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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

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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

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Bibliography Bibliography « « Galileo and Venus Galileo and Venus » »

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 OGG X, 502-

  • 504

504

  • 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

  • Phases of V enus in 1610

Phases of V enus in 1610. O.

. O. Gingerich

  • Gingerich. Journal for the History of Astronomy, XV, 1984: 209

. Journal for the History of Astronomy, XV, 1984: 209-

  • 210.

210.

  • The appearances of V enus and Mars in 1610

The appearances of V enus and Mars in 1610, William Peters, JHA, XV 1984

, William Peters, JHA, XV 1984

  • Galileo,

Galileo, Kepler Kepler and phases of V enus and phases of V enus,

, Stillman Stillman Drake, JHA, XV, 1984 Drake, JHA, XV, 1984

  • Galileo and the discovery of the phases of V enus

Galileo and the discovery of the phases of V enus, Paolo

, Paolo Palmieri

  • Palmieri. JHA XXXII 2001: 109

. JHA XXXII 2001: 109-

  • 129.

129.

  • Cahiers Clairaut n

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)

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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.

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Letter Letter 11 11 december december 1610 1610

to to Giuliano de Medici, Giuliano de Medici, Praha Praha

" "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 Kepler sugested sugested the solution the solution

MACULA RUFA IN IOVE EST GYRATUR MATHEM, MACULA RUFA IN IOVE EST GYRATUR MATHEM, ECC. ECC.

There is a red spot on Jupiter, revolves mathematically, etc. There is a red spot on Jupiter, revolves mathematically, etc.

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Letter 30 Letter 30 december december 1610 1610

to to Castelli , Florence, Castelli , Florence,

".... 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 ..."

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1-…. perfectly circular. With such a figure is maintained for many days, but increases substantially in size.

1

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.

3 2

2- Approaching the same elongation it commenced to lose retundity from the eastern side,

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1

3 2 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. 4

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5- But then returning in the mornings, it will be seen with horns thin and still turned away from the sun;.

5

8- removing approximately three months it will be invisible

8 6

6- It will go on growing toward a half-circle diminishing in bulk;

7

7- then from semicircle it will pass to ail round in a few days, and will be see

that way for many months

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SLIDE 9

?

Ptolemy’s model

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5 8 6 7

1 2 3 4

Galileo Galileo’ ’s conclusion s conclusion

  • 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

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Venus, Venus, Letter 16

Letter 16 june june 1612 1612

So, So, the the sentence sentence I I sent sent : :

Haec immatura a me iam frustra leguntur o. y., Haec immatura a me iam frustra leguntur o. y.,

(In (In vain vain I'm I'm looking looking at at these these things things immature immature o y

  • y. )

. )

means means: :

Cynthiae Cynthiae figuras figuras aemulatur aemulatur mater mater amorum amorum, ,

Venus Venus imitates imitates the the phases phases of

  • f the

the moon moon

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Periods of Venus, dates of Periods of Venus, dates of quadrature quadrature and conjunctions and conjunctions

  • The

The synodic synodic period of Venus is 584 days period of Venus is 584 days

  • The superior conjunction

The superior conjunction occured

  • ccured on 11 may 1610.
  • n 11 may 1610.
  • Calculate the date of the

Calculate the date of the quadrature quadrature, of the inferior , of the inferior 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.

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Periods of Periods of Venus: Venus: quadrature quadrature conjunctions conjunctions

11 may 1610

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Periods of Venus, dates of Periods of Venus, dates of quadrature quadrature and conjunctions and conjunctions

  • 1)

1) Quadrature Quadrature ( (α

α=90

=90° °) 11 may 1610+146 days : 4 ) 11 may 1610+146 days : 4 october

  • ctober

1610 1610

  • Inferior conjunction (

Inferior conjunction (α

α=180

=180° °) 11 may 1610+292 days : 28 ) 11 may 1610+292 days : 28 february february 1611 1611

  • Superior conjunction (

Superior conjunction (α

α=360

=360° °) 11 may 1610+584 days : 11 ) 11 may 1610+584 days : 11 may 1611+219=16 may 1611+219=16 december december 1611 1611

  • 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

26 february february 1611 inferior conjunction 1611 inferior conjunction

  • 11

11 december december 1611 superior conjunction 1611 superior conjunction because the Earth and Venus don because the Earth and Venus don’ ’t move with a circular uniform t move with a circular uniform motion motion

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Sidereal period of Venus : Sidereal period of Venus : T TVenus

Venus

  • angular velocities

angular velocities : : ω

ω ω ωsyn

synVenus

Venus=

= ω

ωVenus

Venus-

  • ω

ωEarth

Earth

  • ω

ωVenus

Venus=

= ω

ωsyn

synVenus

Venus+

+ ω

ωEarth

Earth=

= 2

2π

π/584+2

/584+2π

π/365.25=

/365.25= 2

2π

π/

/T TVenus

Venus

  • T

TVenus

Venus=365.25*584/(584+365.25)=224.7 jours

=365.25*584/(584+365.25)=224.7 jours

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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 where the Earth is at the center center of the universe and planets orbit

  • f the universe and planets orbit

around (Venus around (Venus “ “above above” ” or

  • r “

“below below” ” the sun) the sun)

  • Pseudo

Pseudo-

  • Aristoteles

Aristoteles model : Earth ( model : Earth (center) center)-

  • Moon

Moon-

  • Sun

Sun-

  • Mercury

Mercury-

  • Venus

Venus-

  • Mars

Mars-

  • Jupiter

Jupiter-

  • Saturne

Saturne

  • Ptolemeo

Ptolemeo’ ’s s model : Earth ( model : Earth (center) center)-

  • Moon

Moon-

  • Mercury

Mercury-

  • Venus

Venus-

  • Sun

Sun-

  • Mars

Mars-

  • Jupiter

Jupiter-

  • Saturne

Saturne

  • 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

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SLIDE 17

Phases on Venus in geocentric models Phases on Venus in geocentric models

Ptolemeo Ptolemeo’ ’s s model model Pseudo Pseudo-

  • Aristoteles

Aristoteles model model

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Phases on Venus in the heliocentric model Phases on Venus in the heliocentric model

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Tychonic Tychonic model model

Almagestum novum Riccioli 1651

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Distances Venus Distances Venus-

  • Earth and

Earth and angulars angulars diameters diameters

  • Data : Venus

Data : Venus’ ’s diameter : 12 s diameter : 12 100km 100km Jupiter Jupiter’ ’s diameter 143 000km s diameter 143 000km Earth Earth-

  • Sun = 1

Sun = 1 a.u a.u.= 150 .= 150 000Mkm 000Mkm Venus Venus-

  • Sun = 0.723

Sun = 0.723 a.u a.u. . Jupiter Jupiter-

  • Sun=5.2

Sun=5.2 a.u a.u. .

  • Maximum elongation

Maximum elongation

What is the date of the greatest elongation of Venus (angle What is the date of the greatest elongation of Venus (angle β

β)

)

Why is the elongation not equal to 0 Why is the elongation not equal to 0° ° at the inferior conjunction (8 at the inferior conjunction (8° ° in 1610)? in 1610)?

  • Distances

Distances

  • Calculate the distances D Earth

Calculate the distances D Earth-

  • Venus and the apparent diameters of

Venus and the apparent diameters of

Venus at the conjunctions VSC and VIC and at the greatest elonga Venus at the conjunctions VSC and VIC and at the greatest elongation VME tion VME

  • Compare to the apparent diameter of Jupiter at the opposition

Compare to the apparent diameter of Jupiter at the opposition

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Maximum Maximum elongation elongation

∆=… β= α= t=

Date= TVS=90°

11may 1610 S

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Maximum Maximum elongation elongation

∆=0.69a.u. β=46.33° α=136.33°

t=221 days

18 18 december december

TVS=90°

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Elongations and distances Elongations and distances

Date of the greatest elongation : 18 Date of the greatest elongation : 18 december december

  • The real greatest elongation occurred on 16

The real greatest elongation occurred on 16 december december

  • 1610. Our model is a 2D model for a 3D phenomenon,
  • 1610. Our model is a 2D model for a 3D phenomenon,

and the real motions are neither circular nor uniform. and the real motions are neither circular nor uniform.

  • Elongation=8

Elongation=8° ° on inferior conjunction because Venus and

  • n inferior conjunction because Venus and

Earth don Earth don’ ’t orbit on the same plane. The elongation is 0 t orbit on the same plane. The elongation is 0° °

  • nly when a transit occurs (ecliptic latitude of Venus=0
  • nly when a transit occurs (ecliptic latitude of Venus=0°

°) )

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Elongations and distances Elongations and distances

Sup. Sup. conjunction conjunction Max Max elongation elongation Inf. Inf. conjunction conjunction Jupiter opp. Jupiter opp. Distances Distances

1.723 1.723 0.69 0.69 0.277 0.277 4.2 4.2

Ang. Ang. ( (“ “ of arc)

  • f arc)

9.7 9.7” ” 24.1 24.1” ” 60.1 60.1” ” 46.8 46.8” ”

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Drawing of the terminator Drawing of the terminator

Calculate the phase (angle Calculate the phase (angle ε

ε) of Venus on 15

) of Venus on 15 september september 1610 1610 Draw the phase

11 may 1610 4 oct. 1610

Draw the phase

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SLIDE 26

α α=127*360/584=78.3

=127*360/584=78.3° °

∆ ∆2

2=SE

=SE 2

2+SV

+SV2

2-

  • 2SE*

2SE*SVcos(TSV SVcos(TSV)= )= 1.314a.u. 1.314a.u. sin sinε

ε/ES=sin(180

/ES=sin(180-

  • α

α)/

)/∆

∆

Phase angle Phase angle ε

ε=

= 49 49° ° We can draw the phase

Drawing of Drawing of the terminator the terminator

11 may 1610 4 oct.

15 15 september september = 127 days after sup. conj. = 127 days after sup. conj.

S

We can draw the phase

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SLIDE 27

Annexe