Atmospheric Refraction

Why the sky is lifted

Light from a star enters the Earth's atmosphere at an angle and passes through layers of air that become denser towards the ground. Each layer slows the light a little more and bends its path downwards. We see the star along the direction the light arrives from, which is higher than its true geometric direction. Astronomical refraction therefore always raises objects towards the zenith. It changes their altitude, but not their azimuth.

The effect is zero at the zenith, under 1′ above 45°, and grows quickly near the horizon, where it reaches about 34′. That is slightly more than the apparent diameter of the Sun or the Moon. When the lower edge of the setting Sun seems to touch the horizon, the geometric Sun is already completely below it.

Computing refraction

Two simple formulas quoted by Meeus are accurate to a fraction of an arcminute for normal conditions. G. G. Bennett's formula (1982) gives the refraction R from the apparent altitude hâ‚€, the altitude you actually measure. Saemundsson's formula (1986) goes the other way, from the true altitude h computed by an ephemeris to the correction to add:

R = 1 / tan(h₀ + 7.31 / (h₀ + 4.4))          (from apparent altitude)R = 1.02 / tan(h + 10.3 / (h + 5.11))        (from true altitude)h₀ and h in degrees, R in minutes of arctrue altitude = apparent altitude − R

Both assume a pressure of 1010 hPa and a temperature of 10 °C. For other conditions, multiply R by (P / 1010) × (283 / (273 + T)), with P in hectopascals and T in °C. Cold, dense winter air refracts noticeably more than hot summer air.

Refraction at different altitudes

Below about 5° the real refraction depends on the actual temperature profile of the air, and it can differ from any formula by several arcminutes. Precise observations are rarely made so low.

Effects you can see

• Longer days. Rise and set times are computed for the moment the true centre of the Sun is 50′ below the horizon: 34′ of refraction plus 16′ for the Sun's semidiameter. For stars and planets the standard altitude is −34′. Refraction adds a few minutes of daylight at each end of the day, and more at high latitudes, where the Sun crosses the horizon at a shallow angle.
• The flattened setting Sun. When the lower edge of the Sun sits on the horizon, it is lifted by 34.5′, but the upper edge, half a degree higher, is lifted by only about 29′. The Sun then looks about 27′ tall and 32′ wide: an oval flattened by about a sixth.
• The green flash. The atmosphere bends blue and green light slightly more than red, so the last sliver of the setting Sun can turn green for a second or two over a clear, flat horizon such as the sea.
• Coloured stars near the horizon. This atmospheric dispersion spreads a low star into a tiny vertical spectrum, red at the bottom and blue at the top, which is easy to see in a telescope.
• A selenelion. During some total lunar eclipses observers can see the eclipsed Moon and the Sun above opposite horizons at the same time, although geometrically they are exactly opposite each other. Refraction lifts both above the horizon.

Refraction and twinkling

Refraction is a smooth, predictable offset caused by the average structure of the atmosphere. Twinkling (scintillation) is a different effect: small turbulent cells of warmer and cooler air move across the line of sight and make a star's light flicker hundreds of times per second. Both get stronger towards the horizon, which is one reason observers wait for their target to climb high. The sky disk on AstroAlgos lists the altitude of every planet, so you can check how high it is before you observe.

Explore it on AstroAlgos

• Night sky — altitudes of the planets from your location
• Semidiameter — the apparent size of the Sun and Moon
• Horizontal coordinates — altitude and azimuth