Observing the Transit of VenusJune 5, 2012


Point Venus on the Island of Tahiti. So
named because of Captain Cook's observations here in
1769. I visited this spot in 2003 
A Transit of Venus is when the planet passes in front of the sun so we see a dark spot move across its face from earth. Being rare, occuring only twice in a 105 year time span, the next opportunity will be in 2117. I decided to put some effort into observing it with homemade tools as it will be the last opportunity for 99.9% of us. I also wanted to observe sunspots from time to time. Portability was important and a requirement.
Observing the sun has several problems you must deal with:I decided "telescope projection" offered the best approach with my low budget and yet gain high quality images. Since I already own a CELESTRON spotting scope for birding and firearms sighting, building an addon projection screen was straightforward. The scope was set up with a 10 mm eyepiece and the objective had a diameter of 80 mm with a focal length of 420 cm giving f5.2. This gives a magnification with these optics of 42X but the screen can be moved to adjust that value. The normal wedge prism was removed since I didn't need correction it offers for terrestrial viewing but a focusing extension tube was added in its place to provide enough extension for focusing to infinity. The suns image was projected to 4.5 inches in diameter in the final setup.
In the future, I'll make a simple cardboard lightshield or collar that will slip over the outside of the objective end so the suns shadow is blocked from the projected image area. This makes the image easier to see and helps in alignment.
The photo at left shows the setup in the working position. It actually works better than expected. The image was sharp with a number of sunspots visible as well as the shadow of venus.
A "transit of Venus" has been historically the most accurate way to measure the distance from Earth to the Sun. Through the use of Johanne Kepler's equations the "relative" distances between the planets and the sun are easy to determine via his third law. That gives, "relative distances" only but we also need a method of measuring absolute distances. No good method was known to measure earth to sun distance. This is called an AU (Astronomical Unit) and is used as a solar yardstick for measuring other distances in the solar system. A transit allows this to be calculated. Once AU is known, Kepler's law can be applied to determine the rest of the planets and other objects.
In the 1760's Captain Cook was dispatched to the South Seas to observe the 1769 Transit of Venus. Although successful, additional measurement problems contributed toward inaccuracy. Comparing to todays radar measurements the error was only 0.8%. Remarkable for 1769 technology. The captain (his first command) went on to make many new discoveries in the South Seas and launched his career as an great explorer.
The transit approach measures the parallax from two different points on earth. Knowing that along with Kepler's third law:
The third law, published by Kepler in 1619 captures the relationship between the distance of planets from the Sun, and their orbital periods. For example, suppose planet A is 4 times as far from the Sun as planet B. Then planet A must traverse 4 times the distance of Planet B each orbit, and moreover it turns out that planet A travels at half the speed of planet B, in order to maintain equilibrium with the reduced gravitational centripetal force due to being 4 times further from the Sun. In total it takes 4×2=8 times as long for planet A to travel an orbit, in agreement with the law (8^{2}=4^{3}).
By observing venus and the earths orbit and using his third law we determine that the ratio of r_{earth}/r_{venus} = 1.0 /0.723 = 1.384 where 'r' represents the radius of each.
Note: These numbers and approach are greatly simplified because all orbits have an eccentricity of greater than zero which means they are more complex than simple circles. Also, the objects have spin and movement in their orbit during the transit. The radius value changes with time because its really an ellipse. The approach still works fine as long as these factors are taken into consideration if higher accuracy is needed.
Their are several ways to proceed once you have a transit. To measure distances you need a baseline that is known. On earth we can use two different points of observation as long as we can determine the chord distance between them.
This displacement projected on the suns surface will be as follows:
lets assume that D_{separation} = 10,000 km from two viewing points on earth, now on the sun this will be reflected as:
SUN_{separation} = 10,000 x 0.723/(10.723) = 26,101 km with the help of orbit ratios from solving Keppler's third law
or to put it in words, the 10,000 km observer separation on earth shows as a 26,101 km separation on the suns surface. Guess what, we can now measure the diameter of the visible part of the sun by ratioing off our 26,101 km measurement. As it turns out the sun's diameter is approximately 1,392,684 km or with this method, a required image measurement accuracy of 1 part in 53. Not bad as this is easy with good tools. But does it stop here?
No, the best part is still ahead; The Parallax angle between each view of Venus shadow plus knowing the separtion distance on earth allows the solution of the resulting triangle. You measure the angles by recording the path venus takes from each location and then measure the separation. The long legs of this resulting equilateral triangle gives the distance 'd' to the sun.
The easiest way from here is to use the trigonometric law of cosines. The measured diameter of the sun from above equals 1,392,684 km and the angle it presents to a viewer on the earth averages about 0.53^{°}. This can be measured with a sextant or any angle measuring setup with proper filters, telescopes included.
From the law of cosines:
d =
a/sqrt(2(1cos A))
(1)
where a = diameter of sun, km
A = angle of suns disk from
earth, degrees
d = distance from earth to
sun, km
Solving
d = (1.39 x 10^{6})/SQRT(2(1
cos 0.53)) = 1.39 x 10^{6} /SQRT(2 x 4.28 x 10^{5})
= 150,237,000 km (2)
Wow, with simple tools, coordination and basic high school math you can come up with one of the most important measurements in astronomy. Its referred to as an Astronomical Unit (AU) and is the yard stick used to measure distances within the solar system representing 8 minutes, 19 seconds at light speed. Beyond the solar system another unit called the PARSEC = 206.26 x 10^{3} AU or 3.26 light years is used. The AU has a key roll as the reference for the PARSEC.
One of my early images after Venus started crossing the suns surface, location: N48° 08.187', W123° 31.665'. At least 5 sunspots were visible.
Many professional astronomers paid particular attention to this event because its one way that exoplanets can be discovered circling distant stars. By detecting the slight dimming of the starlight, it can be deduced that the shadow of something passed in front. So far many exoplanets have been discovered but most are Jupiter size, not small like earth or venus.