Edmund halley and the venus transit

[adjkgh]

i am sooooo lost in what edmund halley did.

so far i understand that he used parallax and the venus transit to solve for the distance between Earth and sun but how did he exactly do it?

http://www.exploratorium.edu/venus/P_question4.html

the link above explains a lot but it doesn't provide the angle E and the distance between observer A and observer B so i can't exactly find the value of AU.

could someone please explain to me what values did he use for E and the distance between observer A and observer B? and how he got those values.
thanks

 

[HallsofIvy]

Each of the observers would measure the angle the eye-line to Venus makes with the horizon. The difference between the two would be E. Of course, that is also the angle the two lines make when they "cross" at Venus.

Now look at the triangle made by those two lines from observers on Earth and where they cross at Venus. You can measure the distance between the two observers- one leg of the triangle. The distance is called "d" in the picture. To within "experimental error" the distance from each observer to venus is the same: that is an isosceles triangle and dropping a perpendicular to the base forms two identical right triangles.
Now we have a right triangle with one angle V/2 and side opposite that angle d/2. You can calculate the length of the hypotenuse (distance from Earth to Venus) by sin(V/2)= (d/2)/hypotenuse.
Since we know by Kepler's third law ("The cube of a planet’s distance from the Sun is proportional to the square of its orbital period"- since we can measure the orbital period of a planet we can find the ratio of the distance from the sun to that of the Earth. ) that the distance from Venus to the Sun is about 0.72 times the distance from the Earth to the sun, We can use the distance from the Earth to Venus to calculate the distance from the sun to the Earth. Once we know that, we know the proportionality in Kepler's third law and can calculate the distance from the sun to any planet, knowing its period.

 

[adjkgh]

yes i know that much already but i need specific numbers that halley specifically used. i just don't understand HOW and WHAT value he could get the angle E and what specific length did he use for the distance between observer A to obsever B??

thanks for the effort anyway.

 

[plusaf]

do the values matter?

yes i know that much already but i need specific numbers that halley specifically used. i just don't understand HOW and WHAT value he could get the angle E and what specific length did he use for the distance between observer A to obsever B??
thanks for the effort anyway.

i'm a little puzzled. are you saying that if you don't know how far apart the observers on Earth were AND all of their readings of angles, distance, etc., you can't understand the solution?

it doesn't matter. it's the geometry, plus Kepler's law, that provides the answers: if the observers are separated by some distance and they measure two different angles, the distance and the angles themselves provide the answers, whatever they are. you could work it backwards, by assuming the observers were, fore example, 1000 km apart, and deduce what the angles must have been to give the correct distances, or how far apart they must have been to observe an angular difference, E, of some number of degrees [or minutes or seconds, or whatever...]

please tell us more about what part you don't get...

 

[adjkgh]

i'm sorry if I'm too vague haha

i'm doing a physics report on deriving the distance between Earth and the sun by using edmund halley's method. he used the transit of venus. the link that i provided above on my first post explained a lot and i get it. it's just that they didn't give me any numbers. it just says 93 million miles on the bottom but they didn't even tell me what the distance between venus and Earth is. i also understand that you can plug in any distance of obsever A to B but i need to know what HALLEY had put in. did he travel from the north pole to the south pole and measured the distance he traveled and used that in his equations? or did he actually plugged 1000 km and tested out that theory? i need to know what was the distance he plugged in and that angle E. if i knew what angle E was, i could find V and the tan (V/2) and etc.
I've been reasearching for almost 4 days now and my project is due in 3 days and i still can't find his entire mathematical derivations.

so please help? =)

 

[Ouabache]

Halley published his method for measuring parallax using the transit of inferior planets, in Philosphical Transactions Vol. XXIX in 1716. A translation (from Latin) is reprinted http://sunearth.gsfc.nasa.gov/eclipse/transit/HalleyParallax.html . (cool! )
Evidently the scientists who actually took the measurements, had to make some interpretive adjustments. Perhaps you can find their publications too..

 

[HallsofIvy]

yes i know that much already but i need specific numbers that halley specifically used. i just don't understand HOW and WHAT value he could get the angle E and what specific length did he use for the distance between observer A to obsever B??
thanks for the effort anyway.

I'm puzzled then- the website you gave noted that Halley DIDN'T actually do this calculation- he died before the conditions were right. Therefore, he didn't HAVE any specific numbers!

 

[HallsofIvy]

According to this site, http://www.americanscientist.org/template/AssetDetail/assetid/28549/page/1

There were French expeditions in 1761 to observe the transit of Venus to India and Siberia so the distance between "observer A" and "observer B" would be the distance between those. Even better, there were American expeditions to Cape Town, South Africa and Newfoundland, Canada to make the same observations. I say 'even better' because they are farther apart and a little more precise as to exactly where the observations were made. As to what angles they measured, I doubt you will find that in anything other than the formal reports of the expeditions- which probably aren't on the internet!

 

[adjkgh]

wow, I'm really bummed out.

thanks for the links though

 

[Ouabache]

From the same paper I referenced above, there were several shortcomings discussed (see below). Hopefully the scientists who recorded the actual measurements did not rely too heavily on Halley's paper. Their results could very well have been published in one of the http://www.pubs.royalsoc.ac.uk/index.shtml. Following the Royal Society link may assist in your search for such references. If the indices are not easily accessible from your library, perhaps our friends in UK can help..

"The transit of Venus in 1761 proved much less favourable to the proposed purpose than Dr. Halley expected. The motion of Venus's node not being well known, she passed much nearer the sun's centre than he supposed she would; which made the places he pointed out for observing the total duration not proper for the purpose; indeed the entrance of Venus on the sun could not be seen at Hudson's Bay. He made a mistake too in the calculation, in taking the sum instead of the difference, of the angle of the ecliptic with the parallel to the equator, and the angle of Venus's path."

 

[Ouabache]

here is one,
Green & Cook[/url], Charles Green was former assistant to the Royal Obervatory at Greenwich England. Just look up "Philosophical Transactions of the Royal Society, Vol. 61, p. 410, 1771." in the library..