How do scientists measure the distance from earth to the sun?

Question

Owen Atkinson · Accepted Answer

Parallax method is used. I prefer the method detailed in my explanation below, for approximating 1 AU in a smaller unit of distance, with utmost precision.

The equinox is the instant of time that the Sun will be directly overhead at noon here, marking the vernal and autumnal equinoxes (about March 21 for vernal equinox and September 23 for autumnal equinox). The line connecting the centers of the Earth (E) and the Sun (S) passes through equinox. Two locations A an B for observing parallax angle #alpha#, as the angle between the directions, are on the equator, equidistant from the equinox, with longitudes differing by #2beta#. The equinox longitude will be the average of these longitudes. Equinox is near Papa New Guinea Island. The spot on the east might be in the sea and has to be over a naval boat. The line of centers ES will bisect both the #angle ACB = alpha# and #angle AEB = 2beta. The triangle ACB and triangle AEB# are isosceles#. The proof for the following formula is elementary. The Earth-Sun distance #ES = R + r (cos beta + sin beta cot (alpha/2))#, where R = radius of the Sun and r = equatorial radius of the Earth. The Earth's equatorial radius, r, is equal to EA EB. Note the addition of R to make SE = SC + EC = precisely the distance between the centers. 1 AU = the average distance of the Earth from the Sun. The mathematical average is semi-minor axis b and the instant at which SE = b is in the proximity of equinox instant. This is the reason for selecting time and locations in the above manner to get a good approximation, using the appropriate formula, in exactitude. ES = sum of the altitudes from S and E on the chord AB of the Earth #EC = r cos beta + (r sin beta ) cot (alpha/2)#.

Luca de · Answer

undefined Triangulation, also known as parallax, is a technique used by scientists to measure the distance between Earth and the Sun. It involves simultaneously observing Venus's and Mars' positions from different points on Earth, and then utilizing trigonometry to calculate the distance based on the differences in angles. Accurate measurements of this distance have also been made using geometric methods and radar ranging.