Beta Angle Formula

The beta angle is the angle between the orbital plane of the spacecraft and the vector of the sun. The inclination of the orbit is the angle between the plane of an orbit and the equator. The ascending node is the orbital elements used to specify the orbit of an object in the space. The right ascension is the angle between the right vernal equinox to the foot of the hour circle. Here is the beta angle formula for you to calculate the beta angle variation of a polar sun.


β(t) = arcsin( cos(δs(t)) x sin(i) x sin(Ω(t) - Ωs(t)) + sin(δs(t)) x cos(i))


δs(t) = Declination of the Sun
i = Inclination of Orbit
Ω(t) = Position of the Ascending Node
Ωs(t) = Right Ascension of the Sun
β(t) = Beta Angle

Related Calculator:

Find the time of the spacecraft or any object in the space exposed to the sunlight using the beta angle formula and verify the result using the calculator, the link for the calculator is provided below the formula.

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