15/07/2004THE ORBIT OF VENUS1 8th EAAE Summer School De Glind (19-24 July 2004) Roland BONINSEGNA (Belgium)

15/07/2004THE ORBIT OF VENUS2 Use simple observations to: –confirm the heliocentric theory –define Venus orbit –compute Venus distance –compute Venus revolution period OBJECTIVES

15/07/2004THE ORBIT OF VENUS3 Galileo ( )

15/07/2004THE ORBIT OF VENUS4 SUN

15/07/2004THE ORBIT OF VENUS5 SUN

15/07/2004THE ORBIT OF VENUS6 Using the transit times … 11h55 14h27

15/07/2004THE ORBIT OF VENUS7 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?

15/07/2004THE ORBIT OF VENUS8 DateView from Earth Transit times (U.T.) 2004 January 31 1 Sun: 11h55 Venus: 14h27 Elongation: E 2004 March 31 2 Sun: 11h45 Venus: 14h40 Elongation: E 38 E

15/07/2004THE ORBIT OF VENUS9 DateView from Earth Transit times (U.T.) 2004 June 8 3 Sun: 11h40 Venus: 11h40 Elongation: 0° 2004 August 17 4 Sun: 11h45 Venus: 08h45 Elongation: W

15/07/2004THE ORBIT OF VENUS10 DateView from Earth Transit times (U.T.) 2004 October 15 5 Sun: 11h27 Venus: 09h06 Elongation: W 2005 March 29 6 Sun: 11h46 Venus: 11h46 Elongation: 1° S

15/07/2004THE ORBIT OF VENUS11 Calculating the elongation angle - Results 2004 January 3138° E 2004 March 31 44° E 2004 June August October March 29 0° 45° W 35° W 1° S

15/07/2004THE ORBIT OF VENUS12 Sun Earth 38°

15/07/2004THE ORBIT OF VENUS13 S E 44°

15/07/2004THE ORBIT OF VENUS14 Measure each Sun – Venus distance

15/07/2004THE ORBIT OF VENUS15 Measure each Earth – Venus distance

15/07/2004THE ORBIT OF VENUS16 Complete the table SUN - VENUSEARTH - VENUS 1 mm Mean Distance Sun – Earth = mm

15/07/2004THE ORBIT OF VENUS17 Example of results SUN - VENUSEARTH - VENUS 1 83 mm130 mm 271 mm 472 mm71 mm mm Mean 74 mm Distance Sun – Earth = 100 mm

15/07/2004THE ORBIT OF VENUS18 Find the place of Venus for dates 3 and Draw Venus orbit

15/07/2004THE ORBIT OF VENUS19 SUN - VENUSEARTH - VENUS Mean 74 mm Distance Sun – Earth = 100 mm 100 mm = 1 Astronomical Unit = 15 x 10 7 km Mean official Sun – Venus distance: A.U.

15/07/2004THE ORBIT OF VENUS20 DATEELONG. (°) PH. (%) APP. DIAM. (”) EARTH- VENUS (A.U.) (1) 2004 Jan 3138 E7515 (2) 2004 Mar 3144 E5024 (3) 2004 Jun (4) 2004 Aug 1745 W5024 (5) 2004 Oct 1535 W7515 (6) 2005 Mar 291 S10010 Using your measures, calculate … OFFICIAL VALUES

15/07/2004THE ORBIT OF VENUS 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/ d

15/07/2004THE ORBIT OF VENUS22 Eastern Elongation (evening) Western Elongation (morning) 2004 March November June January August August March October June January d

15/07/2004THE ORBIT OF VENUS23 0 The Venus synodic revolution period d

15/07/2004THE ORBIT OF VENUS24 0 The Venus sidereal revolution period ? d

15/07/2004THE ORBIT OF VENUS25 THE SIDEREAL REVOLUTION PERIOD OF VENUS Remember the value of Venus synodic revolution Period? VsP = 584 d Remember the value of Earth Sidereal revolution Period? ESP = d

15/07/2004THE ORBIT OF VENUS26 THE SIDEREAL REVOLUTION PERIOD OF VENUS VsP = 584 d How to find the value of Venus Sidereal revolution Period? ESP = d 1/VSP = 1/VsP + 1/ESP VSP = d

15/07/2004THE ORBIT OF VENUS27 0 (0) 8/06/04

15/07/2004THE ORBIT OF VENUS28 0 (0) 8/06/ (1) 8/09/04

15/07/2004THE ORBIT OF VENUS29 0 (0) 8/06/ (1) 8/09/ (2) 8/12/04

15/07/2004THE ORBIT OF VENUS30 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/05 Value of one Venus sidereal revolution? 225 d

15/07/2004THE ORBIT OF VENUS31 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/ (4) 19/04/05

15/07/2004THE ORBIT OF VENUS32 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/ (4) 19/04/ (5) 19/07/05

15/07/2004THE ORBIT OF VENUS33 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/ (4) 19/04/05 5 (5) 19/07/ An other Venus sidereal revolution! (6) 31/08/05

15/07/2004THE ORBIT OF VENUS34 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/ (4) 19/04/05 5 (5) 19/07/ (6) 31/08/05 77 (7) 1/12/05

15/07/2004THE ORBIT OF VENUS35 0 (0) 8/06/ (1) 8/09/ (2) 8/12/ (3) 19/01/ (4) 19/04/05 5 (5) 19/07/ (6) 31/08/05 77 (7) 1/12/ (8) 13/01/05 Value of one Venus synodic revolution? 584 d

15/07/2004THE ORBIT OF VENUS36 References Gray B.J., 2002, Guide 8 software: Laurel C. et al., Celestia software The Torbay Astronomical Society: View of the solar system (in different languages): solarviews.com/ss.html Winther Mogens, Seeing is believing: Amtsgym-sdbg.dk/as/venus/ven-dist.htm