Disturbance Environment for Earth Orbiting Satellites
Satellites orbiting the earth, experience the following disturbance torques:
- Gravity gradient torque
- Magnetic field torque
- Torque due to solar radiation pressure
- Torque due to aerodynamic drag
The strength of these torques varies with the altitude. For example, gravity gradient and magnetic field torques are strong in the Low Earth Orbit (LEO). On the other hand, the torque due to aerodynamic drag is practically non-existent in LEO and beyond, but it is the most dominant torque in the very low earth orbits. Torque due to solar radiation pressure is constant across orbits but increases as one moves closer to the Sun.
The disturbance torques can not only change the attitude of the satellite but also influence the choice of sensors and actuators. For example, in the Low Earth Orbits (LEO), where the magnetic field is quite strong, we can use magnetic torquer rods to apply control torques. However, the torquer rods may not be the ideal choice in a geostationary orbit where the magnetic field is not strong enough to produce a decent amount of control torque. Star sensors – devices that provide high accuracy attitude measurements – are not preferred in the Van Allen Belts. This is because the charge coupled devices (CCD) used in the star sensors are highly sensitive to the extreme radiation that is characterises Val Allen belts. Inner Van Allen belts extend from 1,600 km to 13,000, and the outer belts from 19,000 km to 40,000 km.
Gravity gradient torques
The gravitational force on a satellite in orbit varies along the length of the satellite. As a result of this, for elongated objects in orbit, the Center of Gravity (CG) may be offset from the Center of Mass (CM). This creates a torque called the Gravity gradient tortue. This is hard for us to imagine becaue, gravity, as we experience on earth is fairly constant – the force we experience on top of a two-storied building is not different from the force we experience on the street!
It is worth noting that the location of CG is a function not only of the mass configuration of the satellite, but also its current attitude.
Magnetic Torque
Satellite carry a number of electronic equipment that generate a residual magnetic field inside the vehicle. The dipole moment of these fields is of the order of \(0.1 - 20\, \mathrm{A \cdot m^{2}}\) and is a function of the spacecraft size. In addition to this, the satellite also moves in a region that is inside the spehere of influence of earth’s magnetic field. If the magnetic dipole corresponding to the residual field is not aligned with the earth’s field, then the dipole experiences a torque given by \(\mathbf{D \times B}\), where \(\mathbf{D}\) is the dipole moment corresponding to the residual field, and \(\mathbf{B}\) is the strength of earth’s magnetic field. Clearly, the torque vanishes when \(\mathbf{D}\) is aligned with \(\mathbf{B}\). We see this torque in action when the earth’s magnetic field pulls a compass needle until the needle is aligned with earth’s magnetic field.
For calculating the torque experienced by the satellite dur to earth’s magnetic field, it is sufficient to consider the earth’s magnetic field to be eminating from a giant bar magnet hiding inside the earth. However, we must remember that it is just an approximation and earth’s magnetic behaviour is much more complex.
Torque due to solar radiation pressure
Sunlight is a stream of photons. When an object is lit by sunlight, the photons strike the object and transfer their momentum due to which the object experiences some pressure. The actual pressure experienced by the object is a function of the material properties of the object. Materials with good reflectivity experience more pressure than those with good abosorbitivity. For example, a perfect reflector, like an ideal mirror, will experience a pressure that is twice the pressure experienced by a perfect absorber.
Solar radiation pressure torque results from an offset from the center of gravity of the satellite. Radiation pressure on a satellite can be thought to be acting on a single point called the center of pressure. A torque results whenever the center of pressure is offset from the center of gravity of the satellite (or any surface that is exposed to the Sun).
To understand how solar radiation pressure affects dynamic of a satellite, imagine a flat surface on the satellite that is exposed to the Sun. Also imagine that half of the plate us painted black and has higher absorbtivity than the other half. When sun rays awash the surface, the two halfs experience different pressures because of their different material properties. This creates an offset between center of pressure and center of gravity of the surface which results in torque.
In general, a satellite will have surfaces with different material properties simultaneously exposed to the Sun. For example, solar arrays absorb more radiation than a polished mettalic surface. Moreover, different surfaces surfaces are at different angles to the Sun. Surfaces that are directly facing the Sun receive more radiation and experience more pressure than those that are at an angle.
While solar radiation pressure can really influence the dynamics of a spacecraft, the magnitude of the torque gets stronger as the spacecraft gets closer to the Sun. As we see in the next article, torque due to radiation pressure is not the strongest disturbance torque experienced by a satellite.
Torque due to atmospheic drag
Atmospheric drag results in a torque when the center of atmospheric pressure is not aligned with the center of gravity of the spacecraft.
Atmospheric drag is a significant force on earth. If you are wondering why I am calling it significant, try cycling against the wind on a windy day! Drag is a lesser evil in space because the atmospheric density plummets exponentially with altitude. Spacecraft in very low orbits, like the International Space Station, do encounter enough number of particles to cause a noticeable effect. In fact, in these orbits, drag is stronger than all other disturbances. However, it fades in strength as one moves to higher orbits in LEO, and practically disappears at Medium Earth Orbits (MEO).
References
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NASA. NASA’s Van Allen Probes Spot an Impenetrable Barrier in Space. https://www.nasa.gov/content/goddard/van-allen-probes-spot-impenetrable-barrier-in-space Accessed on July 19, 2019
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S R Starin and J Eterno. 19.1 Attitude Determination and Control System