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Earth and Space Sciences · 术语表

什么是 Triangulation？

Definition 1.6 High School Earth and Space Sciences · 第 1 章 — Measuring the Earth

Triangulation locates distant points by a chain of triangles: one side, the baseline, is measured on the ground with great care; all the angles of the triangles are measured from their corners; every other side is then computed.

Left: a chain of triangles stretched along a meridian from a measured baseline AB; the arcs mark two of the many angles measured with the instrument. Right: the height h from C, written in two ways, gives the sine rule. — Left: a chain of triangles stretched along a meridian from a measured baseline $AB$ ; the arcs mark two of the many angles measured with the instrument. Right: the height $h$ from $C$ , written in two ways, gives the sine rule.

示例

Example 1.9 (One triangle)

A baseline $AB = 8.000\,\mathrm{km}$ is measured; from $A$ the signal $C$ is seen at $70{}^{\circ}$ from the direction of $B$ , from $B$ at $60{}^{\circ}$ from the direction of $A$ . Then $C = 50{}^{\circ}$ and

AC = \frac{8.000 \times \sin 60^\circ}{\sin 50^\circ} = \frac{8.000 \times 0.8660}{0.7660} \approx 9.044\,\mathrm{km}, \qquad BC = \frac{8.000 \times \sin 70^\circ}{\sin 50^\circ} \approx 9.814\,\mathrm{km}.

No distance but the baseline was walked.

Example 1.10 (The meridian of the metre)

In March 1791 the metre was defined as one ten-millionth of the distance from the pole to the equator along a meridian. To find that distance, two astronomers, Jean-Baptiste Delambre and Pierre Méchain, measured by triangulation the meridian arc from Dunkirk, on the North Sea, to Barcelona, on the Mediterranean — almost seven years of work, Delambre in the northern two thirds, Méchain in the southern third. The two towns differ by $9.646{}^{\circ}$ of latitude; on the modern ellipsoid the arc between their parallels is $1072.2\,\mathrm{km}$ long. Knowing the length of an arc and its difference in latitude gives the length of a degree; the shape of the Earth then gives the whole quarter meridian. Platinum standards of the new metre were made in 1799 and kept in the national Archives.

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