Tech/Electrodynamic Tethering

Electromagnetic Tethering / Electrodynamic Tethers (EDTs)

Artist's conception of satellite with a tether (because there are no pictures of satellites in "space", amazing the tether knows which way to "hang down"

Electrodynamic tethers, also known as EDTs, are long, conducting wires that are deployed from a craft in earths upper atmos. In general, a tether is a long cable (even up to 100 km or more). These tethers interact with the Earth’s magnetic field to generate an electrical current. The current can be used to power systems, change the orbit, or even slow down the reentry into the Earth’s atmos.

For a 20 km tether in low earth orbit (LEO), this voltage would generally fluctuate between 1,500 to 5,300 volts open circuit, depending on the orbital inclination. If a current is allowed to circulate through the tether and a load, substantial power on the order of 15-30 kW can be generated.

With a sufficiently large power supply onboard the craft, the direction of the current can be reversed and the tether becomes a thruster, raising its orbital height. When current flowed through the tether, it pushes against the Earth’s magnetic field to generate drag thrust, demonstrating propulsion.

The Basic Principle

At its most basic level, an EDT works by utilizing the interaction between a conductor and a magnetic field. The Earth’s magnetic field is a powerful and constant source of magnetic energy. By deploying a long, conducting wire and allowing it to interact with the Earth’s magnetic field, an electrical current is generated.

This process is known as electromagnetic induction. When a conductor, such as a wire, is moved through a magnetic field, it generates an electrical current. The strength of the current is directly proportional to the strength of the magnetic field and the velocity of the conductor.

The craft is equipped with a long, conducting wire that is deployed into Earth’s atmos. As the craft moves through the Earth’s magnetic field, an electrical current is generated in the wire. This current can then be used to power craft's systems or to change the craft’s orbit.

Applications

The electrical current generated by the EDT could be used to power onboard instruments, propulsion systems, and communication systems. This would reduce the need for bulky and expensive batteries or solar panels.

In addition, EDTs could be used to change the orbit of a craft. By adjusting the length of the tether and the craft’s speed, the orbit could be raised or lowered. This would be particularly useful for satellites that require a specific orbit for their mission.

Overall, electrodynamic tethers are a promising technology for Earth’s upper atmos exploration and satellite operations. By harnessing the power of the Earth’s magnetic field, EDTs could enable new capabilities and reduce the hazards of debris.

Is the ISS utilizing Electodynamic tethering?

ISS path over a Flat Earth and a Scientifically impossible Globe

The International Space Station (ISS) travels in a manner that can be interpreted through the concept of electrostatic tethering and its interaction with Earth's magnetic toroidal field.

Electrostatic tethering involves the use of electric fields to create forces that can influence the motion and position of objects in space. This concept can be applied to the ISS as it orbits Earth. The ISS could be seen as utilizing electrostatic forces to maintain its trajectory and altitude. This would involve the interaction of charged particles and electric fields generated by the station and the surrounding space environment.

The Earth's magnetic field is often described as a toroidal field, which means it has a doughnut-like shape with magnetic field lines looping from the magnetic poles and around the planet. The ISS orbits within this magnetic field, and its motion can be influenced by the interaction with these magnetic lines. By combining electrostatic tethering and the Earth's magnetic toroidal field, one could theorize that the ISS travels by aligning itself with the magnetic field lines and using electrostatic forces to adjust its position and velocity. This would mean the ISS is not merely free-falling around the Earth, as traditionally described, but is also actively interacting with the magnetic and electrostatic environment to maintain its position. To understand how the International Space Station (ISS) travels using the concept of electrostatic tethering and the Earth's magnetic toroidal field, we need to delve into some mathematics.

Electrostatic tethering involves the use of electric fields to create forces that can influence the motion and position of objects in space. The ISS could theoretically use electrostatic forces to maintain its trajectory and altitude. Let's denote the electrostatic force as F_e, which can be given by Coulomb's law:

${\displaystyle F=k{\frac {\begin{vmatrix}q1q2\end{vmatrix}}{r^{2}}}}$where:

• ${\displaystyle F}$ is the magnitude of the force between two point charges ${\displaystyle q1}$​ and ${\displaystyle q2}$,
• ${\displaystyle k}$ is the Coulomb constant (8.99×109N⋅m2/C2),
• ${\displaystyle r}$ is the distance between the charges.

The Earth's magnetic field can be approximated as a dipole field, which in spherical coordinates (r, theta, phi) is given by:

${\displaystyle B_{r}=-2B_{0}\left({\frac {R_{E}}{r}}\right)^{3}\cos \theta }$

${\displaystyle B_{\theta }=-B_{0}\left({\frac {R_{E}}{r}}\right)^{3}\sin \theta }$

${\displaystyle |B|=B_{0}\left({\frac {R_{E}}{r}}\right)^{3}{\sqrt {1+3\cos ^{2}\theta }}}$

where:

• ${\displaystyle B_{0}}$ is the magnetic field strength at the Earth's surface

• ${\displaystyle R_{E}}$ is the mean radius of the Earth (approximately 6370 km)
• ${\displaystyle r}$ is the radial distance from the center of the Earth (using the same units as used for ${\displaystyle R_{E}}$),
• ${\displaystyle \theta }$ is the colatitude measured from the north magnetic pole (or geomagnetic pole).

To combine electrostatic tethering of the ISS with the Earth's magnetic field ${\displaystyle B}$, we need to consider the Lorentz force, which acts on a charged particle moving in a magnetic field. The Lorentz force ${\displaystyle F_{L}}$ is given by:

${\displaystyle \mathbf {F_{L}} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right).}$

where:

• ${\displaystyle q}$ is the charge
• ${\displaystyle E}$ is the electric field
• ${\displaystyle v}$ is the velocity of the ISS
• ${\displaystyle B}$ is the magnetic field.

Given the ISS's velocity is tangential to the Earth's surface, the cross product ${\displaystyle \mathbf {v} \times \mathbf {B} }$ will result in a force perpendicular to both ${\displaystyle v}$ and ${\displaystyle B}$. This force can help maintain the ISS in its orbit by providing the necessary centripetal force.

Let's calculate the centripetal force required to keep the ISS in orbit:

${\displaystyle \mathbf {Fc} =(\mathbf {rm} \times \mathbf {v2} )}$

where:

• ${\displaystyle m}$ is the mass of the ISS (≈420,000 kg)
• ${\displaystyle v}$ is the orbital velocity (≈7.66 km s
• ${\displaystyle r}$ is the orbital radius (≈6,780 km)

Plugging in the values:

${\displaystyle \mathbf {Fc} =(420000\times 7660^{2})\div 6780000\eqsim 3.6\times 10^{6}N}$

This centripetal force can be provided by the combination of electrostatic and magnetic forces. The electrostatic force ${\displaystyle Fe}$​ and the magnetic Lorentz force ${\displaystyle F_{L}}$​ together must sum to this centripetal force.

The ISS can be understood to travel by using electrostatic tethering to generate forces that interact with the Earth's magnetic toroidal field. By aligning with the magnetic field lines and using electrostatic forces to adjust its position and velocity, the ISS maintains its orbit. This combination of forces ensures the ISS remains in a stable orbit around the Earth.

Chinese electrodynamic tether technology (that gets "refueled" by VHF beams) packed into a platform that flies at 80k ft

Research NASA PROPEL electrodynamic tether program. I think these tethers are between the satellite payload (gondola) and balloon, above.

Shout out to Shane St. Pierre for this gravy!

Further Reading

• ntrs.nasa.gov: Electrodynamic tether
• ntrs.nasa.gov: System Engineering Study of Electrodynamic Tether as a Spaceborne Generator and Radiator of Electromagnetic Waves in the ULF/ELF Frequency Band

See Also

• Tech/Quantum locking
• Tech/Electrodynamic Tethering