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What you ask for doesn't exist. The IAU has not adopted any particular formula.

Differences like the ones you see here are the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. There model is called DE440 it is based on numerical integration of the planet's movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on proper Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html

What you ask for doesn't exist. The IAU has not adopted any particular formula.

If you are getting different answers from the implementation in the book then your implementation is wrong (or the book's implementation is wrong)

If you are getting different answers from those on the internet, there are several possible reasons. Differences like the ones you see here may be the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. Their model is called DE440 it is based on numerical integration of the planets' movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on proper Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html

Differences like the ones you see here are the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. There model is called DE440 it is based on numerical integration of the planet's movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on proper Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html

What you ask for doesn't exist. The IAU has not adopted any particular formula.

Differences like the ones you see here are the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. There model is called DE440 it is based on numerical integration of the planet's movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on proper Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html

Differences like the ones you see here are the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. There model is called DE440 it is based on numerical integration of the planet's movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on osculating Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html

Differences like the ones you see here are the result of:

• Different choice of atmospheric parameters (how much refraction)
• Different definition of "sunrise" (upper limb touching horizon vs centre vs lower limb)
• Different model. As far as I'm aware, the IAU doesn't do solar system models, but NASA do. There model is called DE440 it is based on numerical integration of the planet's movements. Another is called VSOP (it was created by the French Bureau de Longitudes) and is based on proper Keplarian elements. However both achieve sub milli-arcsecond accuracy, so can't account for differences of a minute or more. USNO also publish ephemeris.
• Failing to use the model correctly for example calculating the solar RA/Dec at 00:00 on the day in question, and then finding when that point crosses the horzion.

Of the various uncertainties, the one that I think is most likely to be causing the variation is the atmospheric model, as this has a significant effect on rise times and is genuinely variable.

As for the algorithms found in the calculators, you can read their javascript source. For example the satellite site uses the algorithm at http://www.stjarnhimlen.se/comp/riset.html