5. Energy replenishment

After launch it is necessary to replenish the skyhook energy and circularize the orbit. If the orbital eccentricity is small there is no interaction between the skyhook and the atmosphere, so this may occur over many orbits. Electric thrusters are proposed as a suitable technology for maintaining the skyhook orbit. They produce thrust with a high specific impulse, and therefore utilize propellant very efficiently.

The preferred location to apply thrust is the skyhook centroid. A force at this point maximizes energy transfer, the rate of work being the product of the thrust and orbital velocity V0. The skyhook is also very robust at the centroid, and with a local acceleration near zero it is the optimal location for solar arrays to power the thrusters. Note that mass at the centroid does not affect the skyhook structure or energy transfer rate. This means the propulsion system mass and efficiency is of no concern. The key thruster performance characteristics are the efflux velocity and mass flow rate, which together determine the propellant quantity and time needed to achieve energy replenishment.

Electric propulsion has been developed for tasks that require a small thrust with high specific impulse. Examples include orbital transfer and deep space missions, for which ion thrusters are the preferred technology. Energy replenishment requires a high specific impulse and sufficient thrust to limit the replenishment time. A magnetoplasmadynamic (MPD) motor is best suited for this purpose. MPD thruster technology is developmental, but their performance can be inferred from experimental demonstrators.

An MPD thruster creates an electric current in plasma in the presence of a magnetic field. The field may be generated externally by coils or intrinsically by the current itself. In either case Lorentz force acts on the plasma and expels it at high velocity. Laboratory MPD thrusters have demonstrated 5 N of thrust with a mass

rP <sup>¼</sup> <sup>2</sup> r � <sup>v</sup><sup>2</sup> GME � ��<sup>1</sup>

rA <sup>¼</sup> <sup>2</sup> r � <sup>v</sup><sup>2</sup> GME � ��<sup>1</sup>

<sup>2</sup> <sup>¼</sup> <sup>1</sup> � <sup>r</sup>2v<sup>2</sup>

θ GME

The transition to a circular orbit can be achieved with a bi-elliptical transfer maneuver [12]. This involves a prograde impulse at apoapsis to increase the periapsis, followed by a retrograde impulse at periapsis to circularize the orbit. The maneuver can be implemented with a series of small impulses over several orbits, but the single orbit procedure serves to illustrate the process. The velocity changes

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2GME

the payload is released. For the nominal skyhook most orbits have a periapsis smaller than Earth radius, necessitating an impulse during the first orbit to increase the periapsis to avoid reentry into the atmosphere. Only a small impulse is needed for this purpose, which can be provided by a conventional rocket. The rest of the orbital transfer maneuver can be achieved efficiently by employing low thrust

an orientation angle β ¼ 1:6 radians. It enters an elliptical orbit with periapsis 5550 km and apoapsis 71,400 km. A velocity change of 68 m/s at apoapsis increases the periapsis to 6500 km, sufficient to avoid reentry. This can be provided by a chemical rocket with a propellant mass fraction of 0.03. Subsequent circularization of the orbit at the centroid radius requires a velocity change of about 2.8 km/s which can be provided by electric thrusters with a propellant mass fraction of 0.06. This means a reusable vehicle can be used to transport propellant to the skyhook centroid, with only 10% of the initial mass expended as propellant during the journey.

� <sup>2</sup>GME R þ rA

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>R</sup> � <sup>2</sup>GME R þ rA

The initial orbit depends on the skyhook configuration and its orientation when

To illustrate the process consider a vehicle that is released from the skyhook at

Planetary science and space-based astronomy demand increasingly complex infrastructure, and the high cost of launch limits the scope of experiments. A more efficient launch process would allow larger vehicles to be constructed and more ambitious experiments to be undertaken. The orbital skyhook is a fully reusable launch system with high propellant efficiency, and which can be constructed using current materials technology. It can deliver payloads directly to Earth orbit, or to a

Access to orbit is the first stage of any planetary science mission. Typically a launch vehicle places the spacecraft and its propulsion system into orbit to await the appropriate time to commence interplanetary transfer. Because of the high launch cost a low energy trajectory is usually employed. This restricts the available launch

�

s

�

r

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ 1 � e GME rA

> ffiffiffiffiffiffiffiffiffiffi GME R

2GME rA

r

r

ΔVP ¼

2 r � <sup>v</sup><sup>2</sup> GME

e

at apoapsis and periapsis are given by:

Space Access for Future Planetary Science Missions DOI: http://dx.doi.org/10.5772/intechopen.88530

electric propulsion over multiple orbits.

6. Planetary science

61

trajectory for transfer to lunar orbit.

ΔVA ¼

ð Þ 1 � e (25)

ð Þ 1 þ e (26)

(28)

(29)

� � (27)

Figure 3. Skyhook orbital geometry and payload velocity at detachment.

flow rate of 60 mg/s [10]. The MPD thruster is a compact and robust device, but it operates most efficiently at high power levels in the order of 1 MW. It is estimated that a practical MPD thruster could achieve a thrust of 2.5–25 N with an efflux velocity of 15–60 km/s [11].

A thruster with efflux velocity VE and mass flow rate m\_ acting at the centroid can replenish the launch energy EL <sup>¼</sup> <sup>m</sup>0V<sup>2</sup> <sup>0</sup>=2 for a payload m<sup>0</sup> in a period TR given by:

$$
\hbar T\_R = E\_L/\dot{E} = m\_o V\_0/2 V\_E \dot{m} = m\_P/\dot{m} \tag{22}
$$

The ratio mP=mo ¼ V0=2VE is the fraction of payload mass that must be reserved for propellant to replenish launch energy. For an efflux velocity of 50 km/s this ratio is 0.07. This means the amount of propellant needed to replenish launch energy is only 7% of the payload mass. With a realistic mass flow rate of 0.4 g/s the time needed to replenish the energy used to launch a 1000 kg payload is about 2 days. This can obviously be reduced by operating several such thrusters in parallel.

The quantity of propellant needed for energy replenishment is much smaller than the payload mass, but it must be delivered to the skyhook centroid. This can be achieved by having the skyhook launch a transport vehicle into an elliptical orbit, after which it uses conventional propulsion systems to perform an orbital transfer maneuver and rendezvous with the centroid. The analysis concludes by demonstrating that it is possible to deliver propellant efficiently to the skyhook centroid.

Skyhook endpoint kinematics is characterized by near uniform circular motion for both the orbit and the rotation. The velocity may be determined by adding the two rotational velocities as illustrated in Figure 3.

$$v\_r = -V\_0 \sin\left(a\right) + L a \sin\left(a + \beta\right) \tag{23}$$

$$v\_{\theta} = V\_0 \cos \left( a \right) - L a \cos \left( a + \beta \right) \tag{24}$$

The triangle in the figure is fully specified, so all angles can be expressed in terms of the skyhook parameters and endpoint radial coordinate. If the payload detaches at a speed less than escape velocity it enters an elliptical orbit with a periapsis, apoapsis and eccentricity given by:

Space Access for Future Planetary Science Missions DOI: http://dx.doi.org/10.5772/intechopen.88530

$$r\_P = \left(\frac{2}{r} - \frac{v^2}{GM\_E}\right)^{-1} (1 - e) \tag{25}$$

$$r\_A = \left(\frac{2}{r} - \frac{v^2}{GM\_E}\right)^{-1} (\mathbf{1} + \mathbf{e}) \tag{26}$$

$$e^2 = 1 - \frac{r^2 v\_\theta^2}{GM\_E} \left(\frac{2}{r} - \frac{v^2}{GM\_E}\right) \tag{27}$$

The transition to a circular orbit can be achieved with a bi-elliptical transfer maneuver [12]. This involves a prograde impulse at apoapsis to increase the periapsis, followed by a retrograde impulse at periapsis to circularize the orbit. The maneuver can be implemented with a series of small impulses over several orbits, but the single orbit procedure serves to illustrate the process. The velocity changes at apoapsis and periapsis are given by:

$$
\Delta V\_A = \sqrt{\frac{2\mathbf{G}\mathbf{M}\_E - \mathbf{Z}\mathbf{G}\mathbf{M}\_E}{r\_A}} - \sqrt{\frac{(1-e)\mathbf{G}\mathbf{M}\_E}{r\_A}} \tag{28}
$$

$$
\Delta \mathbf{V}\_P = \sqrt{\frac{2 \mathbf{G} \mathbf{M}\_E}{R} - \frac{2 \mathbf{G} \mathbf{M}\_E}{R + r\_A}} - \sqrt{\frac{\mathbf{G} \mathbf{M}\_E}{R}} \tag{29}
$$

The initial orbit depends on the skyhook configuration and its orientation when the payload is released. For the nominal skyhook most orbits have a periapsis smaller than Earth radius, necessitating an impulse during the first orbit to increase the periapsis to avoid reentry into the atmosphere. Only a small impulse is needed for this purpose, which can be provided by a conventional rocket. The rest of the orbital transfer maneuver can be achieved efficiently by employing low thrust electric propulsion over multiple orbits.

To illustrate the process consider a vehicle that is released from the skyhook at an orientation angle β ¼ 1:6 radians. It enters an elliptical orbit with periapsis 5550 km and apoapsis 71,400 km. A velocity change of 68 m/s at apoapsis increases the periapsis to 6500 km, sufficient to avoid reentry. This can be provided by a chemical rocket with a propellant mass fraction of 0.03. Subsequent circularization of the orbit at the centroid radius requires a velocity change of about 2.8 km/s which can be provided by electric thrusters with a propellant mass fraction of 0.06. This means a reusable vehicle can be used to transport propellant to the skyhook centroid, with only 10% of the initial mass expended as propellant during the journey.

#### 6. Planetary science

Planetary science and space-based astronomy demand increasingly complex infrastructure, and the high cost of launch limits the scope of experiments. A more efficient launch process would allow larger vehicles to be constructed and more ambitious experiments to be undertaken. The orbital skyhook is a fully reusable launch system with high propellant efficiency, and which can be constructed using current materials technology. It can deliver payloads directly to Earth orbit, or to a trajectory for transfer to lunar orbit.

Access to orbit is the first stage of any planetary science mission. Typically a launch vehicle places the spacecraft and its propulsion system into orbit to await the appropriate time to commence interplanetary transfer. Because of the high launch cost a low energy trajectory is usually employed. This restricts the available launch

flow rate of 60 mg/s [10]. The MPD thruster is a compact and robust device, but it operates most efficiently at high power levels in the order of 1 MW. It is estimated that a practical MPD thruster could achieve a thrust of 2.5–25 N with an efflux

A thruster with efflux velocity VE and mass flow rate m\_ acting at the centroid can

The ratio mP=mo ¼ V0=2VE is the fraction of payload mass that must be reserved for propellant to replenish launch energy. For an efflux velocity of 50 km/s this ratio is 0.07. This means the amount of propellant needed to replenish launch energy is only 7% of the payload mass. With a realistic mass flow rate of 0.4 g/s the time needed to replenish the energy used to launch a 1000 kg payload is about 2 days. This can obviously be reduced by operating several such thrusters

The quantity of propellant needed for energy replenishment is much smaller than the payload mass, but it must be delivered to the skyhook centroid. This can be achieved by having the skyhook launch a transport vehicle into an elliptical orbit, after which it uses conventional propulsion systems to perform an orbital transfer maneuver and rendezvous with the centroid. The analysis concludes by demonstrating that it is possible to deliver propellant efficiently to the skyhook centroid. Skyhook endpoint kinematics is characterized by near uniform circular motion for both the orbit and the rotation. The velocity may be determined by adding the

The triangle in the figure is fully specified, so all angles can be expressed in terms of the skyhook parameters and endpoint radial coordinate. If the payload detaches at a speed less than escape velocity it enters an elliptical orbit with a

<sup>0</sup>=2 for a payload m<sup>0</sup> in a period TR given by:

TR <sup>¼</sup> EL=E\_ <sup>¼</sup> moV0=2VEm\_ <sup>¼</sup> mP=m\_ (22)

vr ¼ �V<sup>0</sup> sin ð Þþ α Lωsin ð Þ α þ β (23) v<sup>θ</sup> ¼ V<sup>0</sup> cosð Þ� α Lωcosð Þ α þ β (24)

velocity of 15–60 km/s [11].

Planetology - Future Explorations

in parallel.

60

Figure 3.

replenish the launch energy EL <sup>¼</sup> <sup>m</sup>0V<sup>2</sup>

Skyhook orbital geometry and payload velocity at detachment.

two rotational velocities as illustrated in Figure 3.

periapsis, apoapsis and eccentricity given by:

window and increases the transit time. With a more efficient launch process it would be possible to use a larger and more capable propulsion system, and thus to allow a less efficient trajectory. This flexibility could be used to deliver a larger experimental payload, conduct more frequent missions, or achieve a reduced transit time.

Applying thrust at the centroid is beneficial because the structure is most robust

at this point and the local acceleration is near zero. It is necessary, however, to transport propellant to the centroid and a mechanism is proposed to achieve this. A transport vehicle is launched by the skyhook into an elliptical orbit, after which it executes an orbital transfer maneuver to rendezvous with the centroid. This process can be accomplished with a high propellant efficiency using available propulsion

The endpoint mass represents the maximum skyhook payload capacity. This envisages the endpoint carrying a docking mechanism of negligible mass that can accept the payload. The skyhook mass scales linearly with the endpoint mass, and so also with the maximum payload. When an initial system has been established it can be used to launch material to add to the structure to increase the payload capacity. This process is likely to be limited by the access vehicle payload capacity, at which

Planetary science requires increasingly elaborate experiments. Improved launch efficiency allows more ambitious missions to be undertaken, with larger propulsion systems to deliver more massive experiments to the planet of interest with sufficient propellant for soft landing on the planet surface. The renewed enthusiasm of national space programs for a return to the moon could provide the incentive for construction of an orbital skyhook to provide efficient transport to and from the moon. This would make it possible to conduct astronomical observations from the moon with a sensitivity far greater than is possible from Earth, and to exploit lunar

point there is no benefit in further increasing the skyhook mass.

Space Access for Future Planetary Science Missions DOI: http://dx.doi.org/10.5772/intechopen.88530

orbit as a base for launching future planetary science missions.

Defence Science and Technology Group, Edinburgh, Australia

\*Address all correspondence to: colin.coleman@dst.defence.gov.au

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

systems.

Author details

63

Colin Sydney Coleman

provided the original work is properly cited.

An emerging ambition of national space programs is a return to the moon, often extending to the establishment of permanent bases on the moon and in lunar orbit. Planetary science is unlikely to be a primary driver of this initiative, but it stands to be a significant beneficiary. For astronomy the moon offers a low gravity environment free of atmospheric and ionospheric effects, Earth based radio emissions, and interference due to the large number of satellites in low Earth orbit. A skyhook launch system that provides efficient transport to the moon would allow astronomical experiments with far greater sensitivity than is possible with terrestrial instruments.

Lunar orbit is also a favorable location from which to launch planetary science missions. It is close enough for easy access but at a significantly higher energy than low Earth orbit. Complex modules constructed on Earth can be delivered efficiently by the skyhook, while fuel and water can be supplied from the moon at a much lower energy cost. Vehicles returning from the moon could dock with the skyhook as it approaches a minimum energy state, using it to decelerate in preparation for a low speed re-entry while also returning energy to the system. The use of an orbital skyhook for efficient transport to and from the moon is therefore a key enabler of future planetary science missions.

### 7. Conclusions

The orbital skyhook derives its advantage principally from using different propulsion technologies in the various physical regimes experienced during a launch. The payload gains energy by momentum transfer from the skyhook, with this energy being later repaid over an extended period. This overcomes the large energy threshold associated with a launch by drawing from a repository and replenishing it efficiently by electric propulsion.

The focus here is on skyhook configurations that allow access at a low speed relative to the Earth. These can be accessed much more easily, but necessarily rotate rapidly to counter the orbital velocity. This means centripetal force dominates the tension, making it is possible to obtain simple expressions for the skyhook mass properties. With a carbon fiber tether the skyhook mass is about 4600 times greater than the endpoint mass, which represents the maximum launch payload. The skyhook mass can be greatly reduced if a stronger tether material were to become available.

Because the skyhook is an extended structure in a non-uniform field, it is subject to forces and torques that vary with orientation. To represent this behavior the skyhook was modeled as a linear structure comprising two masses connected by an inelastic massive tether. The tether mass properties were represented as a compact object at the mass centroid, and a Newtonian formulation used to obtain the equations of motion. These equations were solved numerically to confirm their validity and investigate the dynamics.

Skyhook energy lost during a launch can be replenished by an electric thruster acting at the centroid. The MPD motor is a suitable propulsion technology for this purpose, and was shown to be capable of achieving energy replenishment in a reasonable time with high propellant efficiency. This result holds regardless of the size and efficiency of the propulsion system because the energy transfer process depends only on the efflux velocity and mass flow rate.

### Space Access for Future Planetary Science Missions DOI: http://dx.doi.org/10.5772/intechopen.88530

window and increases the transit time. With a more efficient launch process it would be possible to use a larger and more capable propulsion system, and thus to allow a less efficient trajectory. This flexibility could be used to deliver a larger experimental payload, conduct more frequent missions, or achieve a reduced

An emerging ambition of national space programs is a return to the moon, often extending to the establishment of permanent bases on the moon and in lunar orbit. Planetary science is unlikely to be a primary driver of this initiative, but it stands to be a significant beneficiary. For astronomy the moon offers a low gravity environment free of atmospheric and ionospheric effects, Earth based radio emissions, and interference due to the large number of satellites in low Earth orbit. A skyhook launch system that provides efficient transport to the moon would allow astronomical experiments with far greater sensitivity than is possible with

Lunar orbit is also a favorable location from which to launch planetary science missions. It is close enough for easy access but at a significantly higher energy than low Earth orbit. Complex modules constructed on Earth can be delivered efficiently by the skyhook, while fuel and water can be supplied from the moon at a much lower energy cost. Vehicles returning from the moon could dock with the skyhook as it approaches a minimum energy state, using it to decelerate in preparation for a low speed re-entry while also returning energy to the system. The use of an orbital skyhook for efficient transport to and from the moon is therefore a key enabler of

The orbital skyhook derives its advantage principally from using different propulsion technologies in the various physical regimes experienced during a launch. The payload gains energy by momentum transfer from the skyhook, with this energy being later repaid over an extended period. This overcomes the large energy threshold associated with a launch by drawing from a repository and replenishing it

The focus here is on skyhook configurations that allow access at a low speed relative to the Earth. These can be accessed much more easily, but necessarily rotate rapidly to counter the orbital velocity. This means centripetal force dominates the tension, making it is possible to obtain simple expressions for the skyhook mass properties. With a carbon fiber tether the skyhook mass is about 4600 times greater than the endpoint mass, which represents the maximum launch payload. The skyhook mass can be greatly reduced if a stronger tether material were to become available. Because the skyhook is an extended structure in a non-uniform field, it is subject

to forces and torques that vary with orientation. To represent this behavior the skyhook was modeled as a linear structure comprising two masses connected by an inelastic massive tether. The tether mass properties were represented as a compact object at the mass centroid, and a Newtonian formulation used to obtain the equations of motion. These equations were solved numerically to confirm their validity

Skyhook energy lost during a launch can be replenished by an electric thruster acting at the centroid. The MPD motor is a suitable propulsion technology for this purpose, and was shown to be capable of achieving energy replenishment in a reasonable time with high propellant efficiency. This result holds regardless of the size and efficiency of the propulsion system because the energy transfer process

transit time.

terrestrial instruments.

Planetology - Future Explorations

7. Conclusions

future planetary science missions.

efficiently by electric propulsion.

and investigate the dynamics.

62

depends only on the efflux velocity and mass flow rate.

Applying thrust at the centroid is beneficial because the structure is most robust at this point and the local acceleration is near zero. It is necessary, however, to transport propellant to the centroid and a mechanism is proposed to achieve this. A transport vehicle is launched by the skyhook into an elliptical orbit, after which it executes an orbital transfer maneuver to rendezvous with the centroid. This process can be accomplished with a high propellant efficiency using available propulsion systems.

The endpoint mass represents the maximum skyhook payload capacity. This envisages the endpoint carrying a docking mechanism of negligible mass that can accept the payload. The skyhook mass scales linearly with the endpoint mass, and so also with the maximum payload. When an initial system has been established it can be used to launch material to add to the structure to increase the payload capacity. This process is likely to be limited by the access vehicle payload capacity, at which point there is no benefit in further increasing the skyhook mass.

Planetary science requires increasingly elaborate experiments. Improved launch efficiency allows more ambitious missions to be undertaken, with larger propulsion systems to deliver more massive experiments to the planet of interest with sufficient propellant for soft landing on the planet surface. The renewed enthusiasm of national space programs for a return to the moon could provide the incentive for construction of an orbital skyhook to provide efficient transport to and from the moon. This would make it possible to conduct astronomical observations from the moon with a sensitivity far greater than is possible from Earth, and to exploit lunar orbit as a base for launching future planetary science missions.
