The formulae are; Dip = 0.97 x Square Root (Ht of Eye in feet) Dip = 1.76 x Square Root (Ht of Eye in meters) Dip is subtracted from the Observed Altitude to give Apparent Altitude. __Refraction__
The deflection of light as it enters/ passes through the atmosphere is known as Refraction. Refraction is stable and therefore predictable above about 15°, below that one needs to consider the characteristics of the atmospheric layers through which the light passes at that time. (Taking the altitude of bodies at less than 15° is usually avoided for this reason.) For altitudes above 15°, a simplified formula is adequate (± 0’.02) Refraction = 0.96/ Tan (Altitude) Refraction tables make assumptions on the layers for low altitudes and should be treated with caution. +/- 2 is not uncommon at an altitude of 2. Refraction is subtracted from the Apparent Altitude to obtain the True Altitude. __Temperature and Pressure Correction for Refraction__
The correction for Refraction assumes a temperature of 10° C and pressure of 1010mb. This may be modified for actual temperature and pressure. A temperature difference of 10° C will alter Refraction by 3% and a 10mb pressure difference will change Refraction by 1%. (0’05 and 0’.02 for an altitude of 30°) The multiplier to correct for Temperature (°C) and Pressure (mb) = Pressure/ 1010 * 283/ (Temperature + 273) __Semi-Diameter__
When measuring the altitudes of the Sun, Moon, Venus and Mars, it is usual to align either the top (Upper Limb) or bottom (Lower Limb) of the body with horizon. This offset must then be removed before comparison with the calculated value. The angular diameter of a body depends on its distance from the Earth. Thus for the Sun the Semi-Diameter varies between 16’.3 in January, when the Sun is closest and 15’.7 in June when it is furthest away. For a lower limb observation, the Semi-Diameter should be added to the True altitude. __Augmentation of the Moon’s Semi-Diameter__
The Earth’s radius is about 1/ 60^{th} of the distance to the Moon. The reduction in distance compared to when on the horizon, has a measurable effect on its size. In contrast the Sun’s distance is 23,000 times the Earth’s radius and the effect is negligible. Augmentation = Sin (Altitude) x Horizontal Parallax Horizontal Parallax is used in the formula as the lunar distance is not provided in a Nautical Almanac. This correction is typically 0’.15 and should be added to the Moon’s Semi-Diameter before applying the Semi-Diameter to the True Altitude. __Parallax in Altitude__
The Parallax correction allows for the difference in the altitude measured on the Earth’s surface versus the altitude that would be measured at the centre of the Earth. The effect of parallax reduces with altitude. It is greatest when the body is at the horizon (Horizontal Parallax) and declines to zero when the body is overhead. The effect is also proportional to the distance of the body. Thus the Horizontal Parallax for the Moon is about 1° but only 0’.15 for the Sun. This correction must be included for the Moon but is usually ignored for the Sun. It can be significant for Venus and Mars, depending on their distance, but is always insignificant for Jupiter and Saturn. (< 0’.05) Sin (Horizontal Parallax) = Earth’s Radius/ Distance of Body After correcting for altitude, the correction is known as Parallax in Altitude. Parallax in Altitude = Horizontal Parallax x Cos (Altitude) Parallax in Altitude should be added to the True Altitude. __Reduction of the Moon’s Horizontal Parallax__
Horizontal Parallax is proportional to the Earth’s radius. Therefore as the Earth’s radius declines with latitude, so does Horizontal Parallax. Correction = Horizontal Parallax * [Sin (Lat) ^ 2] / 298.3 This should be subtracted from Horizontal Parallax before calculating Parallax in Altitude. __Examples of Corrections to a Sextant Observation__
*Add or Subtract* __For a Star__
Sextant Altitude 31° 22’.0 Index Error __ 2’.0__ Depends on the error Observed Altitude 31° 24’.0 Dip __ -3’.0__ Subtract Apparent Altitude 31° 21’.0 Refraction __ - 1’.6__ Subtract True Altitude 31° 19’.4 __90° 00’.0 __ True Zenith Distance __58° 40’.6__ __For the Moon__
Sextant Altitude 31° 22’.0 Index Error __ 2’.0__ Depends on the error Observed Altitude 31° 24’.0 Dip __ -3’.0__ Subtract Apparent Altitude 31° 21’.0 Refraction __ - 1’.6__ Subtract True Altitude 31° 19’.4 Semi-Diameter 16’.5 Add for Lower Limb Parallax (in Altitude) __ 51’.1__ Add True Altitude 32° 26’.8 __90° 00’.0__ True Zenith Distance __57° 33’.2__ __Moon’s Additional Corrections__
Tabulated Horizontal Parallax 59’.9 Latitude Correction __- 0’.1__ e.g. 52° N Horizontal Parallax __ 59’.8__ Tabulated Semi-Diameter 16’.3 Augmentation of Semi-Diameter +__ 0’.15__ Moon’s Semi-Diameter __16’.5__ The Horizontal Parallax must be included but the Latitude correction is often ignored. Similarly the Semi-Diameter must be included but Augmentation is often ignored. |