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In orbital mechanics, the beta angle () is the angle between a satellite's orbital plane around Earth and the geocentric position of the Sun. The beta angle determines the percentage of time that a satellite in low Earth orbit (LEO) spends in direct sunlight, absorbing solar radiation. For objects launched into orbit, the solar beta angle of Inclined orbit and sun-synchronous orbits depend on launch altitude, inclination, and time.
The beta angle does not define a unique orbital plane: all satellites in orbit with a given beta angle at a given orbital altitude have the same exposure to the Sun, even though they may be orbiting in different planes around Earth.
The beta angle varies between +90° and −90°, and the direction in which the satellite orbits its primary body 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 counterclockwise direction and negative if it revolves clockwise. The maximum amount of time that a satellite in a normal LEO mission can spend in Earth's shadow occurs at a beta angle of 0°. A satellite in such an orbit spends at least 59% of its orbital period in sunlight.
where is the solar longitude, is the right ascension of ascending node (RAAN), is the orbit's inclination, and is the axial tilt (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).
The above discussion defines the beta angle of satellites orbiting the Earth, but a beta angle can be calculated for any orbiting three body system: the same definition can be applied to give the beta angle of other objects. For example, the beta angle of a satellite in orbit around Mars, with respect to the Earth, defines how much of the time the satellite has a line of sight to the Earth - that is, it determines how long the Earth is shining on the satellite and how long the Earth is blocked from view. That same satellite also will have a beta angle with respect to the Sun, and in fact it has a beta angle for any celestial object one might wish to calculate one for: any satellite orbiting a body (i.e. the Earth) will be in that body's shadow with respect to a given celestial object (like a star) some of the time, and in its line-of-sight the rest of the time. Beta angles describing non-geocentric orbits are important when space agencies launch satellites into orbits around other bodies in the Solar System.
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