When the earth, Venus and the sun fall into a line in this order, Venus appears to move across the surface of the sun from the earth. This is called the Transit of Venus. The Transit of Venus will occur on June 8, for the first time in the last 122 years. This phenomenon can be seen from Japan. Venus will start to cross the sun about 14:10 (JST) (Fig.1). However, we cannot see the entire transit because the sun sets before Venus finishes crossing the sun.

 Fig.1: Predictions for the Transit of Venus

The black dot is Venus and moves from left to right. This figure assumes that the observer is in the middle of earth. The scale along the track gives the Universal Time. Please add 9 hours for JST. (Presented by NASA)


Fig.2: World Visibility of the Transit of Venus (Presented by NASA)
Entire transit is visible in the yellow area. No transit is visible in the dark blue area because this area is at night.



This Transit of Venus occurs for the first time in the last 122 years. In Japan, last transit was observed in 1874, 130 years ago. So, it is a rare phenomenon and people living today watch the Transit of Venus for the first time on June 8. Then, why is this phenomenon so rare?

Venus comes closest to the earth in a period of 584 days. At that time, Venus and earth fall into a line. But the Transit of Venus does not occur in every 584 days. As the orbital plane of Venus is tilted by 3.4 degrees when compared with that of the earth, there are only two points where the orbital plane of Venus and that of the earth meet (Fig.3). At these points, the earth, Venus and the sun come into a line and the Transit of Venus occurs. The interval of the transit is regularly predicted from the past records (105 years, 8 years, 122 years, and 8 years). The next transit will occur in 2012, 8 years later, but the next transit will occur 105 years later. This phenomenon is very rare and valuable. Now, I am going to introduce the Transit of Venus which was seen 130 years ago.

Fig.3: Orbital planes of Venus and the earth. The degree of inclination is exaggerated in this figure.



There are some records about the observation 130 years ago. The transit of Venus occurred on December 8, 1874 (Meiji 7). It had passed 20 years since Treaty of peace and Amity between the United States of America and the Empire of Japan was concluded and Japan opened the country to the world. It was the era when Japan introduced the Western culture, education, and industry to modernize the country to the European standard.

As the conditions for the Transit of Venus was good in Japan (entire transit was visible), many observers came from overseas. Observation party from France came to Nagasaki and Kobe, American party to Nagasaki, and Mexico party to Yokohama. The observation was successful in Kobe and Yokohama because of a fine weather. Memorial monuments are built in each location in commemoration of the observation. Even an observatory used at that time remains. There were Japanese observation parties in Tokyo and Hakodate, but the detailed record is not left. I am going to introduce the web pages about the observation at Nagasaki, Kobe, and Yokohama at that time in [Links] page.

<For details on each result, see the web pages below!>

Yokohama : http://www.natsuzora.com/may/town/momijizaka.html
Kobe : http://www.city.kobe.jp/cityoffice/83/base/mati/mati03.htm
Nagasaki : http://www.Nagasaki-city.ed.jp/starship


Do you know how to measure the distance between the earth and a star? We use the Astronomical Unit (AU). 1 AU equals the distance between the earth and the sun. We can measure the distance among stars and the whole size of the space using the Astronomical Unit. The Astronomical Unit is very important in astronomy.

However, the exact length of 1 AU was not sure in 1874. Edmond Halley, an astronomer who is famous for Halley's comet, hit upon the idea that 1 AU can be exactly calculated if the Transit of Venus was observed from various locations on the earth. According to this idea, advanced countries in the field of science dispatched observation parties all over the world to put their national prestige on calculating 1 AU on that rare occasion of the Transit of Venus. Japan was chosen as one of the observation point.

You can calculate 1 AU in the same manner. Let's see how to calculate.





We use 'Triangulation' to calculate 1 AU. In the explanation, technical terms of trigonometric function (sin, cos, tan) are used. You may not know about it or you may not good at it. Just scan through this section and refer to the other method which I am going to introduce later.

First, calculate the distance between Venus and the sun (VS) and the distance between Venus and the earth (VE) in AU (Fig.4).
When the line EV becomes tangent to the orbit of Venus, Venus appears to be most farthest from the sun when seen from the earth (greatest elongation). At this time, the triangle ESV becomes a right triangle. When the greatest elongation is q degrees, distance between Venus and the sun and the distance between Venus and the earth are:



The distance between the earth and the sun is 1 AU and the actual greatest elongation is 46 degrees. According to above formula, the distance between Venus and the sun is 0.72 AU and the distance between Venus and the earth is 0.28 AU.



<Let's check it!>
Let's draw a right triangle like Fig.4 whose one angle is 46 degrees actually. The ratio of the three size will be like this: the distance between Venus and the sun is 0.72 times the distance between the earth and the sun, and the distance between Venus and the earth is 0.28 times the distance between the earth and the sun.

When the Transit of Venus is observed from two locations on the earth (A and B), the position of Venus on the sun will be A' and B' in Fig.5.



The distance between A and B can be calculated from the latitude and longitude.
As followings are corresponding in the triangle ABV and the triangle A'B'V,
- Distance between AB and distance between A'B'
- Distance between Venus and the earth (0.28 AU) and distance between Venus and the sun (0.72 AU)



following formula is valid. Then, this formula can be changed like this:
?
[km]

Now, you can calculate the distance between A' and B' on the sun.


Next, let's calculate the actual sun diameter (D) in kilometers.
Before calculating this value, prepare images of transit seen from both observation points and measure the sun diameter on the image. Then, wrap over the two images and measure the separation of Venus' position observed at the same (Fig.6).



As the distance between A' and B' and the actual sun diameter (D) (Fig.5) which we are going to calculate, separation of Venus on the image and the sun diameter on the image (Fig 6) are corresponding each other, following formula is valid.



Then, this formula can be changed like this:

[km]

Now, you can calculate the actual sun diameter.

Let's find out the length of 1 AU in kilometers (Fig.7).
Apparent diameter (sun diameter described in terms of degrees) of the sun is approximately 0.516 degrees.
Using the values of the apparent diameter, sun diameter (D), the distance between the earth and the sun (1 AU), the following formula is valid.



Then, this formula can be changed like this:

[km]
So you can calculate that 1 AU is approximately 150,000,000 kilometers!



<Let's challenge!>
Now let's calculate the distance between Venus and the sun, and the distance between Venus and the sun in kilometers.



There are several methods to watch the Transit of Venus. As it is very dangerous to watch the sun directly, we recommend to project the sun on a paper through a telescope. In this method, many people can observe safely at the same time. Let's calculate the length of 1 AU based on above lesson. Does it really become 150,000,000 km?
And pray for a fine weather because Japan is in the rainy season! This is a very rare chance. Why don't you make full use of this opportunity and watch the Transit of Venus?

We are going to webcast the Transit of Venus almost at real time. For details, see [Program] and [Technical Features] pages.

<Reference> NASA, Sun-Earth Day 2004 Venus Transit
http://sunearth.gsfc.nasa.gov/sunearthday/2004/vt_edu2004_venus_912.htm