How can people measure the exact distance from Earth to the Sun? Or stars, etc?

Question

How could they measure this?

Answer 1

The way the distance from the Earth to the Sun was done centuries ago, was to observe the transit of Venus across the face of the sun. Observers on different parts of the Earth would witness and time the event -- when Venus first crossed onto the 'surface' of the Sun, and when it left the other side. By knowing the distance between the different observations on the Earth and the time which they took place (they were not simultaneous); and by knowing the *relative* distance from Venus to the Sun with the Earth to the Sun, some trigonometric calculations could be performed that gave a pretty accurate distance from Earth to the Sun.

For nearby stars, the distance can be done by parallax. Positions are recorded on photographic film or digital image and 6 months later when the Earth is as far away as it can get in its orbit from the previous picture (2 astronomical units), they take another one and compare the apparent 'motion' of nearby stars compared with stars very far away. By law of sines they can determine the distance to the nearby stars ('nearby', meaning less than a few hundred LY away).

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Answer 2

Two measurements are taken six months apart. This will give the base angles of a triangle, then, knowing the base distance, or the distance between the earth's positions 6 months apart, or about 186,000,000 miles, and using trigonometry, the height of the triangle and, therefore, the distance to the planet, star or galaxy can be determined.

Answer 3

Well, nobody claims to have measured the _exact_ distance, but these distances are known with a greater or lesser degree of accuracy. There are many different ways in which astronomers measure these distances, enough to fill a book or a university course. Mostly they involve geometry and trigonometry, but astronomers also use radar, lasers, and stellar spectra.