With respect of Montreal and Edmonton longitude calculations...
Copilot:
Does this formula assume the Earth is a sphere?
Yes. The standard formula I showed assumes the Earth is a perfect sphere.
In reality, the Earth is slightly flattened at the poles and bulges at the equator, making it an oblate spheroid. The equatorial radius is about 21 km larger than the polar radius.
For sunrise and sunset calculations, however, the spherical assumption works remarkably well because:
The Earth's radius is about 6,371 km.
The flattening is only about 0.3%.
The resulting error in sunrise or sunset times is typically much smaller than other effects, such as atmospheric refraction.
In fact, the largest source of uncertainty is often the atmosphere. Variations in temperature and pressure can shift the apparent sunrise or sunset by a minute or more because they cange how strongly light bends near the horizon.
Modern astronomical software therefore includes corrections for:
Earth's actual shape,
atmospheric refraction,
observer elevation,
the Sun's finite size,
and the precise Earth-Sun geometry on a given date.
An interesting consequence is that if you stand on a hill or in a tall building, you can see the Sun for longer than someone at sea level because your horizon is farther away. From the top of a 100 m hill, sunrise occurs about a minute earlier and sunset about a minute later than at sea level.
For a place like St-Jean-sur-Richelieu (about 45°N), treating the Earth as a sphere gives sunrise and sunset times that are extremely close to the values published by weather services. The atmosphere usually matters more than the Earth's slight flattening.
In a sense, the spherical model is to astronomers what a straight line is to engineers: not perfectly true, but often accurate enough to get very useful answers.
* * *
Quick review of Latitude and Longitude:
No comments:
Post a Comment