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How can we find Dec and R.A of a star by having Dec and R.A of another star.

For example in the following picture , we have that for Errai (Dec: 77 , R.A 23H 40M). How can we find Dec and R.A of Gamma Delphinus. Note that we can't use Polaris for example because of cloud or something else. I want answer for when we have telescope and when we don't have telescope.

Picture from Starry Night

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You can measure the position in the sky of any star; this is its altitude and azimuth. The star's position in the sky depends on its actual position in space, your position on Earth and the rotation of the Earth.

Measuring the position requires some kind of angle-measurer. Such as a quadrant or sextant. You also need knowledge of which direction is North. This can be determined, even if the pole star is not visible, from the location of other stars. A telescope can increase accuracy but the same measurements can be done either with or without a telescope.

You can use your position, and the position of Gamma Cephei in the sky (by altitude and azimuth) to determine the local sidereal time. You can then use the position of Gam Del and the sidereal time to determine the ra and dec of Gam Del.

Other questions discuss the conversion between alt-az to ra-dec Software to convert RA and DEC into ALT and AZ

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