SKY_September2014.pdf

SkyandTelescope.com September 2014 33

on the individual parallaxes of Venus and the Sun. Any

errors in the fi nal results will be proportional to the error

in the original total parallax measurement.

We began our distance calculations by applying the

arctangent of half the parallax angle of 22.83 arcseconds

to half of the foreshortened baseline to estimate rough

distances to Venus and the Sun. Multiple iterations of

the above process converged on individual parallaxes for

Venus and the Sun of 17.72 and 5.11 arcseconds, respec-

tively (the expected values were 17.00 and 4.99 arcsec-

onds). Our fi nal trigonometric calculation using half of

Venus’s individual parallax of 17.72 arcseconds yielded

a distance to Venus of 25.8 million miles. The actual

distance between the centers of Earth and Venus was

26,836,434 miles, for an error of –3.9%. Our calculated

a.u. using Kepler’s third law was 89.3 million miles, natu-

rally also an error of –3.9%.

How Could We Have Done Better?

For this 21st century transit, modern technology enabled

us to virtually eliminate errors in determining the lati-

tudes, longitudes, and times of our observations. So, what

else could we have done better to improve our results? If

Richard had better weather, he could have taken images

with his telescope instead of his telephoto lens, provid-

ing higher resolution. Better weather in West Richland

also would have permitted Richard to take more images,

which might have averaged out more errors.

If Rod had traveled to Tahiti or Australia, we would

have measured a larger parallax. Rod also could have

measured Venus’s diameter correctly at 57.78 instead of 58

arcseconds. Rod could only register images and measure

the parallax to the nearest whole pixel. One pixel made

a diff erence of 1.05 arcseconds, changing the distance

to Venus by more than a million miles and the a.u. by

several million miles. This underscores the technique’s

extreme inherent sensitivity of the results to even tiny

observational errors.

We actually came within a fraction of an arcsecond

(less than one pixel) of the expected parallax result, yet we

ended up with a –3.9% error. This diffi culty is borne out

in a review of results from other successful amateur proj-

ects posted on the internet. They indicate results ranging

from an error very close to ours extending up to 5%.

Our experiences and problems were remarkably simi-

lar to those of astronomers in prior centuries. They had to

compare observations made with instruments of diff er-

ent focal lengths. Many also encountered clouds, which

permitted them to make only a few observations, or none

at all. Circumstances often prevented them from traveling

as far as they would have liked. The graininess of their

photographic plates limited their accuracy in measuring

Venus’s parallax.

The similarities between their problems and ours

made our experiences all the richer. We personally relived

that history, giving us a feeling of connection to observers

of prior centuries. Accordingly, we don’t view our –3.9%

error as a failure, but as yet another similarity. Expedi-

tions of previous centuries never determined the correct

a.u. value either, and we got about as close as many of

them did. Actually measuring the distance to Venus and

the a.u. with our own observations was an extremely

rewarding experience that we will remember for the rest

of our lives. ✦

Avid astrophotographer Rod Pommier is a surgical oncolo-

gist and Professor of Surgery at Oregon Health & Science

University in Portland. Richard Smith is a retired clinical

laboratory technician who has enjoyed amateur astronomy

from his college days.

Using MaxIm DL, the authors

placed the white bar across the

Venus crescents at their widest

points, producing two peaks in

the graph’s red channel. They

projected lines along the sides of

each peak down to the x-axis to

read their width in pixels. The left

and right crescents had parallaxes

of 19 and 22 pixels, respectively.

They converted the average paral-

lax in pixels from all the images

to a parallax angle in arcseconds.

Using the math described in the

text, Venus’s calculated parallax

yielded a distance to the planet

of 25.8 million miles, 3.9% less

than the correct distance of 26.8

million miles. This yielded an a.u.

of 89.3 million miles.

Transit_Experiment.indd 33 6/23/14 12:17 PM