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How do astronomers determine the distance of the Moon using geocentric parallax?

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Diagram illustrating how astronomers calculate the distance to a star using parallax: Earth is shown in two positions on opposite sides of its orbit around the Sun, with lines extending to a nearby star X and further to distant background stars. The apparent shift in star X's position, measured as angle A, is used to determine its distance, with the baseline labeled as 186,000,000 miles. — Parallax Calculating stellar distances.

Astronomers determine the distance to the Moon using geocentric parallax by measuring the difference in the object's apparent position as seen from two widely separated points on Earth.12

Geocentric parallax is defined as the difference in direction of a celestial body as observed from the center of the Earth versus a point on its surface. To calculate this, astronomers observe the Moon from two locations—such as Greenwich and the Cape of Good Hope—that are nearly on the same meridian. By measuring the angles from the zenith at these sites and incorporating data regarding the observatories' latitudes and Earth's known size and shape, they form a triangle (OME, where O is the observer, E is Earth's center, and M is the Moon) to solve for the distance.321

The parallax angle varies with the Moon's altitude, reaching its maximum value when the body is on the horizon. In practice, stars near the Moon are also observed to eliminate errors caused by refraction and instrumentation.21