The process involves making very accurate measurements of the times at which four things happen during a transit of Venus as viewed from Earth.
The beginning of ingress -- the moment at which the small disc of Venus first appears to touch the outer edge of the disc of the Sun. This is called First Contact.
The end of ingress -- the moment at which the disc of Venus is fully inside the inner edge of the disc of the Sun. This is the Second Contact and it happens very soon after First Contact.
The beginning of egress -- some time later, near the completion of the transit, the disc of Venus will again appear touch the inner edge of the disc of the Sun as it moves out the other side. This is the Third Contact.
The end of egress -- very soon after Third Contact, the moment at which the small disc of Venus appears to touch the outer edge of the disc of the Sun as the transit ends. This is called Fourth Contact.
These four timings made at one observation point on Earth are compared to the same timings made at a variety of other observation points, and from this data the Solar Parallax can be derived, and from that, an accurate value for the AU.
I think this link sums up the math and the process fairly well, in a brief and concise fashion:
Entire books have been written about the whole affair. I read a few of them and made an attempt to see the 2004 transit of Venus, but overcast skies waylaid my efforts. The wife and I made a trip to Alaska to try again for the 2012 transit of Venus and it paid off tremendously well. The next ones happen in 2117 and 2125; don't think I'll be around anymore by that time so I'm grateful I got to see one of 'em.
Very nice write up. But I have a question: how does Venus's relative angle of inclination make it more useful than say, Mercury. You can obtain all 4 contacts with Mercury, right?
Or does it have to do with the size of Venus being larger than Mercury (and therefore being easier to measure [along with a longer orbital period])?
You make an excellent point. In theory you could do the same timings with Mercury, but in practice it's very much more difficult, for several reasons. First, its disc is considerably smaller than that of Venus. It moves much faster than Venus, and it's much closer to the Sun -- all of these factors combine to make Mercury far less than ideal for measuring solar parallax.
Its small size, its rapidity and its proximity to the Sun rule out any accurate timings between 1st and 2nd contacts, or 3rd and 4th contacts (that is, the beginnings and endings of ingress and egress). That is to say, accurate timings to be made during the 18th and 19th centuries, when transits were measured with optical instruments and timed with analog clocks.
In short, the margin of error during a transit of Mercury in the 1700's was too great for it to be a viable measurement of solar parallax with any degree of accuracy. It had to be Venus, with its much larger planetary disc, its slower apparent motion during ingress and egress, and its relative midpoint between the Earth and the Sun.
Sir Edmond Halley (same of comet fame) tried to measure solar parallax in pursuit of the elusive AU back in 1677 using a transit of Mercury, but was disappointed with the results. He laid out the case for solving the AU using a transit of Venus, however, and that leads us to your second point:
Angle as a factor... the angle hinders, it does not help!
The angle of inclination for Venus was a huge cosmic "gotcha" for the astronomers of those days. If only Venus were in the same plane as the other planets, then transits of Venus across the face of the Sun would be common and frequent, occurring perhaps a 13 or 14 times per century (like transits of Mercury do).
But alas, transits of Venus happen rarely because of that orbital inclination. The first one to be predicted, observed and recorded was in 1639; the next one wouldn't happen until 1761. Halley went to his grave twenty years prior to that. He knew exactly how to calculate solar parallax and how to derive the value of the AU using a transit of Venus, but he wouldn't live long enough to do it himself.
If it weren't for that damned orbital tilt which makes a transit of Venus such a rare thing, Halley most likely could have solved the AU accurately in his own lifetime. Sometimes I wonder how much farther along we would be if the Astronomical Unit was measured much earlier than it was. The AU gives us the distance from the Earth to the Sun, and from that we get the size of the Solar System, the approximate distances to other stars and an accurate measurement of the speed of light.
Halley knew exactly how to do this in that late 1600's. He tried to use Mercury but it wasn't accurate. Venus was the key, it would provide the answer to the AU. If Venus was in the same plane as the other planets then he could've easily done it himself, and he could have done it more than once or twice. But the odd orbital tilt of Venus delayed the measurement of solar parallax by more than a century.
That's the significance of the inclination. It held back the answer to the AU for a very long time.
Seriously - what a great explanation of an interesting topic. I would've never picked out Venus's angle in OP's photo until you mentioned it. That, combined with the solar parallax lesson, made for some fabulous reading.
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u/CenTexChris Mar 04 '23
The process involves making very accurate measurements of the times at which four things happen during a transit of Venus as viewed from Earth.
These four timings made at one observation point on Earth are compared to the same timings made at a variety of other observation points, and from this data the Solar Parallax can be derived, and from that, an accurate value for the AU.
I think this link sums up the math and the process fairly well, in a brief and concise fashion:
https://www.exploratorium.edu/venus/question4.html
Entire books have been written about the whole affair. I read a few of them and made an attempt to see the 2004 transit of Venus, but overcast skies waylaid my efforts. The wife and I made a trip to Alaska to try again for the 2012 transit of Venus and it paid off tremendously well. The next ones happen in 2117 and 2125; don't think I'll be around anymore by that time so I'm grateful I got to see one of 'em.