Re: Sun's distance (2)

[Leigh Palmer <palmer@SFU.CA>]

> How was the earth's distance from the sun determined using the
> transit of Mercury?

At 7:25 PM -0800 2/22/00, I wrote:

> I think you need observers on two different chords
> (at different latitudes). I'm no expert, however.
> I can do the calculation given those data.

I've now carried out the calculation for circular orbits. The correct
calculation is messier but conceptually no different. The important
facts are that the ratios of the radii of the Earth and Mercury orbits
and the radius of the Sun had been measured very accurately using the
Keplerian model. The reason only the ratios were known is that all
measurements were made by comparing them to a fraction of the Earth's
orbit, and the absolute distance of that fraction could not be
measured. The trick of using two observers at two different latitudes
(heliocentric latitudes, actually) allows a baseline entirely on Earth
to be used for determination of parallax. Angles can be measured very
accurately using the timing of similar contacts (e.g. second and third
contacts) of the transit event. The more eccentric the transit the
better, and central transits yield very poor results if any at all.

Doing the calculation is quite educational. I recommend it. I still
don't know how this can be done with a single transit observation to
high accuracy. One still needs a measureable baseline. I will check
Albert Van Helden's book tonight to see if he explains it.

Leigh