2.1

Launch

The launch accelerations are summarised in the Ariane V launcher manual,⁴ where it is clearly stated that the longitudinal acceleration does not exceed 4.55g (value met at solid boosters’ burnout) and the transverse accelerations do not exceed 0.25g. These values were the ones experienced by the JWST, but future spacecrafts will use different launchers like the new version of the SLS, already selected for the Luvoir launch. The available data for these new generation launchers are scarce and focused on specific mission profiles like lunar missions where they suggest lower accelerations that those generated by the Ariane V. Because of this, the data of the Ariane V have been used.

The accelerations act differently on the shells according to the launch configuration inside the fairing. Referring to the launch configuration of the JWST and the expected one of Luvoir, the strongest longitudinal acceleration would be transferred to the shells as a force acting approximately on the plane of the shell surface, similarly to a shear force. This force tries to make the shell slide away from the reference body along the flight direction. The transverse accelerations act both on the shell surface and perpendicular to it.

Another interesting analysis refers to the dynamical environment generated by the launcher. It is well described in the Ariane V user manual and can be used to evaluate the response of the shell to the vibration loads, but more importantly to this study, to compute the constraint forces to keep the shell in position.

2.2

Orbital manoeuvres during interplanetary transfer

Referring to the JWST mission profile, the orbital transfer from Earth to the L2 libration point included three distinct orbital manoeuvres to carefully tune the trajectory and precisely enter the designed operational orbit around L2, as discussed in the paper by Petersen et al.⁵ and shown in Fig.1 extracted by the aforementioned paper. This paper reports the results of a Monte Carlo simulation to evaluate the ΔV to grant the desired orbital path considering the uncertainties related to the engine performance and thrust times. As a result, the manoeuvres are defined in terms of statistical distributions of the thrust times ΔT and ΔV. The variation of the ΔT is less effective than that of the ΔV, leading to the decision of using the mean ΔT and the worst-case scenario ΔV to compute the accelerations. This introduces a great simplification in the acceleration computation that avoids statistical considerations but still provides meaningful results, shown in Tab.1. A 5% margin over the maximum ΔV is applied to make the computations even more robust. The actual computation of the accelerations is the simple ratio between the total ΔV and the ΔT, that has as reasonable - and likely true - assumption that the manoeuvre is performed at constant engine thrust.

Figure 1.

Representation of the deep space transfer orbit from Earth to the L2 operational orbit. The maneouvres are identified as Mid Course Corrections (MCC). Picture from the work of Petersen et al.⁵

Table 1.

Accelerations generated on the JWST during the Mid Course Correction Manoeuvres (MCCs). Values computed starting from.5

These acceleration values are specific to the JWST mission since its data can be retrieved by literature. The deep orbital manoeuvres for future missions will very likely be different, but the many similarities between JWST and future telescopes like Luvoir lead to the expectation of accelerations in the same order of magnitude for these types of space missions. However, the direction of the forces generated by these accelerations on the shells may change significantly depending on the relative direction of the thrust vector with respect to the shells during manoeuvres. The definitive direction of these forces can be known only once the attitude profile during the deep space transfer is fully defined.

Finally, the vibration profile to evaluate the dynamic loads is not available in the literature for this phase of the mission. Also, future telescopes like Luvoir may employ systems that decouple the dynamic environment of the spacecraft from that of the telescope, making this evaluation potentially completely useless. However, the vibrations induced by the chemical thrusters - if these are used - are for sure way lower than those generated during launch, causing less issues.

3.1

Station keeping manoeuvres

JWST must perform station keeping (SK) manoeuvres every 21 days in order to maintain its designed halo orbit around L2. The total foreseen ΔV for the whole operative life of 10.5 years is of 24.88 m/s. This translates in around 2.37 m/s yearly and consequently around 0.14 m/s per SK manoeuvre, according to the work of Dichmann et al.⁶

Information about the burning time for this operation can not be found and it has been hypothesized based on the fact that MCC2 can be considered as the first station-keeping operation. A linear assumption based on the acceleration has been carried out according to the following equation, where the assumption of constant thrust during the whole station keeping manoeuvre holds:

The direction of this acceleration is variable with the attitude of the spacecraft and of the shell with respect to the thrust direction. Due to the agility and the re-pointing capability of Luvoir, this acceleration may act along all possible directions - tangential to the shell surface or perpendicular to it, with all possible combinations -. The worst case scenario is probably when the acceleration acts completely tangential to the shell, but a comparative analysis shall be performed among the various loading conditions to quantitative find the worst case operative scenario and use it for the constraint system design.

A note shall be done: the computations of the acceleration follow a linear assumption based on MCC2 strategy that may result relatively far from reality, especially on a quantitative level. However, the resulting operative time for a SK single manoeuvre looks realistic. In the case of Luvoir, the value of the needed ΔV will be probably larger due to its bigger dimensions that directly influence the effect of the solar radiation pressure on the orbit and consequently on the actions to counteract it and on the frequency of the momentum damping manoeuvres. SK thruster can also have higher specific impulse leading to shorter burning time and higher accelerations. However, the order of magnitude of SK accelerations previously computed should be realistic and reliable to preliminary dimension a retaining system. Anyway, the computation using real SK strategy data and associated attitude shall be used for a high-fidelity evaluation of the SK accelerations on the shells.

3.2

Slew manoeuvres

Precise values of the attitude accelerations acting on the JWST can be found in the work by Karpenko et al.⁷ related to optimization methods for attitude control and slewing speed. These values are summarised in Tab.2, directly extracted from the previously cited paper and they give a clear idea of the order of magnitude of the applied accelerations and consequent times for slewing.

Table 2.

Agility parameters of the JWST according to different modelling and optimization techniques, data extracted from the work by Karpenko et al.7

Literature gives also some interesting information about Luvoir, especially on its strategies to maximise the coverage of the anti-Sun hemisphere. A presentation by Dewell et al.⁸ places a clear requirement on the repointing performance of Luvoir, which shall access any location in the anti-sun hemisphere in a maximum of 45 minutes with 30 minutes as the design goal. This, together with the geometry of the telescope and especially the distance from the center of rotation, is enough to compute the in-plane accelerations acting on the mirrors that shall be counteracted in order to avoid the misalignment of the magnets and the consequent loss of performance or of the shell. The gimbaling system of Luvoir permits a pitch movement of 90° of the primary mirror and of the tower where the instruments are mounted - discussed in the paper by Tajdaran et al.⁹ -, as shown in Fig.2. However, the gimbal performance and its acceleration cannot be found in literature. The values for this acceleration are nevertheless computed considering the data related to the JWST listed in Tab.2 combined with the operative time requirements enlisted in the work by Dewell et al.⁸ The roll motion is not considered since it would expose the telescope to the sunlight and it would rarely happen and at negligible angular accelerations. Based on the images of the Luvoir telescope, some dimensions of interest can be retrieved. Also, considering that yaw rotation happens around the central point of the whole spacecraft – a very plausible assumption derived from a symmetric AOCS configuration-, the maximum distance between the primary mirror and the centre of the rotation is R_y ≈ 2.7m. Same reasoning for the pitch rotation but considering that it happens at the gimbal point, the distance between the center of rotation and the primary mirror is then R_p ≈ 5.45m. These distances are highlighted in Fig.3. All the data are now available to evaluate the linear accelerations acting on the mirror due to yaw (a_y), pitch (a_p) and the combined acceleration (a_t) increased by a 10% margin to compensate for the unknowns related to the pitch rotation and to the AOCS system of Luvoir. This is a very serious worst-case scenario – probably even not feasible due to the limitations of the attitude control system - since all the accelerations are at their maximum at the same time.

Figure 2.

Representation of the gimbal rotation of Luvoir to improve the accessibility time to the complete anti Sun hemisphere. Here the rotation is up to 60° but the maximum capability is of 90°, making the main mirror pointing straight to Nadir. Picture from the work of Tajdaran et al.⁹

Figure 3.

Representation of the distances of the primary mirror from the center of rotations of the Luvoir telescope. Picture elaborated starting from the final design report of Luvoir.¹⁰

To grant the full coverage of the observable hemisphere, the slew capability shall grant a yaw slew range of 180° and a pitch rotation of 90°, both shall happen in a 30 minutes time window. Based on the assumption of a linear angular motion at a constant acceleration and deceleration - uniformly accelerated angular motion -, some iterations to define the yaw angular acceleration led to the following values:

is the maximum angular velocity during the yaw rotation,. Using the uniformly accelerated angular motion assumption,it is possible to compute the acceleration times t_acc and the time spent at constant angular speed t_ω to verify that the time constraint of 30 minutes is respected:

As discussed earlier, the pitch rotation of the telescope is performed with the gimbal rotation of the telescope alone. The computations related to its angular acceleration are performed like those of the yaw computation. is the maximum angular velocity during the yaw rotation, . Again, t_acc and t_ω for the pitch rotation can be computed to verify that the time constraint of 30 minutes is respected.

Finally, the linear accelerations acting on the shells can be computed. The maximum acceleration due to yaw rotation is computed in Eq.(1), the one related to pitch in Eq.(2), where the 10% margin is added. In Eq.(3), the composed acceleration when the shells are subjected to both the yaw and pitch accelerations is computed.

The computed total acceleration a_p represent the absolute worst case scenario. The related acceleration is the one that shall be counteracted to avoid any sort of misalignment between the shells and their main bodies during the slew manoeuvres. Because of the geometry of the system, these accelerations act on the shell surface and not perpendicular to them, on a first approximation where the primary is considered as flat. The generated forces are shear forces that make the shell slide away from the reference body and a constraining system shall be considered to avoid this effect.