Parallax and the sizes of bodies

Parallax is the difference between the direction of a body seen from the observer’s place and from the Earth’s centre. The diurnal horizontal parallax p is the angle at which the Earth’s equatorial radius R is seen from the body; for small angles the distance is D = R / p (p in radians), or D = 206,265 · R / p″ if p is in arcseconds. For the Moon p ≈ 57′ (3422″), giving D ≈ 384,400 km; the Sun’s parallax is only ≈ 8.8″. In the past the distance to the Moon was found by parallax and the distance to the Sun by observing the transits of Venus in 1761 and 1769 and in 1874 and 1882. Since 1961 distances to Venus, and later to other bodies, have been measured by radar: if a radio signal’s round trip takes t, then D = c·t/2. In 2012 the IAU fixed the astronomical unit at exactly 149,597,870,700 m.