If the weather changes, does the position correction of the same low-altitude star also change?
In addition to how high a star is, air pressure and temperature also affect how light bends in the air.
Sky coordinates and observations
In the previous refraction experiments we fixed the standard atmosphere. Now keep the direction constant and try to change the air pressure or temperature; you can also do the opposite, knowing the direction you see and estimate the geometric direction without refraction.
Guess first
Keeping the true height the same and changing the air pressure and temperature, will the refraction remain the same?
Show answer and explanation
will change — Air pressure and temperature affect the refractive properties of air.
Then connect experience and science
First determine what the input means
To give the true height, you need to correct it upward; to give the visible height, you need to subtract refraction. The independent variables of the two formulas are different.
Real → Visual: Sæmundsson; Visual → Real: Bennett
Let the air pressure change
The approximate correction in this lesson is proportional to the air pressure. It is not a complete weather forecast.
R times P/1010
Temperature also affects corrections
Under the same pressure, cooler air usually produces greater refraction; this formula uses an approximate temperature factor.
R is then multiplied by 283/(273+T)
Uncertainty should be retained in low-altitude results
The original book uses the upper and lower edges of the sun to illustrate that the disk will be flattened due to different corrections at different altitudes. The atmosphere is not stable near the true horizon.
Bennett: R=cot(h-view+7.31/(h-view+4.4))
Expand the calculation
Rreality→视 = 1.02 / tan(h真+10.3/(h真+5.11)) R视→reality = 1 / tan(h视+7.31/(h视+4.4)) fsky气 = (P/1010) × 283/(273+T) h视 = h真 + fsky气 Rreality→视/60 h真 = h视 − fsky气 R视→reality/60
Height is measured in brackets, R is expressed in arc minutes, P is expressed in hPa, and T is expressed in degrees Celsius. First choose whether the input is real or apparent height, and then use the corresponding formula; the two empirical formulas are not strictly inverse to each other.
give it a try
Use the standard air pressure temperature first, and then lower the temperature. Entering "real height" and entering "seen height" are opposite problems. Do not mix the two formulas.
No need to memorize symbols
- h/h view
- True/apparent height, degrees
- R
- refraction angle minutes
- P/T
- Air pressure hPa/temperature °C
Algorithm, accuracy and scope of application
Complement Bennett's inverse approximation, P/T scaling and calculation of solar disk oblateness in 16.a of the original book. For an example with a diameter of 32′, the apparent height of the lower edge is 0.5° and the true lower edge is inferred, and the diameter is added and the upper edge is inferred forward; the two approximations do not constitute exact reciprocity, and the accuracy of the model cannot be covered up by forcing round-trip equality.
my understanding check
When the apparent height has been given, how should the true height be estimated?
Subtract refraction correction — The direction seen is usually elevated and needs to be reversed.
Can the meteorological factors in this lesson replace real weather observations?
cannot — It is only an approximate scaling of the standard formula.
What happens if the upper and lower edges of the sun refract differently?
The optic disc may become flattened — What changes is the visual shape.
First distinguish what altitude is known, and then choose the formula; low-altitude observations, especially low-altitude observations, cannot treat the standard atmosphere as real weather.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 16 chapter