Sun-centred Orbits

Solar sails are ideally suited for long-term inter-planetary missions. Missions which involve a number of different targets are ideal for solar sails that do not have to increase the contained propellant for longer missions. All inter-planetary missions start with the escape from the earth’s sphere of gravitational influence. Once out of the earth’s gravity, the sailcraft is in a sun-centred orbit. The satellite then continues to change its orbit to finally rendezvous with the target planet or orbiting body. The satellite must change its relative orbit velocity to the target to be captured by the target planet’s sphere of gravitational influence.

The optimal relative sun angle for changing the satellite’s orbit was determined by Wie[1, p. 750–751] as

35.26◦. This angle is determined by maximising the force component, which is perpendicular to the unit vector from the sun to the surface of the sail (F⊥S¯⊥, see Figure 2.1). A satellite can increase its orbit

altitude by maintaining the optimal sun angle to produce a solar thrust that increases its linear velocity around the sun. The solar radiation pressure stays constant for a body maintaining an orbit altitude of 1AU

around the sun, but a solar sail in a sun-centred orbit is not bound to this constraint. The solar radiation pressure at a distancercurrentfrom the centre of the sun is derived from the area of a sphere

P (rcurrent) = Ps r _r

earth

rcurrent

, (3.5.8)

wherePsis the solar radiation pressure at 1AU,rearthis the radius of the earth’s orbit or the value of 1AU. This results in an increase in solar radiation pressure when the satellite gets closer to the sun, with the inverse true when moving further away. A simulation containing the sun with all the inner-planets was created to investigate the motion of a solar sail in a sun-centred orbit.

(a) Vector definition of solar sail in sun-centred orbit

−1.5 −1 −0.5 0 0.5 1 1.5 −1.5 −1 −0.5 0 0.5 1 1.5

(b) Top view of solar sails in sun-centred orbit

Figure 3.25 – Solar sail orbiting around the sun

Two high performance solar sails (characteristic acceleration = 0.14 mm/s2 _{were simulated for 2 years}

(730 days) in a sun-centred orbit. Each escaped from an earth-centred orbit. The first satellite kept its sail

ξ = 35.26◦(see definition in Figure 3.25a) to produce a force component opposing its current velocity and the second kept it atξ = −35.26◦ to generate a component to increase the orbit energy of the satellite. The resulting orbits and distances from the sun is shown Figure 3.25b. The green satellite spiralled closer towards the sun and the blue satellite increased its orbit altitude. Figure 3.26 shows a number of scenarios of a solar sail at different angles relative to the incoming photons. Figure 3.26a shows that the altitude change is much more effective when the sail is pointing at35.26◦ to the solar rays than simply pointing straight towards the sun. Pointing straight to the sun does extract the most solar thrust, but does not have a large component in the satellite’s existing velocity vector. The pointing accuracy of the satellite is investigated in Figures 3.26b and 3.26c. The results show that a pointing error of5 − 10◦will not affect the final orbit altitude that much. This pointing performance requirement can easily be achieved by a large spinning solar sail. Figure 3.26d shows that the satellite moving away from the sun is beyond halfway to Mars after two years. Mars is 1.5AU away from the origin of the sun. The satellite reducing its orbit energy has lowered its orbit altitude and is almost at rendezvous distance with Venus.

3.6

Conclusion

A number of concepts for a spinning solar sail satellite that can perform the required manoeuvres to change its orbit altitude has been introduced in this chapter. Two new solar sail concepts were introduced that combines the advantages of spinning and 3-axis stabilised solar sail satellite. The required subsystems to implement such a solar sail in a CubeSat-sized technology demonstrator were discussed. The attitude

0 200 400 600 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Timev(days) Orbitvaltitudev(AU) 35.26deg Sunvvector Velocityvvector

(a) Maximum altitude change

0 200 400 600 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Time (days)

Orbit altitude (AU)

35.26deg 30deg 25deg 20deg

(b) Negative pointing error

0 200 400 600 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3

Orbit altitude (AU)

Time (days) 35.26deg

40deg 45deg 50deg

(c) Positive pointing error

0 200 400 600 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Time (days)

Orbit altitude (AU)

35.26deg −35.26deg

(d) Increase and decrease altitude

Figure 3.26 – Orbital elements of orbit-following control mode

dynamics for the new tri-spin conceptual satellite and the other spinning sail concepts were introduced. A method for adding the non-rigid dynamics by means of the satellite moment of inertia was defined. The dynamics of the non-rigid dynamics due to the attitude dynamics were identified. The simplified model of the non-rigid dynamics was used to analyse the wire dynamics. Numerous parameters that affect the outcome of the wire booms were identified. The analysis concluded that the angular rate of the sail has the dominant effect on the wire boom dynamics. A simulation program was created to investigate the manoeuvres for changing the altitude of an orbit, whereupon the sun-following and orbit-following attitude manoeuvre sets were investigated for a satellite in an earth-centred orbit. A solar sail was placed in a sun- centred orbit and the performance investigated with different pointing angles relative to the incoming photons. The required attitude manoeuvres for an earth-orbiting satellite and a sun-orbiting satellite were identified. The conceptual satellite will deploy its sail and wire booms from a spinning platform. The deployment will have an effect on the attitude of the satellite. Methods for deploying a spinning sail are investigated in Chapter 4.

Chapter 4

Deployment Design and Implementation

4.1

Introduction

The spinning solar sail satellite spins continually. The centrifugal force from this spin can keep wire booms stiff and rigid. Wire booms are advantageous due to the simplicity of their construction, storage and deployment when compared to semi-rigid booms. The rotating wire booms and sail are deployed by deployment mechanisms. In the case of the tri-spin satellite, the rotating mechanism is attached to a motor within the satellite body. In a standard spinning solar sail, this mechanism is attached to the satellite body. The deployment mechanism needs to be compact and deploy the wire booms reliably.

The IKAROS satellite (see §2.3.1) is the only rotating solar sail satellite that has deployed its sail successfully. The method for deploying the sail entailed two phases[12]. The first was the deployment and release of the wire booms. The10 mwire booms were released when the satellite had an angular rate of 20 rpm. The angular rate reduced as the length of the wire booms increased. After the wire booms were deployed completely, the sail clips were released. These clips prevented the deployment of the sail along with the wire booms. Sakamoto et al.[86] discusses the manner in which the sail was attached and folded in its stowed configuration to unfurl successfully. Many of these methods can be applied to deploy other spinning solar sails.

Figure 4.1 – IKAROS deployment procedure[6]

This chapter introduces an active and a passive deployment method. The dynamics of each method are investigated to identify the deployment influence on the rest of the satellite and the deployment controllers that are needed. A mechanism that is designed and built to perform active or passive deployment in an earth environment is discussed and the practical results are compared to the theoretical models. Further experiments to investigate the wire boom dynamics are also presented.