Worlds in Points of Light. What to Expect

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Worlds in Points of Light What to Expect Vision and Intellect Week Path of the planets 1 Learning from light 2 Planet diversity 3 Remote

instruments, intimacy) (Up-close and personal) (Check on reality) Robert Dick rdick@robertdick.

Record keeping - preservation of knowledge (Hipparchus 190-120 BCE) Naked Eye - qualitative, cultural narratives (oral histories) -

accuracy ~1/30-deg (~2 arc minutes (1600 ADE) Time Arab Astronomy Date Stars Sextants (size = precision) Sun Based on Ptolemaic System -

1 Worlds in Points of Light What to Expect Vision and Intellect Week Path of the planets 1 Learning from light 2 Planet diversity 3 Remote sensing 4 Planetary evolution 5 Extra-solar planets 6 (Naked-eye observing) (Vision and intellect) (Planetary astronomy) (Magic instruments, intimacy) (Up-close and personal) (Check on reality) Robert Dick rdick@robertdick.ca February 28-April 4, 2018 Today Visibility (Acuity and Colour) Clarity through Abstraction The Door Opens on Intellect Visual Techniques Record keeping - preservation of knowledge (Hipparchus BCE) Naked Eye - qualitative, cultural narratives (oral histories) - accuracy limited to ~1/2 degree (Moon) Visual Instruments (Sextans/Octants ~1000 ADE) - sights to fix eye s position in instrument - accuracy ~1/30-deg (~2 arc minutes (1600 ADE) Time Arab Astronomy Date Stars Sextants (size = precision) Sun Based on Ptolemaic System - practical, unifying Translated Almagest to Arabic Samarkand Observatory and Sextant 15 th Century Diffused across Africa and southern Europe Enabled translation into Latin for posterity Astrolabe 220 BCE Present 1

Visual Precision Natural Light Levels at Night Illuminance Full Moon is natural

Colour Vision Luminance 1cd 1m 20,000 cd/m 2 1m 1m Moon is very bright, but ~

Venus 15,000 Mars 4,000 Jupiter 800 LEDs Sun 3x109 Nat l materials little blue

retinal damage Blurry Blue Limits to Visual Acuity (Simulated) rods rods/cones

2 Visual Precision Natural Light Levels at Night Illuminance Full Moon is natural limit (silvery grey) 1/10th brightness to read a book Pupil diam. = 6mm Sextant arm = 1.6m /100th = night walk-about - a practical limit Scotopic Better sight ~0.5mm Photopic Tycho Brahe Sextant 17th Century Sources of Light Limits to Colour Vision Luminance 1cd 1m 20,000 cd/m 2 1m 1m Moon is very bright, but ~ 1/1000 streetlight (1-4 million cd/m2) Full Moon 6,000 cd/m2 Moon Candle 20,000 Venus 15,000 Mars 4,000 Jupiter 800 LEDs Sun 3x109 Nat l materials little blue Colour (visual spectrum) SUN Dovercourt at Churchill Prolonged staring 1M cd/m2 retinal damage Blurry Blue Limits to Visual Acuity (Simulated) rods rods/cones cones cones/rods rods sensitivity greater in periphery but resolution low colour greater in centre but sensitivity low Poor resolution in blue light Cell spacing in retina 2

Peak Sensitivity 100:1 Rods 505 nm (Green) Cones - 592 nm (Yellow/orange) Photopic Day and Night Vision Scotopic Colour & Points of Light Countryside

luminance (some colour) Yellow = off-white, Red = ruddy [low saturation] Most stars silvery grey (zero-saturation) Complex / Accurate The Renaissance

Observations and Mathematics Kepler Visual obs.

Handshake 1643-1727 Newton Mathematics Theoretical Astronomy Dynamics of Solar System Mercury Venus Kepler Obs.

52 163.76 3.534 140.7 870.8 6,976 26,820 1.524 5.202 9.551 19.11 29.94 3.540 140.8 871.3 6,983 26,850 Why are they not exact? Newton s Laws (1687) 1.

3 Peak Sensitivity 100:1 Rods 505 nm (Green) Cones nm (Yellow/orange) Photopic Day and Night Vision Scotopic Colour & Points of Light Countryside at Night Very low luminance Shades of silvery grey Scene has a grainy texture Points of Light Photographic View Visual View Brightest stars - high luminance (some colour) Yellow = off-white, Red = ruddy [low saturation] Most stars silvery grey (zero-saturation) Complex / Accurate The Renaissance Era Theory explains Observations Ptolemy Copernicus Simple / Inaccurate Kepler s Laws Newton s Law of Gravity Beyond vision Profound insight Observations and Mathematics Kepler Visual obs. by Tycho Brahe Culmination of an era Observations Abstraction Geometry of Solar System Rotation of sling = Orbit Tension in rope = Gravity Generational Handshake Newton Mathematics Theoretical Astronomy Dynamics of Solar System Mercury Venus Kepler Obs. & Math (P 2 =a 3 ) P[yrs] P 2 A [AU] a Earth Mars Jupiter Saturn Uranus Neptune ,976 26, ,983 26,850 Why are they not exact? Newton s Laws (1687) 1. Law of Inertia [ΣF=0 then constant inertia or m v = 0] [force change in momentum] 2. F = ma [unbalanced force α acceleration] [F = 0 acceleration] 3. Equal and Opposite Reaction of forces [ΣF = 0 for constant motion] Kepler - P 2 α a 3 or P 2 = const. x a 3 Newton defined the value of const. [GM s / 4π 2 ] 3

4 Get Kepler from Newton 1/3 Start with basic dynamics where r = length of string Apply Newton s 2 nd Law Newton s Law for Gravity 2/3 Apply Newton (units help keep the math right) Centripetal acceleration (a) causes string tension F = mass x accel. so Tension = m p a c [N = kg m/s 2 ] [N = kg m/s 2 ] Tension = m p a c = m p v 2 /r [kg m/s 2 ]=[kg m 2 /s 2 / m ] v = circumference / period = 2π r / P [ m/s ] So a c = (2π r / P) 2 / r [ m 2 /s 2 / m ] x Bolas Cord V, P T m p r T = tension P = period R = length V = speed m p = mass Acceleration due to gravity a = G (M s +m p ) /r 2 [m/s 2 ] = [(const) kg/m 2 ] (M s = Sun s mass, m p = planet s mass, r = orbital radius) (G = constant of proportionality gravitational constant [m 3 /Kg s 2 ]) Newton s 2 nd Law F = m a N = [Kg m/s 2 ] So, Gravity Force F = m p a = m p {G (M s +m p ) /r 2 } Newton s Law for Gravity 3/3 Optical Resolution For circular stable orbits the Centripetal force = Gravity force Bollo Cord Newton s Gravity m p (4π 2 r 2 ) = m p G (M s +m p ) r P 2 r 2 Sun s mass >> planetary mass so M s +m p ~ M s m p (4π 2 r 2 ) = m p G (M s +m p ) r P 2 r 2 r 3 = GM s P 2 or a 3 α P 2 [Kepler s 3 rd Law] 4π 2 Rearrange the terms d (pupil diam.) 6 mm λ ~ 5 x 10-6 m Resolution λ / d = 5 x 10-6 m / m = radians = 2.9 arc minutes You can trick the eye with a viewing sight (like Tycho), but you don t improve the detail Real improvement by λ and/or d bluer light, larger lens (telescope) Resolution Resolution of Telescopes Optic Diam. Eye (6 mm) Binos (50 mm) Sml Tele. (200 mm) Hubble Tele. (2.4 m) Resolution limited by visual acuity atmospheric limit ~0.3 to km on Moon θ = λ / diam. = 0.5x10 6 m / diam. (meters) 4

Limits to Visual Acuity Keep looking up Brightness Colour - Resolution

(~ a period @ 24 m) But, the lens is poor quality Venus = 0.

Information Bronowski, Jacob - Assent of Man www.youtube.com/watch?

Observations confirmed theory Pannekoek, A.

Interscience, 1961 Notes and Video Presentations Backyard Observations

5 Limits to Visual Acuity Keep looking up Brightness Colour - Resolution Theoretical resolution of human eye ~1/200 Moon = 1/6 arcmin. (~ a 24 m) But, the lens is poor quality Venus = 0.17 arcmin (today), [1 maximum] Jupiter = 0.8 arcmin (48 ) Pluto = 0.01 arcmin (0.6 ) We need to see better if we are to learn more Interesting Information Bronowski, Jacob - Assent of Man (A still-remarkable 13-part BBC Series) The Modern Era Observations confirmed theory Pannekoek, A. - A History of Astronomy ( Dated interpretation of history) Interscience, 1961 Notes and Video Presentations Backyard Observations Dr. Simon Hanmer RASC Ottawa Centre Retrograde Loop pm Robert Dick, Rideau Ferry, ON 5

What they Saw The Points of light What they Saw The Points of light Non-diurnal motion Speed depends on planet Differences in brightness Ecliptic -

path Stepwise approximation Stepwise approximation Curve as steps get smaller A Critical View Learning to see What to you see What don t you see

6 What they Saw The Points of light What they Saw The Points of light Non-diurnal motion Speed depends on planet Differences in brightness Ecliptic - Plane of the Sun and Planets August 8, 2012 August 8, 2012 Babylonian Astronomy ~2300 BC to ~500 BC Path across sky Cultural Constraints * * Curved path Stepwise approximation Stepwise approximation Curve as steps get smaller A Critical View Learning to see What to you see What don t you see When did you see it What does it mean Brightness high Luminance = limited Dynamic Range Glare few shades of grey Poor Dynamic Range Good Dynamic Range 6

The Human Condition. Worlds in Points of Light. Fields of Study. What to Expect. Lure of Naked-Eye Observing. Today. Remote.

The Human Condition. Worlds in Points of Light. Fields of Study. What to Expect. Lure of Naked-Eye Observing. Today. Remote. Worlds in Points of Light (Naked Eye Observations) Star-like Worlds My Background https://carleton.ca/linr/early-spring-2018-session/class-notes/ Robert Dick rdick@robertdick.ca February 28-April 4, 2018