How was the distance to the sun measured in the 1700s?

On Mon, 19 Apr 1999, Stephen wrote:

> In 1675 the Danish astronomer Olaus Roemer determined the speed
> of light by using the moons of Jupiter. His value, "they" tell
> me was slightly innacurate because he used an inaccurate value
> for the diameter of the Earth's orbit. My question: How was
> the diameter of the Earth's orbit determined in that time period?

Thanks for a rather intruiging question that took a little bit of
digging, and I still don't have a definitive answer. It is widely
acknowledged that Roemer was the first person to prove that light had a
finite speed, although Galileo had suggested it in 1638.

There were a few means of measuring the size of Earth's orbit in the
1600s, but I don't know which method was in vogue at the time of Roemer's
work. Aristotle (the ancient greek) had proposed one means - measuring
the angle between the Earth, moon and sun at the time of the
first-quarter moon. Without going into details (it is a geometrical
argument in most undergraduate-level astronomy books), Aristotle
estimated the sun to be about 19 times further away than the moon. (It's
really 400 times further away.) One can also use similar arguments to
get the relative distances via solar or lunar eclipses.

The trick then becomes measuring the distance from the Earth to the
moon. This is possible using parallax effects. Observers on different
sides of the Earth will see the moon in a slightly different location in
the sky, just as two people standing far apart will notice a certain
object (say a tree some distance in front of them) in a slightly
different direction. If the size of the Earth is known (and it was known
fairly accurately), and the parallax angle is measured, it is possible to
calculate the Earth-moon distance. This is not too difficult to measure,
but it is hard to measure accurately.

It is also possible to measure the distance to the sun by measuring the
parallax of an asteroid whose orbit is fairly well-known. It essentially
boils down to knowing the relative sizes of the Earth's orbit, the
asteroid's orbit, and the Earth-asteroid distance.

These days, we measure the distance to the sun by bouncing radar beams
off of other planets (such as Venus), and using geometry to find the
sun's location. (Radar doesn't bounce off the sun very easily!)

Thanks for you question.

Sincerely,
Kurtis Williams

Back to the Ask An Astronomer page.