Just had a question .Venus transit observations would be useful for calculating AU Can Any body explain HOW? - Prabodhan
The data you will need for this determination is the perpendicular distance between two observed transit paths of Venus across the face of the Sun as seen from two widely separated locations on Earth - this is where the contact timings will come in. One can relate, using similar triangles - this perpendicular distance of the two observed chords, the distance between the two observation points, Earth Sun distance, and Venus Sun distance.
Venus
Sun distance can also be expressed in terms of Earth Sun
distance
and the maximum elongation of Venus - that is - the angular distance
between Venus and Sun keeps changing going through zero at the
time of transit - so, once before or after the transit, there will
be a time when the angular distance will go through a maximum - at
such times the Sun, Venus Earth angle is 90 degrees - and Sun- Venus
distance can be expressed in terms of SUn-Earth distance and the
maximum elongation.
One
will also need an estimate of the ratio of the perpendicular distance
between the two observed transits and the Solar disk.
Anyway, as I said, I will try
and put this together in an article
format
with figures
- maybe someone else in the group also has
similar
material or links to such material.
How can we calculate the AU from the venus transit? - Rishabh Arora
Rishab,
A complete answer to this question needs diagrams. I will try to
outline the principle involved The fundamental technique of measuring
distance to a distant object is to view it from two different locations and
measure the angle
formed by the two lines of sight. To measure this angle you need a
background even further than the object whose distance you are
measuring. For example
1. Stretch your hand and hold your index finger in line with your
nose.
2. Close one eye and look at the background with the other.
3. Change to the other eye. You will see the background jump!
4. If you know the angle made by the background objects at your
finger and
5. The distance between your eyes
6. You can calculate the distance from your nose to your outstretched
finger!Ofcourse this is trivial bu the technique works in other situations
Now imagine Venus as your finger. Positions A and B on earth as your
two eyes and the background as the solar disc whose angular dimension
is accurately known. By measuring the parallactic displacement of
venus on the solar disc, you can measure the distance from the Earth
to Venus at transit. It is clear, that this distance is the
difference between the radii of the orbits of Earth and Venus i.e.
(Re -R v). The ratio of the radii Rv/Re is easily obtained by
measuring the maximum angular separation between Venus and the Sun.
This second observation can be done frequently and is not as rare as
a transit. Combining the two results, Re which is the distance
between the Earth and the Sun can be calculated in terms of
kilometers.Some of the links in this group have diagrams of the
geometry of Venus transit, which may further help you in understading
the technique. - Nirupama Raghavan
An article describing a
simple understanding of AU determination from transit observations was uploaded
to the files section of the VenusTransit group site
http://groups.yahoo.com/group/VenusTransit/files/The%20geometry%20of%20transits.doc.
This is also available
at http://rathnasree.htmlplanet.com/geometry1.htm