Re: Sun's distance (2)

[Gary Karshner <karshner@STMARYTX.EDU>]

Hugh,
        It wasn't Ceres which I think is in the astroid belt but Eros which has
been in the news of late that was used to determine the AU in the 1940's.
I, an astronomer, am also at something of a loss in how to determine the AU
from transit observations. You know the orbital period of a planet to high
precision. A transit gives you the time it takes to cross the angular disk
of the sun (about 30 minutes of arc) to potentially a high precision
(ignoring diffraction). The ratio of angle seen from the Earth to the
faction of its orbit the planet travels in this time goes as the ratio to
the planets distance from the earth to the planets distance from the sun.
As Robert so kindly reminded me there is way to determine the ratio of
these two numbers. Now I have to find out the answer. Edmund Halley was the
first to discover this method.
        Robert, the method you describe for the ratio of planetary distances was
used by Kepler to determine the relative distances of the planets used in
finding his laws. The only problem with your description is that the value
of G limits the accuracy of the method in absolute terms, you have to some
how eliminate GMs from the calculations!
        My celestial mechanics and historical astronomy books are at home, so tune
in tomorrow.

Gary

> I don't think I can answer this question (in fact I know I can't),
> but I think that the most precise determination of the size of the
> astronomical unit (A.U.) prior to the development of radar involved
> the determination of the distance between the earth and the asteroid
> Ceres in the late 30s when Ceres was particularly close to the earth,
> close enough that its distance could be determined accurately by
> triangulation. Given that distance it is a relatively straightforward
> application of Kepler's third law to determine the A.U., knowing the
> orbital periods of both Ceres and the Earth, and therefore their
> respective distances from the sun in A.U.
>
> Of course the actual calculation took several years (interrupted by
> WWII) in order to make the precision of the result as high as
> possible I don't think the final result was announced until the early
> 50s.
>
> >
>
> Hugh Haskell
> <mailto://hhaskell@mindspring.com>
>
> Let's face it. People use a Mac because they want to, Windows because they
> have to..
> ******************************************************
Gary Karshner

St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU