Essen, horizontal view

# Transit of Venus, June 8th, 2004

Essen, equatorial view

## Project 6: The Transit of Mercury on May 7th, 2003

On May 7th, roughly between 5.15 UT and 10.40 UT, a Mercury transit will happen, that means Mercury will cross the sun's disc. Because of the geometrical circumstances to be very similar to those of the Venus transit in June 2004 this event offers an excellent occasion to exercise observing, photographing and measuring a transit.

Animation of Merkur's transit (M. Federspiel) Merkury's positions between 5.30 UT and 11.30 UT,
"recorded" every 15 minutes from Essen

The main ideas of this project are the following:

1. We will photograph Mercury in front of the sun in the same manner as we will do with Venus next year.
2. To be able to derive the distance to the sun (see the related paper, up to now only in German) we will try to get exact positions of Mercury relative to the sun's disc simoultaneously taken from as many different places of the world as possible.
3. Instead of taking just one position we will track the whole pass of Mercury across the sun because
• there may occur obstacles (clouds, for instance) to photograph exactly at the same time and
• the parallax effect may be too small to be measured by comparing only two pictures.
In this way we hope to become able to apply statistical methods (Gauss' mean square method) to calculate simultaneous positions.

### Method of photographing and evaluating

1. Take photographs of Sun and Mercury all 15 minutes, if possible exactly at 5.30 UT, 5.45 UT, 6.00 UT and so on until 10.30 UT. To be able to determine Mercury's position the whole sun should be on the picture.

2. On every picture, there must be determined
• the center M of the sun's disc,

• the radius R of the sun's disc (in millimeters or pixels),
• the distance r of Mercury from M (in millimeters or pixels, too),
• the direction to north (The best method for this may be to exposure each picture twice without tracking the telescope; the sun then will move by its own diameter in about 130 seconds. If the camera doesn't offer this possibility it may also be suitable to make everytime two different pictures and to compare the sun's positions on both.)

• and the position angle Θ' measured relative to west.

3. To make comparisons possible between pictures of different scale use the relative distance r'=r/R instead of its absolute value r.

4. Distance r' and position angle Θ' are to be transformed into rectangular coordinates:

x' = r'cosΘ'
y' = r'sinΘ'

5. By using Gauss' mean square method these values can be fitted to a line:

x'(Δt) = x0'(t0) + a(Δt)
y'(Δt) = y0'(t0) + b(Δt)

Here, t0 means 8.00 UT and Δt means the time difference to t0 (Δt<0 means before 8.00 UT).

A typical table of results may look like the following (You can download an appropriate Excel worksheet here!):

Name
geogr. position
Time (UT)    Δt in s     r'=r/R    pos. angle Θ'    x'=x/R    y'=y/R
5.30-9000
5.45-8100
6.00-7200
.............
8.000
.............
10.309000

6. Additionally, we should try to measure the exact time for the first, second, third and forth contact of Mercury:

Perhaps, we will try to derive the distance to the Sun by comparing different transit durations measured at different locations. This method was historically proposed by E. Halley and used for the evaluation of the last Venus transits. (The pictures above and the proposal for the table below, we get from another transit project in Switzerland.

 1st contact UT[hh:mm:ss] perhaps now probably just now probably over shurely over

7. Using these formulas it will be possible to calculate the relative parallax angle f  for different observers to arbitrary times:

8. To get the absolute parallax effect we must know the angular radius ρS of the sun's disc in absolute terms (e.g. in arcminutes):

Δβ = f ρS

We will try to get our own measures for ρS (see project 4).

Horizontal view from Essen Equatorial view from Essen
("Horizontal view" means to keep the lower edge of the picture horizontal, i.e. parallel to the local horizont, while in the "equatorial view" the left and right hand sides of the picture are kept parallel to the celestial north-south-direction.)

Other Mercury Transit Sites:

On each of these sites you will find further useful links.

Mercury really did it! (First impressions and First Evaluations)

## The distance to the Sun determined, for the first time (see the evaluation page) !

By evaluating pictures of the transit of Mercury, we got the following results:

• piS=7.0" (from own pictures and diagrams)
• piS=8.6" (from professional pictures)

Prof. Dr. Udo Backhaus
last modification:  March 28th, 2008