15/07/2004 THE ORBIT OF VENUS 1

THE ORBIT OF VENUS

8th EAAE Summer School

De Glind (19-24 July 2004)

Roland BONINSEGNA

(Belgium)

15/07/2004 THE ORBIT OF VENUS 2

• Use simple observations to:

– confirm the heliocentric theory– define Venus orbit– compute Venus distance– compute Venus revolution period

OBJECTIVESOBJECTIVES

15/07/2004 THE ORBIT OF VENUS 3

Galileo (1564-1642)

15/07/2004 THE ORBIT OF VENUS 4

SUN

15/07/2004 THE ORBIT OF VENUS 5

SUN

15/07/2004 THE ORBIT OF VENUS 6

Using the transit times …

11h5514h27

15/07/2004 THE ORBIT OF VENUS 7

The Earth achieves one rotation (360 degrees) in 24 hours.What is the value of the rotation angle in 1 hour?

…to calculate the elongation angle.

15°

For 2004 January 31…

Sun transit time: 11h55

Venus transit time: 14h27

2h32min = 2.53h

38°Elongation angle?

15/07/2004 THE ORBIT OF VENUS 8

Date View from Earth Transit times (U.T.)

2004 January 31

1

Sun: 11h55Venus: 14h27Elongation: E

2004 March 31

2

Sun: 11h45Venus: 14h40Elongation: E

38 E

15/07/2004 THE ORBIT OF VENUS 9

Date View from Earth Transit times (U.T.)

2004 June 8

3

Sun: 11h40Venus: 11h40Elongation: 0°

2004 August 17

4

Sun: 11h45Venus: 08h45Elongation: W

15/07/2004 THE ORBIT OF VENUS 10

Date View from Earth Transit times (U.T.)

2004 October 15

5

Sun: 11h27Venus: 09h06Elongation: W

2005 March 29

6

Sun: 11h46Venus: 11h46Elongation: 1° S

15/07/2004 THE ORBIT OF VENUS 11

Calculating the elongation angle - Results

2004 January 31 38° E

2004 March 31 44° E

2004 June 8

2004 August 17

2004 October 15

2005 March 29

0°

45° W

35° W

1° S

15/07/2004 THE ORBIT OF VENUS 12

Sun

Earth

38°

15/07/2004 THE ORBIT OF VENUS 13

S

E

44°

15/07/2004 THE ORBIT OF VENUS 14

Measure each Sun – Venus distance

15/07/2004 THE ORBIT OF VENUS 15

Measure each Earth – Venus distance

15/07/2004 THE ORBIT OF VENUS 16

Complete the table

SUN - VENUS EARTH - VENUS

1 mm

2

4

5

Mean

Distance Sun – Earth = mm

15/07/2004 THE ORBIT OF VENUS 17

Example of results

SUN - VENUS EARTH - VENUS

1 83 mm 130 mm

2 71 mm 71 mm

4 72 mm 71 mm

5 71 mm 123 mm

Mean 74 mm

Distance Sun – Earth = 100 mm

15/07/2004 THE ORBIT OF VENUS 18

Find the place of Venus for

dates 3 and 6.

3

6

Draw Venus orbit

15/07/2004 THE ORBIT OF VENUS 19

SUN - VENUS EARTH - VENUS

Mean 74 mm

Distance Sun – Earth = 100 mm

100 mm = 1 Astronomical Unit = 15 x 107 km

Mean official Sun – Venus distance: 0.723 A.U.Mean official Sun – Venus distance: 0.723 A.U.

15/07/2004 THE ORBIT OF VENUS 20

DATE ELONG. (°)

PH. (%)

APP. DIAM.

(”)

EARTH- VENUS (A.U.)

(1) 2004 Jan 31 38 E 75 15

(2) 2004 Mar 31 44 E 50 24

(3) 2004 Jun 8 0 0 58

(4) 2004 Aug 17 45 W 50 24

(5) 2004 Oct 15 35 W 75 15

(6) 2005 Mar 29 1 S 100 10

Using your measures, calculate …

1.126

0.695

0.289

0.706

1.137

1.724

OF

FIC

IAL

VA

LU

ES

15/07/2004 THE ORBIT OF VENUS 21

3

6

Value of the Venus synodic

period?

(1) 31/01/04(2) 31/03/04(3) 8/06/04(4) 17/08/04(5) 15/10/04(6) 29/03/05

584 d

15/07/2004 THE ORBIT OF VENUS 22

Eastern Elongation (evening)

Western Elongation (morning)

• 2004 March 29• 2005 November 3• 2007 June 9• 2009 January 14• 2010 August 20

• 2004 August 17• 2006 March 25• 2007 October 28• 2009 June 5• 2011 January 8

584 d584 d 584 d584 d

15/07/2004 THE ORBIT OF VENUS 23

0

The Venus synodic revolution period

1

584 d584 d

15/07/2004 THE ORBIT OF VENUS 24

0

The Venus sidereal revolution period

? d? d

15/07/2004 THE ORBIT OF VENUS 25

THE SIDEREAL REVOLUTIONPERIOD OF VENUS

Remember the value of

Venus synodic revolution Period?VsP = 584 d

Remember the value of

Earth Sidereal revolution Period?ESP = 365.25 d

15/07/2004 THE ORBIT OF VENUS 26

THE SIDEREAL REVOLUTIONPERIOD OF VENUS

VsP = 584 d

How to find the value of

Venus Sidereal revolution Period?

ESP = 365.25 d

1/VSP = 1/VsP + 1/ESP VSP = 224.7 d

15/07/2004 THE ORBIT OF VENUS 27

0

(0) 8/06/04

15/07/2004 THE ORBIT OF VENUS 28

0

(0) 8/06/04

1

1(1) 8/09/04

15/07/2004 THE ORBIT OF VENUS 29

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

15/07/2004 THE ORBIT OF VENUS 30

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

Value of one Venus sidereal

revolution?

225 d

15/07/2004 THE ORBIT OF VENUS 31

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

4

4

(4) 19/04/05

15/07/2004 THE ORBIT OF VENUS 32

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

4

4

(4) 19/04/05

5

5

(5) 19/07/05

15/07/2004 THE ORBIT OF VENUS 33

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

4

4

(4) 19/04/05 5

(5) 19/07/05

5

6

6

An other Venus sidereal

revolution!

(6) 31/08/05

15/07/2004 THE ORBIT OF VENUS 34

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

4

4

(4) 19/04/05 5

(5) 19/07/05

5

6

6

(6) 31/08/05

7 7

(7) 1/12/05

15/07/2004 THE ORBIT OF VENUS 35

0

(0) 8/06/04

1

1(1) 8/09/04

2

2

(2) 8/12/04

3

3

(3) 19/01/05

4

4

(4) 19/04/05 5

(5) 19/07/05

5

6

6

(6) 31/08/05

7 7

(7) 1/12/05

8

8(8) 13/01/05

Value of one Venus synodic

revolution?

584 d

15/07/2004 THE ORBIT OF VENUS 36

References

•Gray B.J., 2002, Guide 8 software: http://www.projectpluto.com

•Laurel C. et al., Celestia software

http://www.shatters.net/celestia

•The Torbay Astronomical Society:

http://www.halien.com/TAS/

•View of the solar system (in different languages): http://www. solarviews.com/ss.html

•Winther Mogens, Seeing is believing:

http://www. Amtsgym-sdbg.dk/as/venus/ven-dist.htm