Applications of trigonometry in astronomy

How Is Trigonometry Used in Astronomy? |

Trigonometry is the branch of mathematics that is concerned with the study of angle measurements. Specifically, trigonometry involves the study of the quantities of angles, and how those impact other measurements and quantities involved in the equation at hand. Given two angles of a triangle and knowing what we do about the values of all three angles as a whole -- which is largely a study of geometry -- trigonometry is the science used to determine the measurement and other values associated with that third angle as well as the three sides of the triangle being studied.

Trigonometry has many real-life applications and one of the lesser-known but most important of those is the way in which the study is used by astronauts. In calculating, for example, the distance from Earth to a particular star, astronauts may very well know enough to apply trigonometry to solve an unknown quantity.

The Study of Distances

For example, if the distance between two stars is known, or the distance from one star to the Earth but not the distance to a third, the arrangement can be treated as a triangle, and trigonometry can be used to calculate the missing distance. Astronauts may also use triangular calculations — and, thus, trigonometry — to calculate the speed at which they, or a particular celestial body, are moving.

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For example, if a body appears to be moving at a particular speed in relation to an object whose distance from the body is known, then the distance that the astronaut is from that body can be calculated. The process is relatively simple, and involves simply calculating the unknown distance in relation to the speed at which the astronauts are traveling. This can help determine how far away an object is in relation to any particular speed, and how long it would take to reach it while traveling at that speed.

Should a star appear to be traveling at a fixed rate in relation to the Earth or another known object, astronauts may use surrounding objects whose distance and speed are known to create the equations needed, in trigonometry, to calculate the unknown — here, the orbit speed and trajectory of that unknown body.

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  • If two objects are moving at particular speeds and are known to be a certain distance apart, that third object can be treated as the X factor of the equation and its distance and speed, in the terms by which those others are known, can be calculated with ease. A major aspect of the work done by astronauts involves the use of mechanical inventions and their manipulation in order to perform tasks otherwise not possible in the space environment. The definition of the parallax angle may be determined from the diagram below:.

    How is trigonometry used in astronomy?

    The position of a foreground star is measured when the Earth is at position A. Two images of a nearby star taken with the Earth at positions A and B in the diagram above. If the parallax angle, p , is measured in arcseconds arcsec , then the distance to the star, d in parsecs pc is given by:. It is important to note that in this example we assume that both the Sun and star are not moving with a transverse velocity with respect to each other.

    If they were this would complicate the picture as presented here. Most of the formulas, used in related astronomical computation, are trigonometrical.

    The Study of Speed

    Three great circles on the planet's surface form a spherical triangle. Spherical trigonometry formulas connect the lengths of arcs of this triangle with the angles of the triangle. There is similarity between these formulas and 2-D formulas.

    How is trigonometry used in astronomy? Astronomy Introduction to Astronomy Astronomy Basics. Apr 16, The ships over seas and the planes, at the top altitudes, trace nets of spherical triangles..