reckless
03-July-2004, 01:15 PM
Afocal digital images taken through the author's 114mm reflector with Baader filter and 32mm Plossl + 2x Barlow at our (Highlands Astronomical Society (http://www.spacegazer.com/)) observatory at Culloden Moor, Inverness, Scotland on 08 June 2004
Current accepted value of the astronomical unit, IERS (1992), is 149,597,870 km
Eric's value determined from the 08 June 2004 transit is 149,618,134 km
Difference = 20,264 km (equivalent to an error of only 0.014%)
Scroll down to see how I processed the digital images of the Transit, predicted the Contact Point times, and submitted the resultant data to the European Southern Observatory (http://www.vt-2004.org/participate/) in order to work out my value for the astronomical unit, and how this value compares to others participating in the VT-2004 Project.
------------------------------------------------------------------------------------------------
In order to calculate the AU value I needed the exact timings of one or more of the Contact Points 1, 2, 3, or 4.
First contact occurs when the dark edge of Venus’s disk first touches the bright solar background.
Second contact marks the instant when the Sun first surrounds the entire disk of Venus completely.
Third contact occurs when the edge of Venus again touches the Sun’s edge.
Fourth contact is defined as the instant when the disk of Venus can no longer be seen silhouetted against the Sun.
------------------------------------------------------------------------------------------------
I didn’t have a time recorded from the day and I also couldn’t be sure that any of the images I had taken were the exact time of contact.
I did have, however, series of images through both Contact 3 and 4 events.
I tried to plot the distance between the edges of Venus and the Sun at the different stages of Contact 3 but, due to the "black drop" effect, it was very difficult deciding where the edge of Venus, and, especially, the edge of the Sun actually was in order to make the measurements.
Undeterred I have had another go with Contact 3, refining my technique to, hopefully, give a better, more reliable result.
The evening before the transit I set my digital camera’s time using a radio controlled clock and tested it out to ensure that my personal reaction time was taken into account.
The series of images I took were all at the same focal length setting and using the same telescope eyepiece set up. All image processing, cropping, etc. using Adobe Photoshop was carried out so that no dimensional distortion was introduced.
The original series of images are shown below left for Contact 3 and 4 and I then tried to see if I could get better edge definition by tweaking the contrast, brightness and also unsharpening. While I was carrying out the latter I thought I would see what some of the other tools did and I came across a feature under Filter, Stylize called Find Edges. I was very encouraged by the outcome and, after further tweaking contrast and brightness I obtained the result shown in the centre images below.
I then copied the image onto a Microsoft Powerpoint canvas and selected a “doughnut” shape to represent Venus. I decided on the eventual size by trial and error and when it “felt” right to me (not particulary scientific or mathematical but it seems OK). I then made the “doughnut” semi-transparent so I could best fit it over each image in the series. Next I selected an arc-line and best placed it in the middle of the thick line which was the Sun’s edge.
I then chose a fine grid using the Powerpoint Draw options and placed one of the fine solid grid lines on the arc-line at the diametric postion of Venus. I then read off the distance from the arc-line to the edge of Venus and expressed the distance in “arbitrary grid units” (AGU). I reported the time of each imaged event in “seconds after midday BST”. The datum points and results are shown in the right images below. Note that I was working off full screen sized plots so it was fairly easy to determine the distances.
I then processed this data using Microsoft Excel and plotted a linear regression analysis graph which worked out the equation and correlation coefficient for me.
------------------------------------------------------------------------------------------------
Contact 3
The correlation coefficient (R-squared) was 0.96 which indicates a pretty good fit.
The equation was y = -17.58x + 222.27, where x = distance of Venus leading edge to Sun trailing edge in AGU, and y = seconds past midday BST.
By definition, x = 0 when Venus leading edge exactly contacts the Sun edge.
Therefore, y = 222.27 seconds past midday BST at this contact point.
This equates to a Contact 3 time of 12h 03min 42.27sec BST or 11h 03min 42.27sec UT.
Contact 4
The correlation coefficient (R-squared) was 0.97 which indicates a very good fit (similar to Contact 3).
The equation was y = -15.882x + 1375.1, where x = distance of Venus trailing edge to Sun trailing edge in AGU, and y = seconds past midday BST.
By definition, x = 0 when Venus trailing edge exactly contacts the Sun edge.
Therefore, y = 1375.1 seconds past midday BST at this contact point.
This equates to a Contact 4 time of 12h 22min 55.1sec BST or 11h 22min 55.1sec UT.
------------------------------------------------------------------------------------------------
Contact 3 Images and Data
http://members.aol.com/astrophotos/contact3au.jpg
Contact 4 Images and Data
http://members.aol.com/astrophotos/contact4au.jpg
------------------------------------------------------------------------------------------------
The Contact Point time data and observatory location data were submitted to the European Southern Observatory Venus Transit website for processing with the resultant output:
Name: Eric Walker
Observation: Direct filtered visual observation, 114mm reflector
Observatory: Culloden Moor Observatory, Latitude: 57.478°N, Longitude 4.0939°W
http://members.aol.com/astrophotos/DataSendMap.gif
For each of the timed contacts the following were calculated:
- the value of the average distance of the Earth from the Sun (astronomical unit, AU)
- the corresponding value of the angle under which would be seen the Earth radius from the centre of the Sun (Solar parallax Pi)
- their shifts from the exact values Diff.(AU) and Diff.(Pi)
- the percentage error of these values
Instants (UT) AU (km) Pi (") Diff.(AU)(km) Diff.(Pi)(") Error
1 - - - - - -
2 - - - - - -
3 11h 03m 42.27s 149561505 8.7963 36365 0.0021 0.024%
4 11h 22m 55.10s 149674762 8.7896 76892 0.0045 0.051%
Average AU = 149,618,134 km
Average Pi = 8.7930"
Average error = 0.014%
The graph below shows the distribution of the measures of astronomical unit obtained by participants in the VT-2004 Project, namely:
- the number of observers for every slice of the values of the astronomical unit is represented by a vertical bar
- my own measure is represented by a green line
- the currently accepted exact value by a red line
http://members.aol.com/astrophotos/Gauss.gif
"All the best from Scotland"
Current accepted value of the astronomical unit, IERS (1992), is 149,597,870 km
Eric's value determined from the 08 June 2004 transit is 149,618,134 km
Difference = 20,264 km (equivalent to an error of only 0.014%)
Scroll down to see how I processed the digital images of the Transit, predicted the Contact Point times, and submitted the resultant data to the European Southern Observatory (http://www.vt-2004.org/participate/) in order to work out my value for the astronomical unit, and how this value compares to others participating in the VT-2004 Project.
------------------------------------------------------------------------------------------------
In order to calculate the AU value I needed the exact timings of one or more of the Contact Points 1, 2, 3, or 4.
First contact occurs when the dark edge of Venus’s disk first touches the bright solar background.
Second contact marks the instant when the Sun first surrounds the entire disk of Venus completely.
Third contact occurs when the edge of Venus again touches the Sun’s edge.
Fourth contact is defined as the instant when the disk of Venus can no longer be seen silhouetted against the Sun.
------------------------------------------------------------------------------------------------
I didn’t have a time recorded from the day and I also couldn’t be sure that any of the images I had taken were the exact time of contact.
I did have, however, series of images through both Contact 3 and 4 events.
I tried to plot the distance between the edges of Venus and the Sun at the different stages of Contact 3 but, due to the "black drop" effect, it was very difficult deciding where the edge of Venus, and, especially, the edge of the Sun actually was in order to make the measurements.
Undeterred I have had another go with Contact 3, refining my technique to, hopefully, give a better, more reliable result.
The evening before the transit I set my digital camera’s time using a radio controlled clock and tested it out to ensure that my personal reaction time was taken into account.
The series of images I took were all at the same focal length setting and using the same telescope eyepiece set up. All image processing, cropping, etc. using Adobe Photoshop was carried out so that no dimensional distortion was introduced.
The original series of images are shown below left for Contact 3 and 4 and I then tried to see if I could get better edge definition by tweaking the contrast, brightness and also unsharpening. While I was carrying out the latter I thought I would see what some of the other tools did and I came across a feature under Filter, Stylize called Find Edges. I was very encouraged by the outcome and, after further tweaking contrast and brightness I obtained the result shown in the centre images below.
I then copied the image onto a Microsoft Powerpoint canvas and selected a “doughnut” shape to represent Venus. I decided on the eventual size by trial and error and when it “felt” right to me (not particulary scientific or mathematical but it seems OK). I then made the “doughnut” semi-transparent so I could best fit it over each image in the series. Next I selected an arc-line and best placed it in the middle of the thick line which was the Sun’s edge.
I then chose a fine grid using the Powerpoint Draw options and placed one of the fine solid grid lines on the arc-line at the diametric postion of Venus. I then read off the distance from the arc-line to the edge of Venus and expressed the distance in “arbitrary grid units” (AGU). I reported the time of each imaged event in “seconds after midday BST”. The datum points and results are shown in the right images below. Note that I was working off full screen sized plots so it was fairly easy to determine the distances.
I then processed this data using Microsoft Excel and plotted a linear regression analysis graph which worked out the equation and correlation coefficient for me.
------------------------------------------------------------------------------------------------
Contact 3
The correlation coefficient (R-squared) was 0.96 which indicates a pretty good fit.
The equation was y = -17.58x + 222.27, where x = distance of Venus leading edge to Sun trailing edge in AGU, and y = seconds past midday BST.
By definition, x = 0 when Venus leading edge exactly contacts the Sun edge.
Therefore, y = 222.27 seconds past midday BST at this contact point.
This equates to a Contact 3 time of 12h 03min 42.27sec BST or 11h 03min 42.27sec UT.
Contact 4
The correlation coefficient (R-squared) was 0.97 which indicates a very good fit (similar to Contact 3).
The equation was y = -15.882x + 1375.1, where x = distance of Venus trailing edge to Sun trailing edge in AGU, and y = seconds past midday BST.
By definition, x = 0 when Venus trailing edge exactly contacts the Sun edge.
Therefore, y = 1375.1 seconds past midday BST at this contact point.
This equates to a Contact 4 time of 12h 22min 55.1sec BST or 11h 22min 55.1sec UT.
------------------------------------------------------------------------------------------------
Contact 3 Images and Data
http://members.aol.com/astrophotos/contact3au.jpg
Contact 4 Images and Data
http://members.aol.com/astrophotos/contact4au.jpg
------------------------------------------------------------------------------------------------
The Contact Point time data and observatory location data were submitted to the European Southern Observatory Venus Transit website for processing with the resultant output:
Name: Eric Walker
Observation: Direct filtered visual observation, 114mm reflector
Observatory: Culloden Moor Observatory, Latitude: 57.478°N, Longitude 4.0939°W
http://members.aol.com/astrophotos/DataSendMap.gif
For each of the timed contacts the following were calculated:
- the value of the average distance of the Earth from the Sun (astronomical unit, AU)
- the corresponding value of the angle under which would be seen the Earth radius from the centre of the Sun (Solar parallax Pi)
- their shifts from the exact values Diff.(AU) and Diff.(Pi)
- the percentage error of these values
Instants (UT) AU (km) Pi (") Diff.(AU)(km) Diff.(Pi)(") Error
1 - - - - - -
2 - - - - - -
3 11h 03m 42.27s 149561505 8.7963 36365 0.0021 0.024%
4 11h 22m 55.10s 149674762 8.7896 76892 0.0045 0.051%
Average AU = 149,618,134 km
Average Pi = 8.7930"
Average error = 0.014%
The graph below shows the distribution of the measures of astronomical unit obtained by participants in the VT-2004 Project, namely:
- the number of observers for every slice of the values of the astronomical unit is represented by a vertical bar
- my own measure is represented by a green line
- the currently accepted exact value by a red line
http://members.aol.com/astrophotos/Gauss.gif
"All the best from Scotland"