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Fuel consumption for interplanetary missions of solar sailing

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Abstract

The orbits of solar sails can be changed by adjusting the sail’s attitude through external control torques. The resulting momentum will be changed, either provided by a typical attitude control subsystem or by a propellantless device. This paper investigates the extra momentum input and fuel consumption for a typical attitude control subsystem. The minimum-time transfer trajectories are designed for two rendezvous missions using both indirect and direct methods, generating continuous and discrete attitude histories, respectively. The results show that the momentum variation is almost wholly due to the solar radiation pressure. The feasibility of using tip-mounted microthrusters for attitude control is evaluated. The results show that less than 0.1 kg of propellant are required for an interplanetary transfer mission when pulsed plasma thrusters with a specific impulse of 700 s and a thrust of 150 mN are mounted at the tip of a 20 m square solar sail. The fuel consumptions of two transfer missions indicate that a tip-mounted pulsed plasma thruster is a viable technique for the attitude control of a solar sail.

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Abbreviations

µ:

Gravitational constant of the Sun, Nm2/kg

β :

Lightness number of the solar sail, dimensionless

m :

Mass of the sailcraft, kg

t 0 :

Time of sail departing from the Earth, MJD (Modified Julian Day)

t f :

Time of sail arriving at the target body, MJD (Modified Julian Day)

F s :

Solar radiation pressure acceleration, m/s2

R :

Position vector of the sail with respect to the Sun, m

V :

Velocity vector of the sail with respect to the Sun, m/s

λ R , λ V :

Lagrange multipliers of the position and velocity vector, dimensionless

Ψ:

Constraints equations for the sail at initial time

Π:

Constraints equations for the sail at final time

γ 0, γ f :

Lagrange multipliers related to initial and final time constraints, dimensionless

n :

Unit vector along the sail normal, a unit vector

k :

Position and velocity vector of the Earth with respect to the Sun, m

g :

Velocity vector of the Earth with respect to the Sun, m/s

s :

Position and velocity vector of the target object with respect to the Sun, m

a :

Velocity vector of the target object with respect to the Sun, m/s

α :

Pitch angle of the sail normal with respect to sunlight, rad

ᾶ:

Angle measured from λ V to sunlight, rad

δ :

Clock angle of the sail normal with respect to sunlight, rad

θ :

Rotational angle along the sail normal, rad

ψ :

Sphere coordinates of the sail’s position as measured from the equinox, rad

ϕ :

Sphere coordinates of the sail’s position as measured from the ecliptic planes, rad

H :

Hamilton function of the system, dimensionless

e :

Unit vector perpendicular to the sunlight in the plane spanned by sunlight and λ V , a unit vector

A o2b :

Transition matrix from the orbital frame to the body-fixed frame, an orthogonal matrix

ω o2i :

Angular velocity of the orbital frame, rad/s

ω b2o :

Angular velocity of the body-fixed frame relative to the orbital frame, rad/s

ω b2i :

Angular velocity of the body-fixed frame, rad/s

H :

Angular momentum of the sail, kg m2/s

M c :

Control torque, Nm

M s :

Solar radiation pressure torque, Nm

J x , J y , J z :

Moment of inertia, kgm2

η :

Cm/cp offset, m

I M :

Integration of the control torque along the reference transfer trajectory, Nms

I p :

Extra momentum input due to the precession, Nms

I s :

Extra momentum input due to solar radiation pressure torque, Nms

I q :

Extra momentum input due to attitude maneuver, Nms

L :

Moment arm of the thruster relative to the mass center, m

I bit :

Impulse bit the microPPT, Ns

d arm :

Moment arm for the thruster, m

M m :

Maximum control torque of the thruster, Nm

Δm q :

Fuel consumption of attitude maneuver, kg

Δm s :

Fuel consumption for canceling the SRP torque, kg

q :

Unit vector along the rotation axis

κ :

A positive weight constant for minimum-time performance, dimensionless

c :

A positive weight constant for augmented Lagrange method, dimensionless

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  1. School of Aerospace, Tsinghua University, Beijing, 100084, China

    ShengPing Gong & JunFeng Li

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Correspondence to ShengPing Gong.

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Gong, S., Li, J. Fuel consumption for interplanetary missions of solar sailing. Sci. China Phys. Mech. Astron. 57, 521–531 (2014). https://doi.org/10.1007/s11433-013-5236-9

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