Application of symmetrical motorized momentum exchange tethers for two-way Earth–Mars transportation

As we venture deeper into space and establish bases and orbital stations on celestial bodies, it is imperative to develop sustainable space transportation methods that minimise propellant usage. Currently, the most common method for Earth-Mars transfers is through chemical propulsion systems. While the chemical propulsion system is well established, it has several drawbacks, including low efficiency, high propellant mass requirements, thermal limitations, and operational complexity. Momentum exchange tethers, which, in theory, can operate without the need for any propellant, offer an innovative alternative to these propulsion systems. Especially, in a symmetrical tether, the COM lies at the centre of the length. If both the equal mass payloads are released at the same time, then the orbit of the tether does not change. Additional delta-v can be generated by the libration (oscillation) or rotation of the tethers, which can be induced by a motor facility. Though there are various investigations into space tethers, there is a gap in the use of symmetrical tethers for interplanetary transfers. In a research article recently published in Space: Science & Technology, researchers from University of Strathclyde addressed this gap by developing a conceptual symmetrical motorised momentum exchange tether (MMET) logistic system for continuous 2-way payload transfer between Earth and Mars.

First, two strategies that use dummy payloads to facilitate 2-way continuous transfer between Earth and Mars are presented. Fig. 1 shows a 2-stage tether system which has been used by many others and which is also employed in this work. The tether that is closer to the departure planet is labelled T₁, and the other tether that is further away is labelled T₂. Planet “E” represents Earth, but the procedure remains the same for Mars. Payload p₁, which is parked in orbit 1, is the specific payload that needs to be transferred to the other planet. T₂ carries 2 dummy payloads labelled d₁ and d₂. In Strategy 1, both tethers are rotating prograde, as shown in Fig. 2:

• Step 1: T₁ captures p₁ from orbit 1 and d₂ from T₂. Therefore, T₂ releases d₁ to T₁ as it simultaneously also releases d₂ into orbit 5.
• Step 2: T₂ captures p₁ from T₁ and d₂ from orbit 5. T₁ has released p₁ to T₂ and has also simultaneously released d₁ into orbit 1.
• Step 3: T₂ accelerates, then releases p₁ into hyperbolic escape trajectory (HET) 6 once the desired escape velocity is reached. T₂ releases d₂ into orbit 4.

In Strategy 2, T₁ is rotating prograde, and T₂ is rotating retrograde, as shown in Fig. 3.

• Step 1: this is conceptually identical to step 1 for strategy 1, but the angular velocity of T₁ must be high enough so that p₁ can be released directly into HET4.
• Step 2: T₁ releases p₁ into HET4 while simultaneously releasing d₁ into orbit 1.

Both strategies can potentially employ the same sort of return. The desired payload to be captured, say p₁, will arrive along hyperbolic return trajectory (HRT) 4 (Fig. 3) or HRT6 (Fig. 2). Strategy 2, compared with strategy 1, has a reduction in the number of required steps and simplifies the overall procedure but assumes that tether T1 is strong enough to withstand the higher centripetal load. In view of the operational simplification that it offers, strategy 2 is henceforth considered in this paper

Then, methodology to determine the orbital parameters, tether sub-spans, angular velocities, and orbital decay are elaborated.

In this preliminary study, certain assumptions are made as follows:

• The orbits of Earth and Mars around the Sun are considered to be circular and coplanar for the sake of establishing a baseline concept.
• The planets are assumed to be spherical, hence negating any J2 perturbation.

There are 2 conditions to be met while designing the orbits of the tethers and the dummy payloads:

• The relative velocities during handovers/captures must be zero.
• The time period of the higher orbits must be some integer multiple of the time period of the lower orbits. This ensures that after a fixed interval of time, the tethers and payloads are in a straight line in order to enable capture/handover.

Fig. 4 shows the important distances and the tether sub-span considered in this study. Point P marked on the orbits can be either the periapsis or the apoapsis. The sub-span (i.e., L₁ and L₂) is the distance from the COM of the tether to the centre of the payload. Once the payload leaves the planet, dummy payloads d₁ and d₂ and tethers T₁ and T₂ will be in their respective orbits waiting for a long time, until the payload returns from the other planet. Over time, these 4 orbits will potentially decay due to the effects of the local atmospheric drag force. Thus, the dummy payloads and tethers will need to re-raise their orbits by the use of some additional propulsion. The 2-body equations in 2-dimensional Cartesian coordinates are used to calculate the orbital decay. Certain assumptions are made to simplify the calculation process:

• The payloads are spherical, and the motor facility is cylindrical.
• The drag coefficient remains constant.
• Tether drag is assumed to be negligible.

Atmospheric drag is modelled as a quadratic effect in this study. The nominal atmospheric density variation with altitude for Earth and Mars is obtained from the US Standard Atmosphere 1976 data from Curtis and the MarsGRAM report released by the NASA, respectively.

Consequently, results are discussed. Orbits around Earth and Mars are analysed with different orbital parameters. Tables 3 and 4 show some results obtained for certain combinations of l, m, n, r_P1, and a₁ for possible orbits around Earth and Mars, respectively, where l, m, n are the orbital harmonics. For orbits around Earth, we consider result 9 from Table 3, and for orbits around Mars, we consider result 10 from Table 4. Based on chosen Earth and Mars orbits, an example of Strategy 2 is explained. During departure from Earth, T₁ picks up the payload from orbit 1 and the dummy payload d₁ from T₂. this opportunity for transfer arises every revolution of T₂ in orbit 3, i.e., every P3 or 3.695 d. When T₁ reaches point P (after 1 or n revolutions in orbit 2), it launches the payload into HET4 and d₁ into orbit 1. This opportunity arises every P2 or 1.232 d. During returning to Earth, the payload that is returning to Earth is captured by T₁ from HRT4, and at the same time, it must also capture d₁ from orbit 1. T₁ has the opportunity to capture d₁ from orbit 1 each time it completes a revolution, i.e., every P2 or 1.232 d. T₁ releases the payload in orbit 1 and hands d₁ over to T₂ at the same time T₂ catches d₂ from orbit 5. This opportunity also arises after every P3 or 3.695 d. Once the payload is released in orbit 1, it will need to de-orbit on its own using its own propulsion system. The orbits around Earth were simulated for 2.663 years, this being the time for a round trip to Mars, and the orbits around Mars were simulated for 1.945 years, which is the time taken for a round trip to Earth. Results show that the percentage changes of r_P and a are negative and below 1% for most orbits, indicating that the orbital decay is virtually negligible.

Finally, failure analysis for several scenarios is carried out. Some major scenarios are discussed. During the outgoing phase, 2 major failure scenarios can occur. Failure scenario 1 (Fig. 5 A) occurs when T₁ captures p1 from orbit 1 but fails to capture d₁ from T₂. If this happens, T₁ will then be asymmetrically laden and the COM will shift towards p₁. If T₁ immediately releases p₁, then there would not be much perturbation in the orbits of T₁ and p₁. d₁ will be released into HET4, since T₁ has failed to capture it. Failure scenario 2 (Fig. 5 B) occurs when T₁ captures d₁ from T₂ but fails to capture p₁ from orbit 1. If T₁ releases d₁ immediately or after a certain time, d₁ will need to be recovered using a spaceplane. During the return phase, 4 major failure scenarios can occur. Failure scenario 3 occurs when T₁ captures d₁ from orbit 1 but fails to capture p₂ from HRT. This scenario is similar to failure scenario 1. Failure scenario 4 occurs when T₁ captures p₂ from HRT4 but fails to capture d₁ from orbit 1. This scenario is similar to failure scenario 2. Failure scenario 5 (Fig. 6 A) occurs when T₂ captures d₂ from orbit 5 but fails to capture d₁ from T₁. T₂ immediately releases d₂. d₁ is released into HET4 since the failure in capture and a spaceplane will be needed to capture it. Failure scenario 6 (Fig. 6 B), occurs when T₂ captures d₁ from T₁ but fails to capture d₂ from orbit 5. This is similar to failure mode 2, except with T₂.