# Thread: Question on the measurement of the distance of the earth from the Sun

1. ## Question on the measurement of the distance of the earth from the Sun

""In 1672, Giovanni Cassini used a method involving parallax, or angular difference, to find the distance to Mars and at the same time figured out the distance to the sun. He sent a colleague, Jean Richer, to French Guiana while he stayed in Paris. They took measurements of the position of Mars relative to background stars, and triangulated those measurements with the known distance between Paris and French Guiana. Once they had the distance to Mars, they could also calculate the distance to the sun.""

Does anyone know what distance he calculated?

Thanks

2. From the wiki article on the Astronomical Unit:

https://en.wikipedia.org/wiki/Astron...it?wprov=sfti1

Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of “9 1/2” equivalent to an Earth–Sun distance of about 22000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3269 thousand toises.

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3. They deduced that the distance to the sun was 21700 Earth radii. According to Picard's Mésure de la Terre, the radius of the Earth was equivalent to 6375 km. So their estimate of the AU was 138,377,500 km.

Grant Hutchison

4. Thanks and if I might ask a follow on question. In your link there is a gap between Lalande and Newcomb of more than a century. Would that mean Lalande's estimate would have been the one used for the distance in the 1840's? Or are they just leaving out other similar estimates by others in that century plus time period?

5. Originally Posted by Hans
Thanks and if I might ask a follow on question. In your link there is a gap between Lalande and Newcomb of more than a century. Would that mean Lalande's estimate would have been the one used for the distance in the 1840's? Or are they just leaving out other similar estimates by others in that century plus time period?
My google fu came up with this artifact from the Harvard University website about the history of the astronomical unit. The paper says many others (Henderson, Hansen, Foucault, ) refined the measurement during the intervening years between 1771 and 1885. Interestingly it does not mention Lalande.
Mind telling us what you have in mind? Seems like there is a question beneath the question.

6. Ah yes context.

As a hobby I write books set in the late 1830's British Empire. The measurement of the distance from the Earth to the Sun will be a topic of discussion in the officer's mess of the Bombay Artillery on Thursday 17 October, 1839. I need to get an idea what the latest distance would have been and in particular the name and nationality (if French it will cause a tirade from one of the officers who hates the French) of the person(s) who did it. That will lead to a comparison of said distance over the Ghats and Deccan plateau to Poona.

I had been unable to find such information in the books of the period (not astronomy specific) and my google fu is weak when researching a subject I know so little about. I unfortunately do not speak Astronomy.

However

I do know that this site is superb in providing such interesting scientific data! You guys are great!

7. Ah ha, cool. Hopefully this helps you to shape the conversation.

For 1839 it looks like Thomas Henderson's work was the prevailing estimate of 0.96374 AU or 22604 Earth radii.

Based on a quick look at Henderson's works published in the Memoirs of the Royal Astronomical Society (cataloged by Harvard) he was very interested in calculating parallax to various stars and was the first to establish a credible distance to Alpha Centauri.

ETA: And he was a Scot.
Last edited by schlaugh; 2018-May-11 at 02:04 PM.

8. Ah yes a Scotsman, one can do a lot with that! Thanks for the link. I had heard of Henderson as I had previously looked for what was the first star distance that had also been discussed in the book.

9. Originally Posted by Hans
Ah yes a Scotsman, one can do a lot with that! Thanks for the link. I had heard of Henderson as I had previously looked for what was the first star distance that had also been discussed in the book.
He and Struve were fresh on the heels of Bessel's discovery the prior year of the long-sought first parallax (61 Cygni). I would enjoy learning of how the world took their discovery given that the lack of parallax was the main argument against the heliocentric model.

10. Originally Posted by George
He and Struve were fresh on the heels of Bessel's discovery the prior year of the long-sought first parallax (61 Cygni). I would enjoy learning of how the world took their discovery given that the lack of parallax was the main argument against the heliocentric model.
This was one more nail in the geocentric model's coffin. It was like a carpet tack alongside railroad spikes such as Newton's theory of gravity.

11. Originally Posted by Hornblower
This was one more nail in the geocentric model's coffin.
Agreed. The biggest shock was likely how long it took plus how serendipity intervened and gave us stellar aberration along the way. But this is one of those very special coffins, using your apt metaphor, where each nail has a story, much we know about but it's hard for me to get a clear picture of the whole story and how big the "heliocentric mainstream" was and why.

12. Originally Posted by George
Agreed. The biggest shock was likely how long it took plus how serendipity intervened and gave us stellar aberration along the way. But this is one of those very special coffins, using your apt metaphor, where each nail has a story, much we know about but it's hard for me to get a clear picture of the whole story and how big the "heliocentric mainstream" was and why.
I think Newton was the clincher for ruling out a stationary-Earth model as a serious alternative for mainstream scientists, provided they could set aside any lingering philosophical prejudice against an enormously vast distance to the fixed stars. With a purely ballistic model that had a simple formula for gravity and worked well with a heliocentric model in which the planets could be secondary centers for their moons, it was a slam dunk. Any alternative would have needed either a hideously messy ballistic theory or else some sort of mechanical linkage.

13. Originally Posted by Hornblower
This was one more nail in the geocentric model's coffin. It was like a carpet tack alongside railroad spikes such as Newton's theory of gravity.
Aberration of light and the phases of Venus were probably stronger evidence. Newtonian gravity was a mechanism explaining how a heliocentric system could work, and was also able to experience explain satellites, such as the Galilean moons of Jupiter, while the geocentric model really had no mechanism that could explain aberration, Galilean moons, or those new observations with those new-fangled telescopes.

14. Originally Posted by swampyankee
Aberration of light and the phases of Venus were probably stronger evidence. Newtonian gravity was a mechanism explaining how a heliocentric system could work, and was also able to experience explain satellites, such as the Galilean moons of Jupiter, while the geocentric model really had no mechanism that could explain aberration, Galilean moons, or those new observations with those new-fangled telescopes.
Don't forget the Tychonic model, which was quickly adopted when the phases of Venus were demonstrated. It would explain parallax and stellar aberration and, surprisingly, somewhat supported by GR, if you can tolerate a lot of fictitious forces.

The fact that Kepler, Tycho's assistant/partner, favored Copernicus had to have a lot of impact on the scientific community. Kepler knew of magnetism, probably from Gilbert's work, and suggested this was the unifying force, which clearly favored the large Sun over the little Earth as the main influencing and central body.

Perhaps it took Newton to move Tycho's model completely off the table, but I agree with Hornblower that the final nail was achieving stellar parallax because this was so important in the initial rejection to heliocentrism.

15. Originally Posted by George
Agreed. The biggest shock was likely how long it took plus how serendipity intervened and gave us stellar aberration along the way. But this is one of those very special coffins, using your apt metaphor, where each nail has a story, much we know about but it's hard for me to get a clear picture of the whole story and how big the "heliocentric mainstream" was and why.
This is clearly the place for a link to a wonderful series of posts by a historian of science on the twists and turns of the acceptance of heliocentrism, The Great Ptolemaic Smackdown. Optics plays an unexpected role - before diffraction was understood, it was a real problem that other stars appeared much too large to be at all like the Sun at the distances their brightness implied, even in the crudest comparison.

16. Back on the original topic, but as an historic antecedent, I recall that Tycho Brahe attempted to measure the distance to the Sun by looking at the timing between when exactly the half-Moons were, hoping to get a half-million mile base for parallax. If I remember correctly he came up with a value of 24 million miles to the Sun... so he was way off, but this was an attempt to measure it. This is all from something I'd read 20 or 30 years ago, so check the details before quoting me.

17. Originally Posted by ngc3314
This is clearly the place for a link to a wonderful series of posts by a historian of science on the twists and turns of the acceptance of heliocentrism, The Great Ptolemaic Smackdown. Optics plays an unexpected role - before diffraction was understood, it was a real problem that other stars appeared much too large to be at all like the Sun at the distances their brightness implied, even in the crudest comparison.
That looks like a great link! Thanks. [It would seem appropriate that it would be some TOF to give us proper historical context. ]

18. Originally Posted by antoniseb
Back on the original topic, but as an historic antecedent, I recall that Tycho Brahe attempted to measure the distance to the Sun by looking at the timing between when exactly the half-Moons were, hoping to get a half-million mile base for parallax. If I remember correctly he came up with a value of 24 million miles to the Sun... so he was way off, but this was an attempt to measure it. This is all from something I'd read 20 or 30 years ago, so check the details before quoting me.
My attempt to find this came-up short but I did find an interesting paper by Gingerich and Voelkel stating that "Tycho accepted the ancient Greek value of 3' for the solar parallax (which seems to have been the only significant parameter Tycho did not re-establish)." Using a modern Earth radius value, this yields a 7.25 Mkm distance to the Sun but 8 Mkm seems to have been the accepted value (Tycho, Cop., and others), though I don't know why given the Eratosthenes value with 3' would be close to 7Mkm.

[Further, diurnal parallax was, apparently, a very big deal in justifying is Hven observatory. Tycho had already shown with diurnal parallax that an earlier comet and a new star were beyond the Moon, which suggested the Aristotle/Ptolemy/Thomist model had a flaw in the claim of an unchanging ether. He knew that a Mars diurnal parallax should be within his reach since Mars, with his model and Copernicus' but not Ptolemy's, had Mars closer than the Sun.]
Last edited by George; 2018-May-14 at 04:15 PM.

19. Thanks for all the responses. All grist for the mill!

20. Originally Posted by ngc3314
This is clearly the place for a link to a wonderful series of posts by a historian of science on the twists and turns of the acceptance of heliocentrism, The Great Ptolemaic Smackdown. Optics plays an unexpected role - before diffraction was understood, it was a real problem that other stars appeared much too large to be at all like the Sun at the distances their brightness implied, even in the crudest comparison.
Upon reading that Smackdown piece, I will revise my coffin nail metaphor a bit. Now instead of seeing Newton's theory as a railroad spike and Bessel's parallax observation as a carpet tack, I will make both of them 10-penny nails. I had forgotten that Newton himself was not fully satisfied with his theory as an exercise in physics, as he could not make sense out of force or action at a distance.

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