Galileo and the phases of Venus Galileo and the phases of Venus - PowerPoint PPT Presentation

Galileo and the phases of Venus Galileo and the phases of Venus charles-henri.eyraud@ inrp.fr Madrid, 27 november 2009: Adventures in teaching astronomy EAAE-IAU Course on Astronomy Education

Bibliography « « Galileo and Venus Galileo and Venus » » Bibliography Letters and books of Galileo Letters and books of Galileo � 11 december1610 to Giulano de Medicis, OGG X 483 11 december1610 to Giulano de Medicis, OGG X 483 � � 1th 1th january january 1611 to 1611 to Giulano Giulano de Medici, (OGG XI, 11 de Medici, (OGG XI, 11- -12 12 � � 30 30 december december 1610 to 1610 to Benedetto Benedetto Castelli Castelli, (answer to his letter of 22 august 1610) , (answer to his letter of 22 august 1610) � OGG X, 502- -504 504 OGG X, 502 � 30 30 december december 1610 to 1610 to Cristoforo Cristoforo Clavius Clavius , OGG X 499 , OGG X 499- -502 502 � � 12 12 february february 1611 to Paolo 1611 to Paolo Sarpi Sarpi,, OGG XI, 46 ,, OGG XI, 46- -50 50 � � The essayer, 1623 The essayer, 1623 � � Dialogue concerning the two chief world systems 1632, OGG V II, 3 Dialogue concerning the two chief world systems 1632, OGG V II, 350 50- -… … , 366) , 366) � OGG=Opere di Galileo Galilei, ed nazionale, ed by A. Favaro OGG=Opere di Galileo Galilei, ed nazionale, ed by A. Favaro Articles Articles � . O. Gingerich Gingerich. Journal for the History of Astronomy, XV, 1984: 209 . Journal for the History of Astronomy, XV, 1984: 209- - � Phases of V enus in 1610 . O. Phases of V enus in 1610 210. 210. � The appearances of V enus and Mars in 1610 , William Peters, JHA, XV 1984 , William Peters, JHA, XV 1984 � The appearances of V enus and Mars in 1610 � Galileo, Kepler Kepler and phases of V enus and phases of V enus , , Stillman Stillman Drake, JHA, XV, 1984 Drake, JHA, XV, 1984 � Galileo, , Paolo Palmieri Palmieri. JHA XXXII 2001: 109 . JHA XXXII 2001: 109- -129. 129. � � Galileo and the discovery of the phases of V enus , Paolo Galileo and the discovery of the phases of V enus � Cahiers Clairaut n° °5 et 28 (revue du Comit 5 et 28 (revue du Comité é de L iaison E nseignants Astronomes) de L iaison E nseignants Astronomes) � Cahiers Clairaut n

Letter to Castelli, Florence. 30 December 1610 (See Proceedings) Read the letters of Galileo and make Drawings …Know then that about three months ago I began to observe Venus with the instrument, and I saw it round in shape and very small; it went daily growing in bulk and keeping the same rotundity until finally, coming to a very great distance from the Sun, it commenced to lose rotundity from the eastern side, and in a few days was reduced to a half-circle. In that shape it stayed many days, but always growing in size; now it begins to become sickle-shaped; and as long as it is seen evenings it will go on thinning its little horns until they vanish. But then returning [in the] mornings, it will be seen with horns thin and still turned away from the Sun; it will go on growing toward a half-circle until maximum elongation. Then it will remain semicircular for some days, though diminishing in bulk; then from the semi-circle it will pass to ail round in a few days, and will be seen that way for many months, both as morning and [then as] evening star, all round but very small in size.

Letter 11 11 december december 1610 1610 Letter to Giuliano de Medici, Giuliano de Medici, Praha Praha to " Haec immatura a me iam frustra leguntur o, y " Haec immatura a me iam frustra leguntur o, y " " In vain I'm looking at these things immature o, y . . In vain I'm looking at these things immature o, y Kepler sugested sugested the solution the solution Kepler MACULA RUFA IN IOVE EST GYRATUR MATHEM, ECC. ECC. MACULA RUFA IN IOVE EST GYRATUR MATHEM, There is a red spot on Jupiter, revolves mathematically, etc. There is a red spot on Jupiter, revolves mathematically, etc.

Letter 30 december december 1610 1610 Letter 30 to Castelli , Florence, Castelli , Florence, to ".... I began to observe Venus, who, in the evening, was ".... I began to observe Venus, who, in the evening, was perfectly round, and very small ..." perfectly round, and very small ..."

1 2 3 1-…. perfectly circular. With such a figure is maintained for many days, but increases substantially in size. 2- Approaching the same elongation it commenced to lose retundity from the eastern side, 3- and in a few days was reduced with to a half-circle. In that shape it stayed many days but always growing in size.

1 2 3 4 4-now it begins to become sickle-shaped; and as long as it is seen evenings it will go on thinning its little horns until they vanish.

8 7 6 5 5- But then returning in the mornings, it will be seen with horns thin and still turned away from the sun;. 6- It will go on growing toward a half-circle diminishing in bulk; 7- then from semicircle it will pass to ail round in a few days, and will be see that way for many months 8- removing approximately three months it will be invisible

? Ptolemy’s model

Galileo’ ’s conclusion s conclusion Galileo 8 7 1 2 3 6 5 4 � The planets are all dark in nature The planets are all dark in nature � � Necessarily Venus revolves around the sun Necessarily Venus revolves around the sun �

Venus, Letter 16 Venus, Letter 16 june june 1612 1612 So, the the sentence sentence I I sent sent : : So, Haec immatura a me iam frustra leguntur o. y., Haec immatura a me iam frustra leguntur o. y., . ) (In vain vain I'm I'm looking looking at at these these things things immature immature o y o y . ) (In means: : means Cynthiae figuras figuras aemulatur aemulatur mater mater amorum amorum, , Cynthiae Venus imitates imitates the the phases phases of of the the moon moon Venus

Periods of Venus, dates of quadrature quadrature Periods of Venus, dates of and conjunctions and conjunctions The synodic synodic period of Venus is 584 days period of Venus is 584 days The � � The superior conjunction occured occured on 11 may 1610. on 11 may 1610. � The superior conjunction � Calculate the date of the quadrature quadrature, of the inferior , of the inferior � Calculate the date of the � conjunction and of the next superior conjunction, conjunction and of the next superior conjunction, supposing the motions of the Earth and Venus are supposing the motions of the Earth and Venus are circular and uniform. circular and uniform.

11 may 1610 conjunctions conjunctions Periods of Periods of quadrature quadrature Venus: Venus:

Periods of Venus, dates of quadrature quadrature Periods of Venus, dates of and conjunctions and conjunctions α =90 ( α � 1) Quadrature Quadrature ( =90° °) 11 may 1610+146 days : 4 ) 11 may 1610+146 days : 4 october october � 1) 1610 1610 α =180 Inferior conjunction ( α =180° °) 11 may 1610+292 days : 28 ) 11 may 1610+292 days : 28 � � Inferior conjunction ( february 1611 1611 february α =360 Superior conjunction ( α � =360° °) 11 may 1610+584 days : 11 ) 11 may 1610+584 days : 11 � Superior conjunction ( may 1611+219=16 december december 1611 1611 may 1611+219=16 In fact the real dates are a bit different � � In fact the real dates are a bit different � 11 may 1610 superior conjunction � 11 may 1610 superior conjunction 26 february february 1611 inferior conjunction 1611 inferior conjunction � 26 � 11 december december 1611 superior conjunction 1611 superior conjunction � � 11 because the Earth and Venus don’ ’t move with a circular uniform t move with a circular uniform because the Earth and Venus don motion motion

Sidereal period of Venus : T T Venus Sidereal period of Venus : Venus ω : ω � angular velocities angular velocities : � ω syn = ω ω Venus ω Earth ω - ω syn Venus Venus = Venus - Earth � ω ω Venus = ω ω syn + ω ω Earth π / 2 π π /584+2 π /365.25= 2 π /584+2 π syn Venus = 2 /365.25= 2 /T T Venus Venus = Venus + Earth = � Venus � T T Venus =365.25*584/(584+365.25)=224.7 jours Venus =365.25*584/(584+365.25)=224.7 jours �

Phases on Venus in geo and heliocentric models Phases on Venus in geo and heliocentric models � 1) Determine the phases of Venus in geocentric models, 1) Determine the phases of Venus in geocentric models, � where the Earth is at the center center of the universe and planets orbit of the universe and planets orbit where the Earth is at the around (Venus “ “above above” ” or or “ “below below” ” the sun) the sun) around (Venus � Pseudo Pseudo- -Aristoteles Aristoteles model : Earth ( model : Earth (center) center)- -Moon Moon- -Sun Sun- -Mercury Mercury- - � Venus- -Mars Mars- -Jupiter Jupiter- -Saturne Saturne Venus Ptolemeo’ ’s s model : Earth ( model : Earth (center) center)- -Moon Moon- -Mercury Mercury- -Venus Venus- -Sun Sun- -Mars Mars- - � Ptolemeo � Jupiter- -Saturne Saturne Jupiter � 2) Determine the phases of Venus in the heliocentric model, 2) Determine the phases of Venus in the heliocentric model, � where planets orbit around the sun. where planets orbit around the sun. � Copernican system : Sun ( Copernican system : Sun (center) center)- -Mercury Mercury- -Venus Venus- -Earth Earth- -Mars Mars- - � Jupiter Jupiter- -Saturne Saturne