DC Mathematica 2018

And this is the astronomical unit in kilometres, the distance from Earth to Sun.

Lunar Parallax

Stars are not the only celestial objects whose distance to the Earth can be measured using its parallax. The distance of the Earth to the moon has also been measured using the apparent angular displacement of the moon, known as the lunar parallax, when observed from different locations on Earth. Because the moon is close to the Earth, the lunar parallax is large and minimises observation error. There are different ways to measure the lunar parallax: in comparison to background stars (similar to the determination of stellar parallax), and also during a solar eclipse .

Figure 11

The first method of finding the distance of the Earth to the Moon is similar to the previously discussed method of finding the distance of the Earth to a star. Consider this example: the moon is observed at the same time from Selsey, UK and Athens, Greece. The distant star Regulus chosen to be the point of reference for measuring the lunar parallax.

To find the parallax of the moon, the images are imposed upon each other, with either the moon or Regulus as the point of reference. The line p represents the lunar parallax, and it is measured to be 0.3°, giving ϑ in Fig.11 a value of 0.15°. Multiple measurements are taken over the course of the night as the moon moves across the sky, until the maximum parallax angle is found (this correctly orients the Earth and ensures that triangle U p G is isosceles). UG, can be calculated if the longitude and

latitude of Selsey and Athens are known, using the equation given previously .

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