European Solar Polar Orbiter Mission

Variation of Sail Systems Technology Parameters

The sail design specifications in Table 5 assume a 2 μm CP-1 film substrate and main sail booms of specific mass 65.2 g m^-1. We can examine and quantify the effect of varying these parameters, allowing technology requirement specifications to be more accurately defined. We note that during this trade we fix the main boom specific mass at 50 g m^-1 when investigating sail film variations and fix the sail film as 2 μm CP-1 while examining main boom specific mass variations. All other parameters in Table 5 vary according to there relationship with the sail size, for example as sail size increases the mass of sail film coatings will also increase.
The variation of boom specific mass linearly alters the sail size and mass. We note from the trajectory analysis later in this paper that the current launch C₃ sets a maximum launch mass of 620 kg, which corresponds to the minimum Soyuz Fregat 2-1b launch mass from Kourou. Increasing the boom specific mass to 150 g m^-1 we find that the total launch mass, including an ESA system level margin of 20 % is 620 kg. Consequently, to maintain the current mission architecture and time-line, for a 2 μm CP-1 film substrate the maximum boom specific mass is 150 g m^-1, giving a sail size of 165 m.
The variation of sail film substrate material will have negligible impact on the sail system mass as most polyimide films have very similar densities. We therefore quantify the effect of varying substrate thickness for CP-1 film and PET film only, as these two substrates represent the opposite ends of the spectrum. Note however that different polyimide films have significantly different thermal properties and as such can impact the allowed minimum solar close approach. We find that the use of 4 μm PET film results in a sail of side length 174 m, while the use of 5 μm CP-1 film results in a sail size of 198 m. Furthermore we note that 1 μm film, such as a commercially available Mylar film, would require a sail side length of only 140 m. Figure 5 shows the effect on sail mass and launch mass as sail substrate thickness is increased. We note that with an upper launch mass limit of 620 kg we can define the required sail film thickness as 3.2–3.4 μm, depending on film material, for a boom specific mass of 50 g m^-1. Recall a boom specific mass of 65 g m^-1 is ultimately selected along with 2 μm CP-1 film.

Figure 5 Sail film substrate thickness variation versus sail mass and total launch mass. Each pair of lines corresponds to CP-1 and PET film.

Sail / Spacecraft Separation

Following arrival at the 0.48 AU polar orbit we require to perform a sail separation maneuver prior to initiation of the science phase of the mission. The AOCS propellant budget contains 2.2 kg of hydrazine specifically for sail separation and avoidance maneuvers. On separation from the spacecraft the sail characteristic acceleration increases to 0.98 mm s^-2 due to the reduction in non-reflective mass. Modeling the separate sail and spacecraft trajectories we find that the separation distance increases at approximately 1 km per minute, assuming no propulsive burn is performed by the spacecraft and that the sail remains passively stable at a setting of zero pitch to the Sun. It is thus possible that the spacecraft may not require the use of its separation and avoidance propellant contingency to initially separate from the sail. However, if we continue to propagate the two trajectories we find that the sail and spacecraft would go by within 100 km of each other when they both pass over the northern ecliptic pole for the 1^st time, again assuming the sail remains passively stable at a setting of zero pitch to the Sun. It is however likely that the sail will begin to tumble sometime after separation from the spacecraft, as it is now uncontrolled. These initial calculations thus suggest that the spacecraft may only require the use of its separation and avoidance propellant contingency to perform sail avoidance maneuvers once the sail begins to tumble but not immediately following sail separation. As sail separation is clearly a key technology issue these initial findings must be further challenged and should be demonstrated in early sail technology demonstration missions.

Launch Configuration and Visualization

Assuming a 2 μm CP-1 film sail substrate and 65 g m^-1 main sail booms we can investigate the launch configuration and investigate launch fairing compatibility with the Soyuz Fregat 2-1b vehicle. Figure 6 shows that significant volume is available for systems growth and no launch fairing compatibility issues are anticipated. Figure 6 shows the SPO spacecraft on top of the sail deployment box, with the sail booms also shown in their stowed configuration. The main sail booms stow to between one and two percent of there deployed length.Error: Reference source not found The sail film is stowed within the central compartment of the deployment box, revealed only after boom deployment.

Figure 6 Launch configuration and visualization

Trajectory Analysis

We recall that the target solar polar orbit is defined as inclined at 82.75 deg with a right ascension of 255.8 deg plus 0.014 deg yr^-1 from J2000, within a standard ecliptic plane reference frame. Further, it is desirable that the polar orbit be correctly phased with the Earth to aid mission science returns and avoid solar conjunctions.
Transfers to solar polar orbits have been analyzed in parametric studies by Sauer and briefly by Leipold.^{15, 16} After a short optimized spiral to a zero or low inclination circular orbit at the defined minimum solar approach radius, an analytical control law that maximizes the instantaneous rate of change of inclination is utilized to rapidly increase orbit inclination.Error: Reference source not found Following Sauer,Error: Reference source not found we have adopted a multi-phase approach to the trajectory structure. Closer cranking orbit radii enable more rapid acquisition of polar inclinations, and a third outward spiral phase may be necessary to reach the first few resonant orbits (specifically, N = 1, 2, 3).
The variational equations of the modified equinoctial orbital elements are explicitly integrated using an adaptive step-size, variable order, Adams-Moulton-Bashforth method. The thrust vector direction has been defined by two angles to completely cover the outward hemisphere of allowable orientations. These are the pitch angle, , between the sail normal and the Sun-line and the clock angle, , between the projection of the sail normal and a reference direction onto a plane normal to the Sun-line. A direct, parameter optimization scheme was implemented with the controls specified at discrete nodes at the segment boundaries, equally spaced in time between zero and the terminal time. The controls were characterized across each time segment by linear interpolation between the nodes. As the number of nodes was increased then a close approximation to a continuous profile was achieved. Problems requiring more revolutions, or more rapid control variation (usually for lower accelerations) clearly needed more segments. 50 segments (51 nodes) were considered sufficiently accurate to represent the optimized trajectories in this paper. The trajectory optimization problem is to select the variables that minimize the transfer time (objective function) whilst satisfying the end-point boundary conditions (constraints). This was transcribed to a Non-Linear Programming (NLP) problem, solved using NPSOL 5.0, a Fortran77 package based on Sequential Quadratic Programming (SQP).¹⁷ SQP employs a quasi-Newton approximation to the Karush-Kuhn Tucker conditions of optimality, resulting in a sub-problem of minimizing a quadratic approximation to the function of Lagrange multipliers incorporating the objective and constraints. Optimality termination tolerance was set to 2  10^-4, with the constraint feasibility tolerance at 6.69  10^-6. This ensured that final boundary conditions were satisfied to within 1000 km for each position element and to within 0.2 m s^-1 for each velocity element without performing excessive iterations. NPSOL is a gradient-based, deterministic, local search procedure and therefore requires an initial guess for the cone and clock angle profiles and transfer time that is within the proximity of the actual solution, ensuring a feasible solution is obtained. This was established using homotopy methods to map the initial guess to the final answer.¹⁸