In
orbital spaceflight
An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least one orbit. To do this around the Earth, it must be on a free trajectory which has an altit ...
, the beta angle (
) is the
angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle.
Angles formed by two ...
between a
satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope ...
's
orbital plane
The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) an ...
around
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
and the
geocentric position
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, ...
of the
sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
.
The beta angle determines the percentage of time that a satellite in
low Earth orbit
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of the artificial objects in outer space are in LEO, with an altitude never mor ...
(LEO) spends in direct
sunlight
Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere, and is obvious as daylight when t ...
, absorbing solar energy.
The beta angle does not define a unique orbital plane: all satellites in orbit with a given beta angle at a given
orbital altitude
A geocentric orbit or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debris ...
have the same exposure to the Sun, even though they may be orbiting in different planes around
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
.
The beta angle varies between +90° and −90°, and the direction in which the satellite orbits its
primary body
A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
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
Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite ...
.
The maximum amount of time that a satellite in a normal LEO mission can spend in
Earth's shadow
Earth's shadow (or Earth shadow) is the shadow that Earth itself casts through its atmosphere and into outer space, toward the antisolar point. During the twilight period (both early dusk and late dawn), the shadow's visible fringe – sometimes ...
occurs at a beta angle of 0°. A satellite in such an orbit spends at least 59% of its
orbital period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
in sunlight.
Light and shadow
The degree of orbital shadowing an object in LEO experiences is determined by that object's beta angle. An object launched into an initial orbit with an inclination equal to the complement of the Earth's inclination to the ecliptic results in an initial beta angle of 0 degrees (
= 0°) for the orbiting object. This allows the object to spend the maximum possible amount of its
orbital period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
in the Earth's shadow, and results in extremely reduced absorption of solar energy. At a LEO of 280 kilometers, the object is in sunlight through 59% of its orbit (approximately 53 minutes in Sunlight, and 37 minutes in shadow.
) On the other extreme, an object launched into an orbit parallel to the
terminator
Terminator may refer to:
Science and technology
Genetics
* Terminator (genetics), the end of a gene for transcription
* Terminator technology, proposed methods for restricting the use of genetically modified plants by causing second generation s ...
results in a beta angle of 90 degrees (
= 90°), and the object is in sunlight 100% of the time.
An example would be a polar orbit initiated at local dawn or dusk on an
equinox
A solar equinox is a moment in time when the Sun crosses the Earth's equator, which is to say, appears directly above the equator, rather than north or south of the equator. On the day of the equinox, the Sun appears to rise "due east" and se ...
. Beta angle can be controlled to keep a satellite as cool as possible (for instruments that require low temperatures, such as infrared cameras) by keeping the beta angle as close to zero as possible, or, conversely, to keep a satellite in sunlight as much as possible (for conversion of sunlight by its solar panels, for solar stability of sensors, or to study the Sun) by maintaining a beta angle as close to +90 or -90 as possible.
Determination and application of beta angles
The value of a solar beta angle for a satellite in Earth orbit can be found using the equation