Transit of Venus and the Earth-Sun distance
Transit of Venus and the Earth-Sun distance
I've heard that the transit of Venus provides one way of determining the Earth-Sun distance. How is this done, and why is the transit of Mercury not used, as I can't quite figure it out. Thanks.
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granthutchison
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It's a parallax thing.
From different positions on the surface of the Earth, you see Venus take a slightly different line across the face of the Sun (if you're far to the north, you see Venus passing across a more southerly part of the Sun's disc).
Kepler's laws, coupled with observation, tell you how fast Venus is moving in its orbit relative to the Earth, and the relative orientation and sizes of the two orbits - all you're missing is a sense of scale.
You can measure the apparent angular diameter of the Sun's disc very precisely (using a big projected image and the known optics of your telescope), and from that information and Kepler, you can predict how long it would take Venus to move through precisely one solar diameter.
Okay. So now you send out observers to a variety of positions on the surface of the Earth, and you get each of them to establish their exact latitude and longitude very precisely. Now you can calculate the distance between your various observers. Then the observers time the transit of Venus as seen from their location. If you know how long it would take Venus to transit the maximum width of the solar disc, and you know how long the transit really took for a given observer, then you can work out, with great accuracy, how far from the centre of the solar disc that transit occurred. You end up with a bunch of observations, taken at known distances from each other, which produce very accurate measurements of Venus's angular position against the solar disc. You have a known angle, and a known distance between observers - you can use trigonometry to calculate the previously unknown distance to Venus, and from there, via Kepler, you get the overall scale of the solar system.
The reason Mercury wasn't used is because it's farther from the Earth and closer to the Sun, so the parallax seen by Earth-bound observers is necessarily less, and therefore it's much harder to achieve the same proportional accuracy. Other ways of estimating the scale of the solar system (like measuring the position of Mars at opposition) had already tied down the measurement more tightly than anything Mercury could provide.
Grant
From different positions on the surface of the Earth, you see Venus take a slightly different line across the face of the Sun (if you're far to the north, you see Venus passing across a more southerly part of the Sun's disc).
Kepler's laws, coupled with observation, tell you how fast Venus is moving in its orbit relative to the Earth, and the relative orientation and sizes of the two orbits - all you're missing is a sense of scale.
You can measure the apparent angular diameter of the Sun's disc very precisely (using a big projected image and the known optics of your telescope), and from that information and Kepler, you can predict how long it would take Venus to move through precisely one solar diameter.
Okay. So now you send out observers to a variety of positions on the surface of the Earth, and you get each of them to establish their exact latitude and longitude very precisely. Now you can calculate the distance between your various observers. Then the observers time the transit of Venus as seen from their location. If you know how long it would take Venus to transit the maximum width of the solar disc, and you know how long the transit really took for a given observer, then you can work out, with great accuracy, how far from the centre of the solar disc that transit occurred. You end up with a bunch of observations, taken at known distances from each other, which produce very accurate measurements of Venus's angular position against the solar disc. You have a known angle, and a known distance between observers - you can use trigonometry to calculate the previously unknown distance to Venus, and from there, via Kepler, you get the overall scale of the solar system.
The reason Mercury wasn't used is because it's farther from the Earth and closer to the Sun, so the parallax seen by Earth-bound observers is necessarily less, and therefore it's much harder to achieve the same proportional accuracy. Other ways of estimating the scale of the solar system (like measuring the position of Mars at opposition) had already tied down the measurement more tightly than anything Mercury could provide.
Grant