How is the distance between stars and the earth calculated?

Question

Asher Cohen · Accepted Answer

Using stellar parallax.

The apparent angular displacement of a star as seen from two sufficiently apart known locations is known as stellar parallax. The same observatory with a time interval of (sufficiently large integer) N days is a convenient option. If N is the exact number of 24-hour days and #alpha# is the parallax angle, the distance of the star is #sin(Ntheta/2)/sin(alpha/2)# AU, where #theta=360/356.256363# deg = 0.985609113 deg. For conversion to light years (ly), use 1 AU = #1/62900#ly, nearly. The arc of the Earth's orbit for N days subtends N#theta# deg at the Sun. Sample Data: N = 7, #alpha# = 0.003" = 8.333 E-07 deg. The approximation to the distance of the star = #sin(7X0.9856)/sin(8.333 E-07)#AU 8.259 E+06 AU = 131.3 light-years. (It is believed that the radio telescope's parallax precision is as good as 0.001").

Elena Antonova · Answer

undefined Three main techniques are used to calculate the distance between stars and Earth: parallax, spectroscopic parallax, and standard candles, which are objects with known intrinsic brightness that astronomers can calculate their distance from based on their apparent brightness. Parallax measures the apparent shift in a star's position as Earth orbits the Sun. Spectroscopic parallax uses the star's spectrum to determine its luminosity and distance.