Edmond Halley, famous for the comet that bears his name, realized
early in the 17th century that transits of Venus can be used for
distance determinations. Transits of Venus are, however, very
rare and Halley died long before he could test the method.
With the aid of this illustration, it is quite
straight-forward to derive and compute the distance. The
illustration shows the Sun, Venus and the Earth (not to scale!).
From two different locations on the Earth, Venus crosses the solar
disk along slightly
different tracks. Let us call the observation sites on the Earth
locations A and B. Seen from the southernmost point
(A), Venus moves along the line a-a'. Seen from the
northernmost point (B), Venus moves along the line b-b'.
The points A' and B' show the position of Venus on the
solar disk at a particular time. The distance between the lines is
e.
The triangles AVB and A'VB' have the same shape. Let
us denote the distance from Venus to the Sun VS and the
distance from the Earth to Venus JV.
This gives
The Earth and Venus need PJ=365.25 and
PV=224.70 days, respectively, to orbit the Sun.
Keplers 3. law transforms
VS/JV to a relation between PJ and PV.
Then we get
Background information for Method 2:
DETERMINATION OF THE DISTANCE TO THE SUN USING
THE TRANSIT OF VENUS
by Knut Jørgen Røed Ødegaard
A transit of Venus gives us a unique opportunity to measure the
distance to the Sun. Knowing that distance, we can easily
find the other distances in the Solar system using the laws of
Kepler.
When observed from two different locations on the
Earth on the 8th of June 2004,
Venus will cross the solar disk along slightly
different tracks .
Illustration: astronomy.no
If we assume that the observations are made from locations separated by 2000 kms, e=2,62 * 2000 km = 5240 km.
If we draw both lines with the same scale on the solar disk, we find that the diameter of the Sun is 270 times e. This gives 1.4 million kilometers for the diameter of the Sun.
We shall check this during the transit of Venus using observations made all over the globe.
DISTANCE TO THE SUN
How can we use this to calculate the distance to the Sun?
The angular diameter of the Sun, seen from Earth, is approximately 32 arc minutes - the same as the angular diameter of the Moon. (Both the distance to the Moon and the Sun varies slightly because the orbits are elliptical. The angular diameters will therefore vary too. The mean values are however 32 arc minutes.) This is a little bit more than half a degree.
Because the angular diameters of the Moon and the Sun happen to be almost equal, total solar eclipses can occur.
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If we know the absolute, or physical, diameter of the
Sun and the angular diameter of the Sun, it is easy to
calculate the distance to the Sun. Illustration: astronomy.no |
The unknown distance is therefore X = 1.4 million km/0.00925 = approximately 150 million kilometers!
This is the distance of the Sun determined with the aid of the transit of Venus. The necessary measurements can ONLY be made during such a transit. In principle, it could also be done during a transit of Mercury, but the planet is so small and far away that it becomes quite hard to perform sufficiently accurate measurements.
The previous transit of Venus occured in 1882 and the next one will be in 2012. Norway and most of Europe will not be in such a favorable position for viewing the transit until 2247, almost 250 years from now. The coming opportunity is therefore quite unique to say the least!
CONTACT INFORMATION - PRESS CONTACT
Created Dec. 31, 03, last updated June 03, 04 by Knut Jørgen Røed Ødegaard
Adress: webmaster@astro.uio.no