It is now considered whether any significant benefit can be obtained for the mission from un-powered gravity assists. Multiple gravity assists within the inner solar system tend to be prolonged in duration and can be limited in launch window frequency, especially if considering non-resonant combinations. We therefore anticipate that any benefit will occur through use of a single gravity assist maneuver, probably at Venus, as this will allow for a perihelion inside the Venusian orbit. Use of a Mars or Earth fly-by would result in a high aphelion, which is detrimental to solar sailing. Furthermore, it is envisaged that sail deployment will commence only after the final gravity assist, due to navigational difficulties with such a large structure and inaccurate pointing control due to sail flexing. The delayed deployment of the sail will avoid the need for accurate sail navigation and control during the gravity assist, but would require some additional propellant on the spacecraft bus for trajectory correction maneuvers, probably within the AOCS hydrazine budget. Furthermore, the significant level of available launch C3 means that sail deployment prior to a Venus fly-by would have negligible impact on the duration of this transfer.
Launching on 27 December 2017 we perform a 2883 km Venus fly-by 142 days later on 18 May 2017, placing the un-deployed solar sail on a 0.73 AU × 0.52 AU × 18 deg orbit. Following sail deployment on this orbit the primary trajectory goal is to circularize the orbit at 0.48 AU. During orbit circularization it was found that the orbit inclination can be increased slightly with no degradation on the circularization goal, so that the sail arrives on an orbit of 0.48 AU × 0.48 AU × 22.32 deg after 195 days, 337 days after launch. Note that this trajectory analysis was performed using AnD blending, a method which blends locally optimal control laws and allows a more rapid analysis than traditional methods.19 -, 20, 21,22 Each control law is prioritized by consideration of how efficiently it will use the solar radiation pressure and how far each orbital element is from its target value. It has been demonstrated that trajectories found with AnD blending are very similar or better than those found using traditional trajectory optimization methods.Error: Reference source not found, Error: Reference source not found On arrival at the circular 0.48 AU orbit the locally optimal inclination control law is once again used to raise the orbit inclination. The complete orbit transfer duration is 4.13 years from the Venus fly-by, giving a total flight time from launch of 4.52 years. An un-powered Venus gravity assist can thus provide a saving of 0.4 years for a reduced sail acceleration of 0.4 mm s-2. Thus, the use of a Venus gravity assist can as anticipated offer some potential benefits over a conventional mission profile, although the saving in transfer time and sail performance appear modest. This option was not selected as the reference trajectory as at this stage of analysis it was felt a conservative estimate of solar sail technology requirements was required. Moreover, the technological challenge of stowing a sail for approximately 150 days in the space environment prior to an autonomous deployment at 0.6 AU slant range was considered significant, furthermore it was considered problematical to emulate in a technology demonstration mission in-order to reduce the risk. Note, the slight reduction in sail size would be somewhat offset by the increase in required spacecraft mass due to the increase in propellant mass; this was not modeled here. It is noted however that a Venus gravity assist provides some benefit and thus remains a valid option during future analysis.
Fast Mission Option
An alternative mission option would be to employ a 3 phase strategy, to reach a 0.48 AU polar orbit more rapidly. The cranking orbit was set at 0.30 AU, with the minimum solar radius also constrained at this distance. A slight increase in the characteristic acceleration to 0.5 mm s-2, with an increase in the mass of the thermal sub-system, means the sail side length is of order 200 m. The increased launch mass results in a maximum available C3 of 27.9 km2 s-2. The optimized, positive C3 inward spiral time (coplanar) was found to be 320 days. The orbit then cranks up to 82.75° in 706 days. The third phase was then optimized to spiral outwards from the cranking orbit to the final orbit radius of 0.48 AU, in 110 days. The total trip time to polar orbit was 3.11 years, for this fast-mission option, however savings could be made by removing the coplanar transfers. Figure 9 shows the entire 3 phases of the trajectory. While this option offers a significant time saving, the increased risk and cost of a prolonged stay at 0.3 AU, coupled with the increase in sail size meant this option was considered sub-optimal.
The problem of obtaining the correct phasing at arrival on the solar polar orbit was deemed to be best tackled by selecting an arrival date and position on the solar polar orbit that is correctly phased with the Earth. Then the analytical cranking control law was used to propagate the trajectory over a negative time-span, thus reducing inclination. The resultant orbital elements were then used as the initial conditions for a further reverse optimization, back to Earth. Integration over a negative time-span has been used for low-thrust trajectory optimization in the past, for example the early SMART-1 mission studies,23 however it has not previously been used to generate correctly phased solar polar orbits. The arrival position was selected as the north solar pole, with the Earth-Sun-sail angle at 90 deg. The Earth was found to be at this azimuth angle in the early hours of 07 June 2015 (Universal Time), which was thus defined to be the SPO arrival date, allowing for an approximate Earth departure date in 2010.
For a characteristic acceleration of 0.42 mm s-2, the spacecraft is launched on 16 May 2010, with a positive launch excess energy of C3 = 38.84 km2 s-2, the maximum available from a Soyuz Fregat 2-1b from Kourou. A constraint was placed on the minimum solar radius of 0.48 AU. The optimal sail spiral down to the cranking orbit is inclined to 14.42 deg in 457.5 days. This intermediate orbit has a semi-major axis of 0.4828 AU and an eccentricity of 0.0762 AU. The analytical cranking then takes place from 17 August 2011, raising the inclination to 82.75 deg at a circular 0.48 AU solar polar orbit in 1390 days. The complete trajectory is shown in Figure 10, where the total transfer duration is 5.06 years. The maximum Earth-spacecraft distance is 1.654 AU, which is well within the maximum cruise mode slant range of the TT&C system, Table 3.
Figure 10 0.42 mm s-2 reference mission solar polar orbit trajectory
On arrival at the target orbit the sail is jettisoned as discussed earlier. A high fidelity trajectory model was used to propagate the solar polar orbit over 2 years with perturbations from the all the planets out to and including Saturn. As expected the orbital elements deviate by a negligible amount from the nominal values, with the maximum Earth-spacecraft distance found to be 1.45 AU, which is within the maximum science mode and space weather mode slant ranges of the TT&C system, Table 3.
Competing Propulsion Options
The delivery of a spacecraft into a solar polar orbit is a challenging mission concept, as has been seen by the inability of the Solar Orbiter mission to attain a solar polar orbit with current SEP technology.Error: Reference source not found The velocity change requirement to attain a solar polar orbit with chemical propulsion is of order 42 – 56 km s-1, depending on N. Thus, chemical propulsion alone cannot provide a solar polar orbit and we must consider the use of gravity assist maneuvers. In order to reach an aphelion within the Earth’s orbit we must restrict fly-bys to the terrestrial planets. However, the small mass of these planets means that the time to a polar orbit is unrealistically high.
The elimination of both conventional SEP and chemical propulsion as competing systems restricts our analysis to new and novel propulsion systems, such as nuclear electric propulsion (NEP), radioisotope electric propulsion (REP) or Mini-Magnetospheric Plasma Propulsion (M2P2). It is expected that any NEP system will require a large launch vehicle due to the inherent nature of the system, thus eliminating the use of a Soyuz-Fregat vehicle. Meanwhile, the use of a REP system would require extremely advanced radioisotope power sources to compete with solar power. For example, if we replace the solar arrays with an advanced radioisotope power systems (ARPS) of the same mass we would require a power density of 13.5 W kg-1. However, if we add in a 5 kW electric propulsion system the solar array mass rises to just under 80 kg, for a total array surface area of 20 m2, which would require an ARPS specific mass of over 50 W kg-1 in order to match the power mass budgets. M2P2 could potentially provide the required change in velocity needed to attain a true solar polar orbit. This concept is akin to solar sails, but has the advantage of not requiring large structures to be deployed. The drawback to this propulsion method is that the magnetic field generating system mass may be quite high. The lack of viable competing propulsion systems serves to highlight the potential of solar sailing for a solar polar mission concept. We thus conclude that solar sailing offers great potential for this mission concept and indeed may represent the first useful deep space application of solar sail propulsion.
Variation of Minimum Solar Approach Radius
We see from Figure 3 and Figure 7 the effect of varying the minimum solar approach radius on spacecraft mass and transfer duration to the polar orbit. Using the extensive parametric trajectory data set generated we can estimate sail characteristic acceleration requirements for a given minimum solar approach radius and trip time to the 0.48 AU solar polar orbit, for a launch C3 of zero. Thus, by combining sail characteristic acceleration requirements, spacecraft mass and minimum solar approach radius we can quantify the global effect of varying the minimum solar approach radius. During this trade we assume 2 μm CP-1 sail film substrate and 50 g m-1 main sail booms, along with the sail design scaling discussed earlier and the spacecraft masses in Figure 3.
Figure 11 shows the effect of varying the minimum solar approach radius on sail side length. We note that despite the significantly increased spacecraft mass required to survive such a severe thermal environment a minimum sail side length occurs for a minimum solar approach radius of 0.33 – 0.34 AU depending on desired mission transfer duration. A 5-year transfer trajectory can thus be attained with a sail of side length 150 m and minimum solar approach radius 0.34 AU. A similar trade was performed for launch mass versus minimum solar approach radius. It was found that the minimum launch mass varied from 0.34 – 0.36 AU, for trip time 3 – 5 yrs respectively. Thus, the minimum sail size does not provide for a minimum launch mass. However, the launch mass of the minimum sail size configuration for a 5 year transfer was less than 620 kg, the lower bound limit of the Soyuz Fregat 2-1b from Kourou and as such optimizing the launch mass can be considered secondary to sail size optimization. The use of a positive launch energy within this paper allows for a reduction in sail size towards the same value as an optimal (minimum sail size) architecture C3 = 0 launch.
Figure 11 Minimum solar radius versus sail size for 5-yr (…), 4-yr (--) and
3-yr (-) trip times to 0.48 AU solar polar orbit
A Solar Polar Orbiter mission concept has been presented as a Technology Reference Study. The mission utilizes a Soyuz Fregat 2-1b launched from Kourou. The low launch mass of 532 kg, including margins allows for maximum launch energy to be used, providing the sail with an initial Earth C3 in excess of 38 km2 s-2. The use of positive C3 and a single Venus fly-by were shown to reduce the sail performance requirements, though the later was not adopted. The mission primary propulsion system was defined a priori as solar sailing and we find that the required sail is 153 × 153 m for the baseline 5-year transfer mission scenario. However, sail size can be reduced through closer solar approaches despite the significantly increased spacecraft mass required to survive the increasingly hostile environment at low solar radii. Optimal close approach radii were presented to minimize launch mass and sail size, all of which were above 0.3 AU. A comprehensive trajectory study was completed and, for the first time, a trajectory generated to an accurately phased and positioned orbit.
The solar sail and spacecraft technology requirements have been addressed. The sail requires advanced boom and new thin-film technology. The sail was found to be at a low technology readiness level requiring significant further effort. By contrast the spacecraft requirements were found to be minimal, as the spacecraft environment is relatively benign in comparison with other currently envisaged missions. However, the spacecraft design was found to vary in some key areas from a non-sail delivered mission due to, for example, sail pointing accuracy limiting the communications system to X-band and below. Overall, the technology requirements for a Solar Polar Orbiter mission have been clearly identified.
This study was conducted under contract “ESTEC 16534/02/NL/NR: Technical Assistance in the Study of Science Payloads Transported Through Solar Sailing". The authors thank Henry Garrett of the Jet Propulsion Laboratory of the National Aeronautics and Space Administration (JPL-NASA) for his input into the study of potential cruise phase science issues regarding sail interactions with the space environment.
4 Professor, Department of Mechanical Engineering, Member AIAA
5 Science Payload and Advanced Concepts Office, ESTEC
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