On the. Transits of Venus
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1 On the Transits of Venus
2 June 8, 2004
3 June 8, 2004
4 June 8, 2004
5 the crossings of 04 and 12 NASA picture
6 The Orbits of the Two Planets
7 the plane of the ecliptic Sun Earth
8 the two orbits Venus Sun Earth
9 the inclination of Venus s orbit 3.39 Venus Earth
10 the nodes Ascending Venus Descending Earth
11 the green zones A Sun Earth Venus D
12 Size of the Green Zone: The Angles of the Crossings
13 the solar angle: a combination of three things 9?
14 1. the sidereal angle 3.39 Venus Earth
15 the orbital speeds of the planets Venus mi/sec Earth mi/sec
16 the sidereal path of Venus 3.39 ecliptic mi/sec
17 the sidereal path of Venus mi/sec mi/sec 1.29 mi/sec
18 the relative speed from our view mi/sec mi/sec 1.29
19 2. the terrestrial angle 3.22 mi/sec
20 confirmation: ecliptic coordinates of Venus, June 5-6, pm 75 deg 53 m 57 s 0 deg 12 m 49 s 3 am 75 deg 35 m 26 s 0 deg 05 m 25 s drift - 18 m 21 s - 7 m 24 s s s
21 the path from our view 1101 sec 444 sec
22 the terrestrial angle sec 444 sec
23 the apparent crossings ecliptic
24 3. the actual crossings ecliptic
25 the Sun s 2012 drift ecliptic sec 2004
26 the terrestrial angle sec 222 sec
27 the apparent path across the Sun 865 sec sec 222 sec
28 the solar angle 865 sec sec 222 sec
29 The Size of the Green Zone
30 the apparent crossings ecliptic
31 the tangents to the Sun ecliptic 8.9
32 the green zone seen from Earth B 8.9 C
33 the green zone seen from Earth B C
34 the green zone seen from Earth B 2004 transit C
35 the green zone seen from Earth B 2004 transit C
36 the green zone seen from Earth B 2004 transit 2012 transit C
37 measuring the green zone B C
38 measuring the green zone B C 1.7
39 the angular size of the green zone as seen from Earth B C 3.5
40 the angular size of the green zone as seen from Earth Venus Earth 3.5
41 distances Venus Earth 3.5
42 distances 67 Venus Earth
43 the angular size of the green zone as seen from the Sun 1.4 Venus Earth
44 the descending green zone Venus D A Sun Earth 1.4
45 The Occurrence of Descending Transits
46 Earth in orbit: vyear 0 Earth Venus at descending node
47 Venus in orbit: 1 vyear = days Venus node to node
48 Earth in orbit: vyear 1 Earth V at D
49 Earth in orbit: vyear 2 Earth V at D
50 Earth in orbit: vyear 2 Earth V at D
51 Earth in orbit: vyears 0 to 9 vyear number Earth position
52 Earth in orbit: vyears 10 to 19 vyear number Earth position
53 Earth in orbit: vyears 10 to 19 vyear number Earth position
54 Earth in orbit: vyear 13 Earth 0.91 V at D
55 Earth in orbit: vyear 13 = years Earth 0.91 V at D
56 Earth in orbit: vyear V at D
57 Earth in orbit: vyear V at D
58 Earth eventually makes it to just before the Green zone V at D
59 and it cannot miss the green zone. 1.4 V at D 0.91
60 If Earth hits the right third of the green zone 0.46 V at D
61 then 8 years later, it is still in the zone. 1.4 V at D 0.91
62 In the first one, we look towards the left 0.4 V at D
63 to see this kind of transit. 2004
64 Eight years later, we look towards the right 1.4 V at D 0.91
65 to see this one
66 Eight years after the second transit 1.4 V at D 0.91
67 Venus misses right
68 Eight years before the first transit 1.4 V at D
69 Venus missed left
70 The Frequency of Descending Transits
71 Start counting at V at D
72 When is the next descending transit? vyears
73 When is the next descending transit? vyears vyear number Earth position
74 When is the next descending transit? vyears vyear number Earth position
75 When is the next descending transit? vyears
76 At vyear 395 vyear number Earth position
77 At vyear 395 = years vyear number Earth position Earth years
78 Earth returns rightward of the 2004 position V at D
79 and the transit moves left
80 So does the follower
81 The Ascending Node
82 halfway to 395 vyears: vyears = years 2004 V at D
83 prediction on paper vyear number Earth position Earth years
84 prediction in space
85 prediction on paper vyear number Earth position Earth years
86 prediction in space
87
88 NASA Catalog DATE TIME SERIES DEPTH 1631 Dec 07 3: Dec 04 14: Jun 06 2: Jun 03 19: Dec 09 1: Dec 06 13: Jun 08 5: Jun 06 22: Dec 11 23: Dec 08 13: Jun 11 8: Jun 09 1:
89 NASA Catalog DATE TIME SERIES DEPTH 1631 Dec 07 3: Dec 04 14: Jun 06 2: Jun 03 19: Dec 09 1: Dec 06 13: Jun 08 5: Jun 06 22: Dec 11 23: Dec 08 13: Jun 11 8: Jun 09 1:
90 NASA Catalog DATE TIME SERIES DEPTH 1631 Dec 07 3: Dec 04 14: Jun 06 2: Jun 03 19: Dec 09 1: Dec 06 13: Jun 08 5: Jun 06 22: Dec 11 23: Dec 08 13: Jun 11 8: Jun 09 1:
91 gaps since 1631 DATE TIME SERIES DEPTH 1631 Dec 07 3: Dec 04 14: Jun 06 2: Jun 03 19: Dec 09 1: Dec 06 13: Jun 08 5: Jun 06 22: Dec 11 23: Dec 08 13: Jun 11 8: Jun 09 1: ] yr ] ] ] ] 121.5
92 uniform-gaps prediction
93 Earth s predicted year reach
94 Earth s actual year reach
95 and and years
96 back to the start June 2004
97 aphelion is around July 4 June 2004 aphelion
98 near aphelion June 2004 slowest part aphelion
99 Going halfway around June 2004 slowest part
100 Earth covers the slowest part, leaves out the fastest. fastest June 2004 slowest part
101 Earth travels about 99% of the predicted path
102 Venus is likewise late.
103 Venus also had aphelion ahead. Venus aphelion June 2004 aphelion
104 Venus needs about vyear to reach the ascending node.
105 The combination moves Earth s place just under 8 years back
106 uniform-gaps prediction vyear number Earth position Earth years
107 extend Venus s trip by 0.6% vyear number Earth position Earth years
108 shorten earth s trip by 1% vyear number Earth position Earth years
109 Now 2133 is out of the green zone vyear number Earth position Earth years
110 2117 is in. vyear number Earth position Earth years
111 Persistence of the Pairs
112 The descending transits move left
113 The shifting left continues
114 until 3462 and its follower
115 In 3705, Venus barely misses left 3705
116 so that the follower crosses near the middle of the green zone
117 and the next one misses right
118 At the ascending node, they move right from NASA picture
119 faster than the descenders move left
120 By 2854, the followers miss right
121 After 2846, there are single ascending transits until
122
123
124 After the 3713 transit
125 there are single descending transits until
126
127 NASA Catalog DATE TIME SERIES May 23 16: May 21 9: Nov 22 0: Nov 19 13: May 22 14: Nov 22 0: Nov 19 13: May 22 18: Nov 23 0: May 22 23: Nov 23 0: May 23 3: Nov 22 23: May 24 7: Nov 22 23: May 24 11: May 22 4: Jun 08 8: Jun 06 1:29 5
128 According to Fourmilab, the lone transits move slowly left 3713
129 then right, as the ascending transits do now 3713
130 until our followers become followers again
131 The gaps go from DATE TIME SERIES DEPTH 1631 Dec 07 3: Dec 04 14: Jun 06 2: Jun 03 19: Dec 09 1: Dec 06 13: Jun 08 5: Jun 06 22: Dec 11 23: Dec 08 13: Jun 11 8: Jun 09 1: ] yr ] ] ] ] 121.5
132 to DATE TIME SERIES DEPTH 2603 Dec 16 0: Dec 13 13: Jun 15 17: Jun 13 10: Dec 16 23: Dec 14 12: Jun 16 19: Jun 14 12: Dec 18 21: Jun 19 22: Jun 17 15: ] yr ] ] ] ] 129.5
133 to DATE TIME SERIES DEPTH 3332 Dec 20 20: Jun 22 0: Jun 19 17: Dec 23 18: Jun 24 2: Jun 21 19: Dec 25 17: Jun 23 21: ] ] ] ] ] 137.5
134 to variable [ ] [ ] 145.5
135 with thanks to: NASA ( Fourmilab ( _from_earth.html.gz) Sky and Telescope (
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