The entire voyage lasted more than two years and Cook did not lose a man to scurvy, supposedly due to the use of sauerkraut.
Despite the relative failure of the transit measurements, Cook's maps wwere so accurate that they were still in use a century later.
So Angela D, quantum cat. , GrayBold and Nyx are pretty much correct. NASA is not needed.
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Nyx say: NASA isn't need for that measurement, just a bit of basic trigonometry. The first calculation was done by Eratosthenes over 2000 years ago.
Everything else has been refinements of the basic measurement.
http://curious.astro.cornell.edu/about-u...
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Tom S say: For more than four decades now calculation is not needed, the distance can be directly measured, the most accurate way is with laser range-finding techniques.
http://www.lpi.usra.edu/lunar/missions/a...
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Gray Bold say: The easiest way to calculate the distance from the earth to the sun is by using the known distance to one of the other planets. We use radar signals to find the distance to Venus. Signals sent from earth will bounce off the surface of Venus and then travel back to earth where we can detect them. Because radar travels at the speed of light (a quantity that is well known from laboratory experiments) you can easily calculate the distance between Venus and Earth at any time. Now that we know the distance to Venus we can calculate the distance from the Earth to the Sun using trigonometry. Both Venus and Earth travel in almost perfect circles around the earth, so this is a fairly easy calculation.
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Raymond say: NASA?
Why NASA?
The first determination of distance was done in the 19th century (in the 1800s) waaaaay before NASA was created.
It was done the way quantumcalsutrophobe describes.
Nowadays, we (NASA and others) measure directly distances to all inner bodies of the solar system (for example, using radar with pulses sent - and received - through radio-telescopes). Space agencies (including NASA) also do independent measurements to some bodies (for example, Mars, Titan and Mercury) using telemetry from automated probes sent there.