Determining the Scale of the Solar System

[Tog]

Years ago, a friend asked me how we knew how far the Earth was from the Sun. I looked for a really long time, even asking on at least one forum and sending the question to Astronomy magazine. The closest thing I ever got to an answer was "By making detailed Observations of Venus during a Solar Transit."

This was okay for a while, until I realized when the last Solar Transit was. Then I see this in another thread.


The initial measurement had recently been made, though not by Rømer: Hawking is little misleading in that regard. In fact, Richer and Cassini had triangulated the approximate distance to Mars during the opposition of 1671. Rømer announced his results, building on theirs, in 1676.
Cassini's table of Galilean phenomena, used by Rømer, had in fact been drawn up to allow Richer (in Cayenne) to synchronize his pendulum clock with an identical clock used by Cassini (at the Paris Observatory). Of course, the systematic errors Rømer discovered didn't materially affect the original triangulation, because all that was required was that Richer and Cassini had made simultaneous observations. Any errors arising from light travel time across the figure of the Earth were very small compared to their acknowledged errors in synchronization and triangulation.

Grant Hutchison

So, would it be fair to say that the distance to Mars in Miles/Km was determined basically by parallax? Sort of like the way the circumference of the Earth was determined by shadow angle?

[astromark]

A teli drama called 'Longitude' made some years ago if available answers this question very well. By Peter Haws., and the BBC.
I would look around for a mathmatician... those odd people can help you better than I. To find the radius of a circle...

[StupendousMan]

Some years ago, I wrote a document describing the
history of observations of transits of Venus.

http://spiff.rit.edu/classes/phys235/venus_t/venus_t.html

It contains some information on efforts to measure the
distance between the Earth and the Sun. I recommend that
you look especially at the section labelled "Results" at
the end.

The bottom line is that transits of Venus ceased to be
the best method for measuring the distance between the
Earth and Sun by the late 1800s. At that point,
observations of certain asteroids provided better
results.

[antoniseb]

We also know because we've measured the speed of light, and made detailed measurements (and predictions) for the transits and eclipses of Jupiter's Moons. The result shows the diameter of Earth's orbit (OK, the orbit is a low eccentricity ellipse to a very good approximation, but given that the measurement can't be made when Jupiter is behind the Sun, this is close enough).

[Mild mannered]

All this with transits and such is very interesting and a tremendous example of astronomical ingenuity.

What if the solar system contained only us and the sun - how would you know how far away it was then? Is there a way?

[grant hutchison]

So, would it be fair to say that the distance to Mars in Miles/Km was determined basically by parallax?Yep, that's how Cassini and Richer did it. Richer needed to work out his latitude and longitude in Cayenne (to calculate the length of the baseline between Cayenne and the Paris Observatory), and then get his clock into synch with an identical clock in Paris. (This was hampered by the fact that his identical pendulum swung more slowly close to the equator, but that's another story.)
Then they waited for the perihelic opposition of Mars in 1672 (notice I got the date wrong in my earlier post :(), to give themselves a minimal distance to triangulate. Each measured the position of Mars relative to the background stars. The angular difference in position between the two sets of observations gave them their triangulation.
From Kepler, they already had a "scale model" of the solar system, with all the orbital periods squared proportional to radii cubed: so they effectively knew the distance to everything in astronomical units, without knowing how large an astronomical unit was. That single triangulation gave them the scale for their solar system model.

Grant Hutchison

[Tog]

Thanks for the links and the information. Somewhere I had gotten it my head that transits of Venus happened every 1000 years or so, not every 120.

[astromark]

Captain James Cook traveled half way round the world to witness the transit of Venus...we do not need to. If you want to define the method and learn the mathematics. We know how far the Earth is from the sun. NASA has sent the Casinie space craft all the way to Saturn and once there unlocked the Hygens probe which did precisely what it was planed to do. descended through its atmosphere ( Titan ) ,and sent transmissions back through the Casinie craft and to us. All of the fine detail of orbital velocities and distances ... Its historic and correct. I can rest in the knowledge that we know these things well. One hundred and fifty million km.. or for you ninety three million miles... Do you not trust the methods thus far suggested. ?

[Tog]

No. I do trust them. This was just the first time I've actually seem them explained.

I guess an example might have been if I had asked a flower grew and the only answer I could find was "Sunlight and water". It's mostly accurate, but spectacularly useless.

When I first asked, years ago, how we knew the Earth was 93 million miles from the sun, the only answer I could get or find was "Detailed observations of Venus". So I took my calculator and a sheet of paper and started trying to figure it out. I had assumed that it was some sort of Parallax method that plotted the position of Venus at max elongation by taking two measurements the same night. Once when as soon as it was dark enough and a second as Venus set. Then using the distance the observer would have rotated on the surface of the Earth and figuring in the distance covered by the orbits of both planets. There I hit the wall.

If we don't know how far we are from the Sun, then we can't know how far we've traveled in the last 4 hours.

Then I got another clue. Transits. That caused a similar problem. What good were transits if the distance between observation points was not known. Then I seemed to recall reading that a Transit of Venus happens about twice every 1000 years, with the two coming only 8 years apart. That made them amazingly rare. A while later, I saw there would be one in 2004 and 2012, and the little guy that lives in my brain started muttering something. A few years later, he said it out loud.

"How did they observe the transits accurately 600 years before there were telescopes."

This was also the same little guy that pointed out that the Vikings did not use the Moons of Jupiter as a form of clock to navigate the open ocean, for much the same reason. That might have been in that same book now that I think about it.

Anyway. I'm quite satisfied with the explanations given in this thread. Again, I thank you all for explaining it with enough detail to make the answer matter.