Beta Angle


The beta angle is a measurement that is used most notably in spaceflight. The beta angle determines the percentage of time an object such as a spacecraft in low Earth orbit (LEO) spends in direct sunlight, absorbing solar energy. Beta angle is defined as the angle between the orbit plane and the vector from the sun (which direction the Sun is shining from). The beta angle is the smaller angle (there are two angles) between the Sun vector (where the Sun is shining from in the sky) and the plane of the object’s orbit. Note that the beta angle does not define a unique orbit plane; all satellites in orbit with a given beta angle at a given altitude have the same exposure to the Sun, even though they may be orbiting in completely different planes around the Earth. The beta angle varies between +90° and −90°, and the direction the satellite revolves around the body it orbits determines whether the beta angle sign is positive or negative. An imaginary observer standing on the Sun defines a beta angle as positive if the satellite in question orbits in a counter clockwise direction and negative if it revolves clockwise. The maximum amount of time that a satellite in a normal low Earth orbit mission can spend in the Earth’s shadow occurs at a beta angle of zero. In such an orbit, the satellite is in sunlight no less than 59% of the time.

Related formulas


β(t)beta angle (radian)
δs(t)declination of the Sun (deg)
iinclination of orbit (deg)
Ω(t)position of the ascending node (deg)
Ωs(t)right ascension of the Sun (deg)