance squared on nearest surface point versus that at opposite surface point of a diameter. G and the two masses are the same, but the distance changes.

So, for the Moon, we compare 1/(386.064 less 6.378)squared with 1/(386.064 plus 6.378)squared, and get 0.000006937 compared with 0.000006493, the first being 6.84 percent larger than the latter. This means, relative to the Earth’s centre, a force some 3.42% larger on the surface point nearest the Moon, matched by a force 3.42% smaller on the surface farthest behind. This causes the tidal bulge towards the Moon at its side, matched by a tidal bulge “falling behind” at the back. These differences are in Moon gravity-force units.

A similar exercise for the Sun gives a ratio difference (from unity) of only 0.0001728 Sun units across the Earth’s diameter. But when we multiply by 179, to get it in Moon units, we obtain 3.1 percent difference, meaning a force 1.55% (in Moon units) more (than at the Earth’s centre) on the face towards the Sun, matched by a force 1.55% less on the opposite face away from the Sun. Without the distorting effects due to gravity pulls of Moon and Sun, the tidal waters would stay as parts of a perfect sphere about the Earth’s centre, for Earth here assumed to be approximately a perfect sphere.

I need only say that the outcome is the sum of percentages 3.42 and 1.55. Thus, Sun and Moon together give a +5.0 % on the nearest facing surface at new moon, matched by a –5.0% at the point farthest behind. A week or so later the Moon is pulling sideways, relative to the Sun, and we have low (neap) tides. At full moon, the effect (and tides) are again about the same as at new moon. We may see how each “falling behind”, relative to the Earth’s centre, is in effect the same as a negative force pulling in the opposite direction. So Sun and Moon do not tend to cancel out their tidal effects at full moon, although they are on opposite sides of the Earth. The fact is that tidal maximum is much the same. However (Moore page 9), Earth is about 147 million km from the Sun in December, but farther away (152 million km) in June. So this winter nearness to the Sun does cause higher tides in winter.

Satellites:
We equate the two formulae, with gravity force on left equal to satellite mass multiplied by centrifugal acceleration on the right, Msat being satellite mass and Mearth being Earth’s mass:

G* Msat* Mearth /(R*R) = Msat*V*V / R
Here R is the distance of the satellite (on circular orbit) from Earth’s centre.
This reduces to (per kg of satellite mass)
R*V*V = G * Mearth, and the right-side product has constant value 39.8754* 10(13) .
So we have to find values of R and V to satisfy this equation.

1) A near-Earth satellite
Given that the Earth’s radius is about 6400 km, allow 400 km as satellite height above the Earth (assumed here to be a perfect sphere) and thus take 6800 km as satellite distance R from Earth’s centre, which is 6.8 * 10(6) metres. This gives V*V as 58.6402909*10(6), so V is 7657.7 metres (about 4.8 miles) per second. And the orbit length , 2* pye* R is 42.72566 million metres. For the given value of V, it takes 5579 seconds to make one circuit, which is 92 minutes and 59 seconds, roughly an hour and a half, in good agreement with what we have found to happen in the real-world experience. And this satellite supposedly passes over at about 400 km above Earth’s surface.

2) A satellite to stay above a fixed point of Earth’s equator
This means the satellite has a period of about 23hours 56 minutes (86160 seconds), as it makes one complete circuit of its circular orbit in the same time as one rotation of Earth.
So we have 2*pye*R /V = 86160, which gives R / V = 13712.79
And again the other equation gives R*V*V = 39.8754* 10(13).
This leads to V*V*V = 29.078982* 10(9), giving V as 3075.105 metres per second.
And R is found to be 4.2168248 * 10(7) metres, which is 42168.25 km (26,203 miles) above Earth’s centre, roughly 22,000 miles above the Earth’s surface.

Friday, July 11, 2008

Joys of a small Telescope

JOYS OF A SMALL TELESCOPE
A note by Eamon Henry; 10 July 2008

Introduction:Using a small telescope is an acquired taste. A definite advantage is secured, if the first period of viewing is in rural “pitch-dark” conditions. Nebulae and planets can be found and enjoyed, such as the great nebula in Orion, much more easily than under the lit-up conditions of our urban areas.
What follows covers a few obvious themes. First considered are the main features of a “refracting” telescope, in which one views directly the object of interest. By contrast, in a “reflecting” telescope one looks into the side of the telescope tube to see a mirror-reflection image. Next, we list some usual problems encountered in using small refracting telescopes. As an easy first object, the Moon is discussed. Less easy, but of great interest, are a few Solar planets, viewable even in the glare of city lighting. Finally, one may ask what pleasure is to found from such viewing, even in freezing cold winter nights out of doors.
A Small Refracting Telescope Described:
A refracting telescope essentially comprises four parts: 1) a hollow opaque tube with a lens (the “object lens”) at the front; 2) a second much smaller lens (the “eyepiece lens”) fitted in at the back of the hollow tube; 3)a stand of three or four legs to support the tube; 4) a viewfinder (or “finderscope”) attached to the side of the tube. This viewfinder is a small telescope (of magnifying power say five-fold) to find the required typically small star-like object in a larger field of view. Centering this object in the viewfinder cross-hairs should make it visible within the field of view of the main telescope itself, if the viewfinder has been properly aligned in its attachment to the main tube.
Such a small “toy” telescope requires to be kept on viewing-target by hand, whereas more expensive models have electric motors to keep them pointing at the target, by adjusting for the Earth’s rotation, which in some 15 or 20 seconds can move the target-point right across the field of view and out of sight. Other features of the small “toy” type are that it can be rotated horizontally upon its stand, and screws allow elevation of the tube to point upwards as required, with possible further screw fine-tuning of this direction. Also, the eyepiece lens can be moved forward or backwards so as to adjust focusing on the clearest possible image view. This last aspect is rather important.
A small refracting “toy” telescope of Japanese make could cost up to 500 Euros nowadays. The typical main tube is up to one metre long, with the object lens of diameter 6 centimetres having a “focal length” of 90 centimetres (cm). The eyepiece lens can vary, but a sensible lens for this particular telescope is a lens of focal length 1.25 cm. The “power of magnification” is given by the ratio of these two focal lengths, that is 90/1.25, which is 72 for this particular combination. In other words, this lens combination will magnify any object 72 times, which is quite respectable, and works wonder for the Moon. An eyepiece of shorter focal length will give larger magnification, at the cost of a much weaker image of worse quality. Patrick Moore’s book Exploring the Night Sky with Binoculars (1986, Cambridge University Press) gives a very helpful background to the user of a “toy” telescope. Patrick advises a maximum magnification of 50 times per inch of object lens diameter – thus a 6 cm object lens should not be used to magnify an object beyond about 118 times ( 50X6/2.54).
Once assembled properly, the telescope should be left in one piece, except for manipulating the legs for storage indoors. The legs need to be based on a firm level surface, during times of viewing. They are typically connected together by a few light chains, to allow maximum distance apart when supporting the telescope during use.
Some Common Problems:
Several problems are commonly experienced by viewers using the small telescopes described above. Some of the more obvious ones are listed as a) to e) following:
a) A comfortable field of view is possible for the tube pointing between say 10 degrees and 45 degrees above the horizon. Pointing higher involves bending back or other similar neck strain by the viewer. The most comfortable position is to be seated on a small chair behind the telescope legs (typically of wood or plastic and some four feet long) and thus have some comfortable flexibility of shoulders and neck, in following the required tube direction.
b) Getting used to the image being inverted. Thus, a local view of a tree-top shows the top of the tree at the bottom of the picture seen through the telescope.
c) Earth’s rotation causes the target point to move across the field of view from right to left (usually). The inversion effect give the opposite of what we see as the Sun moving across the sky from left to right during the course of the day.
d) Clouds or haze make viewing impossible. Typically the best conditions occur during a clear frosty night, but even here some dew can form on the object lens during a lengthy session out of doors. The lens can be dried off, of course, given that the dew has been recognized.
e) Glare and general brightness, caused by urban street lights and traffic, destroy all delicate features of objects being viewed. The Moon is so strong that it is not seriously affected. Likewise, our four nearest planets have light strong enough to give their outline shapes. But gas-clouds (“nebulae”) are mostly eliminated from possible viewing. By contrast, in a situation of rural “pitch-dark” viewing, the planet Jupiter is surrounded by a globe of light, with possible star-like points indicating its four largest satellites. And gas-clouds such as the great nebula in Orion and the Crab Nebula are clearly visible, with some features showing.

The Moon as an Easy First Object:
Moore’s book has “Lunar Landscapes” as its Chapter 9, giving both photographic and verbal description of the Moon throughout its four-week cycle. The Moon is so large and bright that one could view it from indoors through a clean glass window. A magnification of 72 times gives some remarkable views of craters and cracks. Being large implies that the viewfinder is not needed, unlike the case of a planet. Also, one can get some experience of adjusting for the object moving slowly across the field of view, so as to get back again to the top right point of starting a second pass, and so on. This helps towards similar adjustment for a small object like a planet.
Planets Venus, Mars, Jupiter and Saturn:
Venus is the easiest to recognize, as the “morning star” and the “evening star”. It is usually very bright, and appears as a clear orange-coloured half-moon shape, which can vary in size. Mars is small but strongly red in colour, and will show only an oval red disk. Jupiter gives a very bright and steady light if visible in the late evening, and shows (in urban conditions) an oval-shaped yellow-green globe. Saturn also is rather bright if visible in the late evening, and in the telescope looks silvery-grey, with suggestion of partial ring as well as globe under magnification 72 times. All of these planets, of course, on average pass over us as much during our day-time as during our night-time, so that viewing them after sunset between say 6.00p.m.(winter time) and midnight is possible only in some years during October-March. Regarding Mars, Jupiter and Saturn, if recognized at say 6.00p.m.fairly low-down in the eastern sky, they gradually progress at same time 6.00p.m. from east to west over the following six months.
What Pleasure is to be Had in Viewing:
A few thoughts may give the basis for satisfaction through these kinds of telescope viewings, even with a “toy” instrument.
No telescopes were available, as far as is known, before about 1600 A.D. Even the ancient brilliant Greeks were not able to invent a telescope, simple though it is as comprising two lenses in a tube. The best-known names of earliest viewers, who adapted telescope designs for their own purposes, are Galileo Galilei (1564-1642) and Isaac Newton (1642-1727). Thus, with at least 70-fold magnification we are seeing the heavenly bodies in a way that nobody could see them before 1600 A.D. The Moon excepted, things above generally could only be seen as points of light. Comets, of course, showed large on occasion.
There is also great satisfaction in being able to look “here and now” at some bright object in the sky, rather than depending on someone else’s pictures. As a final advice, in suburban conditions, one should find a dark alley or the centre of a large open space in a park, to improve viewing. Getting away from direct glare of lighting helps considerably towards a satisfactory viewing result.

Monday, July 7, 2008

Newgrange and the Sun-God


NEWGRANGE AND THE SUN-GOD
A story by Eamon Henry. Date: 31 January 2004.

The BBC Horizon program of last Thursday night discussed a bronze disk found recently in north-east Germany, and dated to about 1600 BC, and identified with local copper-mines as its raw material. The disk has religious symbols of the Sun (life-giver), crescent Moon (indicating time-change) and the Pleiades(“seven sisters”) star-group used as a calendar for spring-to-autumn agricultural work. This disk also has the “Sun’s Boat”, later found in Egyptian religious carvings, which supposedly carries the Sun around and back under the earth to be in place tomorrow morning.

Under such stimulation I yesterday revisited our National Museum (Kildare Street) to look again at a roof-stone from the Newgrange sun-temple (built probably during 3500-2500 BC), which interests me a lot because it has line etchings scored by chiselling. Helped by some Gaelic words explained in Dinneen’s Irish-English Dictionary(1927 edition), I can better explain Newgrange as Dagda the Sun-god dying at the mid-winter solstice, but (if sky is clear) shining at sunrise of some four mid-winter mornings into the centre of the Newgrange “temple”. He thus fertilizes the womb of mother earth, which gives (new) birth to his son Aongus (the ancient Irish god of sexual love). Dagda has another name “Eochaidh Oll-Athair”, the second word meaning “Father of all things” i.e. Creator-God. Aongus is frequently called “Aongus an Bhrogha” meaning “Aongus of the fairy mansion” i.e. of the Newgrange sun-temple mound. In the 17th-century Gaelic “Fiannic” literary fiction, this same mound is called “Brugh na Boinne”, meaning “the fairy mansion beside the river Boyne”, and is treated as the home of the same Aongus.

We expect all etchings at Newgrange to be directly connected with the Sun-god. I now can make some sense of some of them, as follows:

FIRST: The roof-stone has its etchings filled and blackened by pitch or some such material. I see clearly a horse’s head, ears and shoulders facing right, above/behind which appears the sun-disk giving out rays like curly hair. Then further behind (and to the left) are undulations suggesting sea-waves. So this could represent Dagda on his horse rising out of the sea at morning and/or possibly passing above or through the western sea so as to get back again for tomorrow morning. The horse-head may have a studded cap on top, but with clear bridle strings and rein coming in the right place towards a rider’s hand. There is also a leg with bent knee in the right place for a rider, down the horse’s flank.

SECONDLY: There are several spirals etched on the Newgrange pillar-stones, not yet the “Maze of Crete” design, which I will treat below. Starting at mid-winter sunrise, the Sun does a low loop in the sky and then supposedly returns under the earth to repeat a slightly larger higher loop starting slightly to the left of yesterday’s. And so on to mid-summer, at which it makes the largest highest loop through the sky. Your imagination must guess (for circa 3000 BC) how it loops down below on the way back. Such etched spirals represent this 3-dimensional process, on a flat surface.

THIRDLY: From mid-June to mid-December the Sun apparently repeats the process in the opposite sunrise direction (left to right). But suppose (to avoid confusion) we treated this as a “mirror-image” of the loops of mid-December to mid-June, then we would have a double set of loops (supposedly close together). This could well be the origin of the “Maze of Crete” design, not appearing as such at Newgrange, where five complete spirals (some having connecting ends) appear, as well as several partial ones, on the large stone in front of the Newgrange actual passage entrance. The mid-winter Sun shines through the “roof-box” and shaft directly above this stone, into the central chamber, if the sky is clear.

POSTSCRIPT:
As a brief background to all this, we may draw on the “Chronology of World Events” (in particular, page 1688 of the Oxford Encyclopedic English Dictionary, 1991 edition). The period 4000-3200 BC mentions “Farming spreads to western and northern Europe…construction of monumental tombs in megalithic technique in .. British Isles…Use of horse …on steppes north of Black Sea… Plough and cart widely adopted in Europe”. The period 2500-2300 BC mentions “Beaker cultures bring innovations (copper-working, horses,…woollen textiles) to Atlantic seaboard”. So we may conclude that by roughly 2400 BC the Boyne valley area around Newgrange had farming (both tillage and livestock, including horses), with ploughs etc. But we should also allow the possibility that etchings on any stones of the Newgrange sun-temple could have been made long after the original structure was built.

The Sun-god was (and still is) crucial for crop-growing during the spring and summer. I now consider an etching on the lower left-hand corner of the roof-stone, namely two heavily-etched squares joined at one corner. These could represent two tillage-fields fenced in, to keep grazing animals out. Or, they might represent one tillage-field and one field for grazing animals e.g. cows.

Inside the lower square near one edge is a T-shaped small carving (heavily-scored). This could represent the vertical (coulter) and horizontal (ploughshare) blades of a plough. It could also represent some other farming implement such as a pick-axe. Nearby in this square is a heavily-scored dot, which could represent a grain-seed being sowed.
We see many groups of these square or diamond-shaped etchings on the pillar-stones of the Newgrange passage into the inner chamber, and elsewhere. They might represent tillage-fields and grazing animals being put under the aegis of the Sun-god.
Below to the right of these two squares, on the roof-stone of central interest, etchings appear which suggest a pear and apple together, and separately a further pair of cherries or fruits or nuts joined together.

But, most interesting, top left on the roof-stone are several circular etchings together forming a (lower) biggish half of a sun-like object, with spiky rays coming out below. This makes sense as the crescent Moon. Below this and facing left, is a quite credible donkey’s head and neck. So we could interpret this as the Moon riding a donkey across the sky in the opposite direction to that of the Sun - which it surely does as it apparently moves from west (new moon) to east (full moon) over the first two weeks of every lunar month. And to the farthest left at the top we find wavy lines facing the Moon’s donkey – these could credibly represent the changing sea tides, always observed as matching the changes in the Moon.

Monday, June 23, 2008

REFLECTIONS ON THE W.B. YEATS EXHIBITION
By Edmund (Eamon) Henry; 12 June 2008


Foreword
This brief note covers our visit this morning to the Yeats exhibition at the National Library, at the kind invitation of the Terenure Enterprise Centre to our Active Senior IT Society, with Ms Ann Moriarty leading us. Some 2000 documents are available, including many of William Butler Yeats’ original manuscript poems and letters on actual display. A detailed coverage is not intended here.

A few aspects of this extraordinary man who lived between 1865 and 1939 will be touched on below. This writer has had Yeats’ poetry in his bloodstream since childhood, which may come as no surprise, given that he grew up on the edge of “the Yeats’ country”, only some four miles to the south of Knocknarea, the hill that features in several of Yeats’ poems in a County Sligo setting. His poem “The Lake Isle of Inishfree” and other similar pieces were on our national school menu.

Great Mental Energy
His large and varied output occurred from about 1885 right up to about September 1938, the date of his “epitaph” poem “Under Ben Bulbin”, through a period of some fifty-three years. The Nobel Prize for Literature awarded in 1923 indicates the unusually high quality of his output of poetry and plays. His successful launching of the Abbey Theatre about 1904, with Lady Gregory and others, is a further landmark achievement. He was made a Senator of the Irish Senate in 1922, which enabled him to promote his views on how to improve some aspect of education within the Freestate. Because of failing health, he resigned from the Senate in 1928. All this shows how Yeats could get things done so well.

Versatility with Strangeness
This writer claims little knowledge of Yeats’ dramas as such. However, it is generally known that he experimented widely with dramatic formats, including the Japanese “Noh” drama forms. His poetry also covers the full range of human experience, in fresh and delicate expression. In line with some of Francis Ledwidge’s greatest pieces, Yeats in his poem “The Stolen Child” describes “ferns that drip their tears over the young streams”, an indication of his sensitive handling of nature events, combined with elven (fairy) dimensions.

A “strange” or “un-Irish” aspect of Yeats was his heavy involvement with the occult, especially through his wife Georgie, a spirit medium, whom he married in October 1917. We may recall that this practice was much used by people such as Arthur Conan Doyle, the creator of “Sherlock Holmes” the famous crime sleuth. Doyle wanted very much to contact the spirit of his only son who was killed in the 1914-18 War. Among all this there was the iconoclast Harry Houdini, who when allowed to join a séance frequently showed the fraudulent nature of the supposed communication with the spirit world.

Empathy with Plain People, the “Native Irish”
A very likeable quality of Yeats was his insight and empathy with “the plain people of Ireland”, as one might put it. This was by no means to be expected from someone typical of a Protestant upper-middle class background. Several of his earlier poems treat rural themes, about a Father Gilligan, a Fiddler of Dooney, and various other “native Irish” themes, from the native point of view. Having John O’Leary, a definite Fenian, as his chosen mentor might shed further light on this aspect. The so-called Irish Revival brought Yeats into the company of John Synge, Douglas Hyde, Lady Gregory and others, all intent on creating a culture based on the “native Irish” mentality and language, even if in English translation. It seems that Yeats did not know any Gaelic language as such. However, English versions of many folk-tales were available, such as Joyce’s “Old Celtic Romances”, which admittedly have a bit more to them than occurs for the fiddler of Dooney. The “Tain Bo Cuailne” (cattle raid of Cooley) gave in English translation much material to Yeats to work with, including the characters Cuculainn and Maeve, from early medieval sources.

Outlook Patriotic and Stoic
A further likeable quality of Yeats was his emphatic support of Irish Nationalist causes and persons generally. Several poems praise characters such as John O’Leary, the 1916 executed leaders, and Rodger Casement. A handicap for Yeats was his inability to read original Gaelic poetry and prose, much of which was not available in English translation. This implies that much written by the native Irish since say the year 1600 he could not directly access. A related problem may have been his not knowing the meaning of many place-names in their Anglicized versions of Gaelic originals. For example, in his poem “Red Hanrahan’s Song about Ireland”, he refers to a cleft on the south side of Knocknarea as “Clooth-na-Bare” as pouring out a rain flood. The Gaelic name is “Cluid na Bear” meaning “the nook of the bears”, indicating that wild bears used to live there at one time. This fact is quite worthy to bear mention in a poem, if readers will bear with my presumption! In this context, it is of course feasible that friends such as Douglas Hyde could readily answer any place-name questions he might raise.

In his “epitaph” poem “Under Ben Bulbin” he expresses the hope “that we in coming times may be still the indomitable Irishry”. We could think about this, in circumstances where only one out of two or three voters turns out to vote on an important political matter, in spite of vigorous advice from both Church and State to go and vote. Yeats’ hope is indeed close to that of at least a century earlier, expressed in the slogan “Erin go Brath”, meaning “may our Ireland last until the Day of Judgment”.

Regarding final things, his epitaph is contained in the same poem. Now carved on his tombstone at Drumcliffe, County Sligo, it reads: “Cast a cold eye on life, on death. Horseman, pass by!”This outlook is close enough to that of the Graaeco-Roman Stoics of some two thousand years ago, which can be summarized as follows: “Keep your mind in a calm state, well above the level of passions which you must keep under control, and accept death as a perfectly natural and good event”.

Eamon Henry