SKY_September2014.pdf

32 September 2014 sky & telescope

Astronomical Experiment

Using MaxIm DL’s Graph Function, the average

diameter of Venus’s disk in Rod’s images was 55.33 pixels.

Because Rod measured Venus’s diameter as 58 arcsec-

onds, the image scale was 1.05 arcseconds/pixel. We also

used the Graph Function to measure the width of the

bright parallax crescents in each fl attened “Diff erence”

image. The dual crescents permitted two measurements

of the parallax per image, which would help average out

motion and seeing artifacts. The crescents produced tall

The authors aligned and superimposed their photos on the previ-

ous two pages to create this image. By stacking and processing

the images in Photoshop, all similar portions of the image were

blacked out. Venus’s parallax appears as two bright crescents

pointing in opposite directions, indicating only the portions of

Venus’s disk that did not coincide in the two pictures.

Pommier used MaxIm DL to calculate the diameter of Venus’s disk in pixels. The graph on the left shows the pixel brightness along

the white bar over Venus. One end is on the edge of Venus’s disk and the brightness value in the red channel at that point was read on

the y-axis. Pommier measured Venus’s diameter by determining at which pixel on the x-axis the brightness returned to the same value.

Because he measured Venus’s disk to be 58 arcseconds across, he could determine that the average image scale in his photographs

was 1.05 arcseconds per pixel.

twin peaks in the red channel on the graphs. We drew

lines along each side of the peaks and projected down to

the x-axis to read the width of each peak in pixels. The

average of the 14 readings was 21.78 pixels. Multiplying

that by the image scale yielded an average parallax of

22.83 arcseconds.

But this measured result is not just the parallax of

Venus; it’s the combined parallaxes of Venus and the Sun.

Even the Sun has a parallax for observers separated by

2,213 miles. Thus, when Rod aligned the Sun in Richard’s

images to the Sun in his pictures, he added the Sun’s

parallax to Venus’s parallax. We would have to know the

distance to the Sun, the very value we seek, to calculate

its expected parallax and subtract it from the total mea-

sured parallax to get Venus’s individual parallax, which is

what we needed to calculate the distance to the Sun. This

paradoxical problem seemed circular and insoluble. Fortu-

nately, an elegant mathematical solution exists that doesn’t

require any a priori knowledge of the Sun’s distance.

The total measured parallax can be used to calculate

an approximate distance to Venus. That permits calculat-

ing an approximate distance to the Sun using Kepler’s

third law. That can then be used to calculate a rough

estimate of the Sun’s parallax. That estimate can be sub-

tracted from the original total parallax, yielding a better

estimate of Venus’s parallax. The revised Venus parallax

can be used to repeat the calculation, yielding a better

result. Multiple iterations of this process will converge

ROD POMMIER / RICHARD SMITH

Transit_Experiment.indd 32 6/23/14 12:17 PM