Beta angle
Encyclopedia
The beta angle is a value 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.
= 0o) for the orbiting object. This allows the object to spend the maximum possible amount of its orbital period
in the Earth's shadow, and results in extremely reduced absorption of solar energy. At a LEO of 280 kilometers the object in orbit 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 that follows the terminator
results in a beta angle of 90 degrees (
= 90o), 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
. These orbits can be taken advantage of 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 its solar panels or to study the sun by maintaining a beta angle as close to +90 or -90 as possible.
was in service on missions to the International Space Station
, the beta angle of the space station's orbit was a crucial consideration; periods referred to as "beta cutout" , during which the shuttle could not safely be launched to the ISS, were a direct result of the beta angle of the space station at those times. When the orbiter is in-flight (not docked to ISS) and it flies to a beta angle greater than 60 degrees, the orbiter goes into "rotisserie" mode, and slowly rotates around its X-axis (nose to tail axis). For flights to ISS, the shuttle can launch during an ISS beta cutout if the ISS will be at a beta less than 60 degrees at dock, and throughout the docked phase. Therefore, the mission duration affects launch timing when the beta cutout dates are approaching.
Spaceflight
Spaceflight is the act of travelling into or through outer space. Spaceflight can occur with spacecraft which may, or may not, have humans on board. Examples of human spaceflight include the Russian Soyuz program, the U.S. Space shuttle program, as well as the ongoing International Space Station...
. The beta angle determines the percentage of time an object such as a spacecraft in low Earth orbit
Low Earth orbit
A low Earth orbit is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km...
(LEO) spends in direct sunlight, absorbing solar energy. Beta angle is defined as the angle between the orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
plane and the vector from the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
(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
Plane
-Physical objects:* Aeroplane or airplane, a fixed-wing aircraft* Plane , a woodworking tool to smooth surfaces* Platanus, a genus of trees with the common name "plane"* Acer pseudoplatanus, a tree species sometimes called "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.
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 a polar orbit at local noon or midnight results in an initial beta angle of 0 degrees ( = 0o) for the orbiting object. This allows the object to spend the maximum possible amount of its orbital periodOrbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
in the Earth's shadow, and results in extremely reduced absorption of solar energy. At a LEO of 280 kilometers the object in orbit 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 that follows the terminator
Terminator (solar)
A terminator, twilight zone or "grey line" is a moving line that separates the illuminated day side and the dark night side of a planetary body...
results in a beta angle of 90 degrees (
= 90o), 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 equinoxEquinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...
. These orbits can be taken advantage of 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 its solar panels or to study the sun by maintaining a beta angle as close to +90 or -90 as possible.
Application of beta angles
The above discussion defines the beta angle of satellites orbiting the Sun, 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. This is however a minor detail, as so few satellites are in orbit anywhere but around the Earth. Beta angles describing non-geocentric orbits are important when space agencies launch satellites into orbits around other bodies in the solar system; that said, because of how rare such launches are, beta angles are almost exclusively understood to describe satellites in low Earth orbit with respect to the sun (the solar vector).Determining a beta angle
When the space shuttleSpace Shuttle
The Space Shuttle was a manned orbital rocket and spacecraft system operated by NASA on 135 missions from 1981 to 2011. The system combined rocket launch, orbital spacecraft, and re-entry spaceplane with modular add-ons...
was in service on missions to the International Space Station
International Space Station
The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...
, the beta angle of the space station's orbit was a crucial consideration; periods referred to as "beta cutout" , during which the shuttle could not safely be launched to the ISS, were a direct result of the beta angle of the space station at those times. When the orbiter is in-flight (not docked to ISS) and it flies to a beta angle greater than 60 degrees, the orbiter goes into "rotisserie" mode, and slowly rotates around its X-axis (nose to tail axis). For flights to ISS, the shuttle can launch during an ISS beta cutout if the ISS will be at a beta less than 60 degrees at dock, and throughout the docked phase. Therefore, the mission duration affects launch timing when the beta cutout dates are approaching.