An equation to determine day length?

Question

Given latitude and the time of year, how do you calculate day length? Am I right in understanding that day length changes fastest around the equinoxes and slowest around the solstices, so linear regression is not possible.

Answer 1

There is no simple equation. It is a complex problem in spherical trigonometry. You are correct that day length changes fastest around the equinoxes and slowest around the solstices.

A slightly simpler intermediate problem:

Given the effective angle of planetary inclination and latitude, calculate day length.

Then you relate the date to the effective angle of planetary inclination, which changes constantly as the planet orbits it's sun.

Answer 2

First you need to know the Sun's declination (δ). The best way to find this is with an almanac or computer ephemeris. If you don't have one, a rough answer is given by the following equation:

δ = sin[((n - 70)/365)*360] * 23.44

... where n is the day number for the year (Jan 1=1, Dec 31=365) and the argument of the sin function is in degrees.

Knowing the declination, the length of daylight can be computed as follows:

H = arcos[-tan(φ) tan(δ)] / 7.5

Where H is the hours of daylight and φ is your latitude. This formula neglects atmospheric refraction, parallax, and the size of the solar disk.

Answer 3

Daylight Length By Latitude

Answer 4

Since the meteor was on a radial trajectory, it doesn't have any angular momentum of its own. By sticking to the Earth's surface, it increases the moment of inertia. Because angular momentum must be maintained, increasing the inertia decreases the angular velocity by the same proportion, and hence lengthens the day. The relevant numbers are the mass of earth and mass of the meteor (not volume, but I guess you could estimate that they have the same density).