User:Pgramsey/sandbox

The value of a solar beta angle for a satellite in Earth orbit can be found using the equation

$$\beta=\sin^{-1}[\cos(\Gamma)\sin(\Omega)\sin(i)-\sin(\Gamma)\cos(\epsilon)\cos(\Omega)\sin(i)+\sin(\Gamma)\sin(\epsilon)\cos(i)]$$

where $$\Gamma$$ is the ecliptic true solar longitude, $$\Omega$$ is the right ascension of ascending node (RAAN), $$i$$ is the orbit's inclination, and $$\epsilon$$ is the obliquity of the ecliptic (approximately 23.45 degrees for Earth at present). The RAAN and inclination are properties of the satellite's orbit, and the solar longitude is a function of Earth's position in orbit around the sun (approximately linearly proportional to day of year relative to the vernal equinox).