A Transit Surprise - The AU
Posted: Thu Aug 16, 2012 5:50 am
If you are reading this, you probably saw, or wanted to see, the Venus Transit that occurred on June 5/6. For me, this event started out to be "Just let me see the thing" evolving to "Gee, if I can get some pictures that would be great!" Well, I did get pictures that captured all that I could hope for, including the brief, albeit cloud-hampered, moment of 2nd contact.
The AU?
Amongst the many pictures made public in the following days and weeks, SDO (Solar Dynamics Observatory) provided beautifully clear, high-resolution images of the entire transit. About the time I thought I was done, I realized
that if I could find SDO pictures taken at the same time as mine, I could directly measure the difference in Venus' position (parallax) against the sun! This alternate approach to Halley's parallel-chord method (requiring timings of the entire transit) made this exercise possible for me. Therefore, after some (quite a bit 
) of work, I could calculate the Sun's distance. Without any planning, I suddenly found myself as a participant, not just an observer; amazed that my modest pictures could be used to calculate a famously sought-after distance (the AU) that set the foundation for cosmic distance measurements! Indeed, I felt honored.
So now the challenge was in the details: How to do this and to what accuracy could I achieve? Fortunately, three things ended up in my favor. First, the Sun had a healthy number of sunspots which were excellent reference points for comparison with SDO's pictures. Second, the SDO (observer #2) provided a large baseline distance because of its geosynchronous orbital radius (26,200 miles!), and third, the projected orbital distance component (for the parallax calcuation) happened to be near its maximum. SDO's "perfect" images challenged me to to do the best I could with what I had, and conduct the analysis with as much attention to detail as I could muster. Keep in mind that throughout this process, estimating the Sun's distance was the goal; all the while, following the path of not knowing absolute orbital positions. The work paid off - I was successful and very satisfied with the results. Below are the pictures which show 6 Venus images, of which 5 (with sunspots) were used for solid parallax measurements and the subsequent AU estimate.
Simply put, the angular length of the green arrows are the parallaxes to measure in the composite overlay (left). For the zoomed-in 6th comparison (right), the yellow arrow shows a measured 122 arcsecond separation. The accurately known angular diameters of Venus and the Sun, the measurable separations of key sun spots, and the SDO's time-stamped, high resolution, full-sun detail provided me what I needed to accurately compare my pictures. The relative positions of Earth and Venus wrt the Sun are also accurately known => trigonometry now permits calculating the Earth-Sun distance, and finally, the AU.
The AU?
Amongst the many pictures made public in the following days and weeks, SDO (Solar Dynamics Observatory) provided beautifully clear, high-resolution images of the entire transit. About the time I thought I was done, I realized
that if I could find SDO pictures taken at the same time as mine, I could directly measure the difference in Venus' position (parallax) against the sun! This alternate approach to Halley's parallel-chord method (requiring timings of the entire transit) made this exercise possible for me. Therefore, after some (quite a bit ) of work, I could calculate the Sun's distance. Without any planning, I suddenly found myself as a participant, not just an observer; amazed that my modest pictures could be used to calculate a famously sought-after distance (the AU) that set the foundation for cosmic distance measurements! Indeed, I felt honored.So now the challenge was in the details: How to do this and to what accuracy could I achieve? Fortunately, three things ended up in my favor. First, the Sun had a healthy number of sunspots which were excellent reference points for comparison with SDO's pictures. Second, the SDO (observer #2) provided a large baseline distance because of its geosynchronous orbital radius (26,200 miles!), and third, the projected orbital distance component (for the parallax calcuation) happened to be near its maximum. SDO's "perfect" images challenged me to to do the best I could with what I had, and conduct the analysis with as much attention to detail as I could muster. Keep in mind that throughout this process, estimating the Sun's distance was the goal; all the while, following the path of not knowing absolute orbital positions. The work paid off - I was successful and very satisfied with the results. Below are the pictures which show 6 Venus images, of which 5 (with sunspots) were used for solid parallax measurements and the subsequent AU estimate.
Simply put, the angular length of the green arrows are the parallaxes to measure in the composite overlay (left). For the zoomed-in 6th comparison (right), the yellow arrow shows a measured 122 arcsecond separation. The accurately known angular diameters of Venus and the Sun, the measurable separations of key sun spots, and the SDO's time-stamped, high resolution, full-sun detail provided me what I needed to accurately compare my pictures. The relative positions of Earth and Venus wrt the Sun are also accurately known => trigonometry now permits calculating the Earth-Sun distance, and finally, the AU.
The Results?
For 5 parallax measurements, I calculate the AU to be 94.6 ± 2.3 million miles.
Today's value for the AU = 92.956 million miles
Pretty good for someone who just wanted to see the thing!
For me, the real value of this exercise does not lie in the answer. Considering this effort was totally spur-of-the-moment, getting any answer is a real bonus. I couldn't ask for anything more.
To reflect what this meant to me, I can't help but imagine an appreciative smile from Sir Edmund Halley
For 5 parallax measurements, I calculate the AU to be 94.6 ± 2.3 million miles.
Today's value for the AU = 92.956 million miles
Pretty good for someone who just wanted to see the thing!
For me, the real value of this exercise does not lie in the answer. Considering this effort was totally spur-of-the-moment, getting any answer is a real bonus. I couldn't ask for anything more.
To reflect what this meant to me, I can't help but imagine an appreciative smile from Sir Edmund Halley