If M and m are the masses of Earth and the Moon, r the mean distance, P the sidereal period of revolution of the Moon about Earth, and G the constant of gravitation, G(M + m) = 4π 2 r 3/P 2 where π = 3.14. In practice, stars near the Moon are observed also to eliminate errors of refraction and instruments.Īnother method rests on a comparison of the force of gravity at Earth’s surface with its value at the Moon. Angles z 1 and z 2 are observed, and other data are obtained from the latitudes of the observatories and the known size and shape of Earth. Lunar parallax is directly determined from observations made at two places, such as G, Greenwich, Eng., and C, the Cape of Good Hope, that are nearly on the same meridian. Hipparchus (150 bce) determined the Moon’s parallax to be 58′ for a distance of approximately 59 times Earth’s equatorial radius, as compared with the modern value of 57′02.6″-that is, a mean value of 60.2 times. The first parallax determination was for the Moon, by far the nearest celestial body. The solar parallax is usually derived from measurements of the positions of other bodies of the solar system. The numerical values generally given are those of the equatorial horizontal parallax. The definitions of lunar and solar parallax must be further refined because of the spheroidal figure of Earth. For all bodies except the Moon, p is so small that it does not differ appreciably from sin p, and it is usually expressed in angular measure. When z = 90°, sin p = a/ r, and this value is called the horizontal parallax or, briefly, the parallax. With an angular distance z from the zenith, Z, it can be found from the triangle OME that sin p = a/ r sin z. If the Moon is directly overhead, the parallax is zero, and parallax is greatest when the body is on the horizon. This varies with the altitude of the Moon. If O is the observer on the surface of Earth, E the centre of Earth, and M the position of the Moon, then the angle OME is the parallax. The parallax of the Sun or Moon is defined as the difference in direction as seen from the observer and from Earth’s centre. The largest measured stellar parallax is 0.75″, for the nearest star, Alpha Centauri the smallest that can be directly measured is about 25 times smaller, but indirect methods discussed below permit calculation of the parallax, inversely proportional to the distance, for more and more distant objects but also with more and more uncertainty. For the Sun and Moon, the base line used is the distance between two widely separated points on Earth for all bodies outside the solar system, the base line is the axis of Earth’s orbit. In the determination of a celestial distance by parallax measurement, the base line is taken as long as possible in order to obtain the greatest precision of measurement. The two positions of the observer and the position of the object form a triangle if the base line between the two observing points is known and the direction of the object as seen from each has been measured, the apex angle (the parallax) and the distance of the object from the observer can be found simply. The measurement of parallax is used directly to find the distance of the body from Earth (geocentric parallax) and from the Sun (heliocentric parallax). Parallax, in astronomy, the difference in direction of a celestial object as seen by an observer from two widely separated points. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.
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