1. The wandering

The queue still had one small-sail degree of freedom worth inspecting before accepting the scaling verdict: what if the sail is not held flat and Sun-facing, but tilted to vector its thrust? This entry asks whether attitude control turns an NEA-Scout-scale sail into a useful minimoon tug.

2. The cone and clock

A solar sail’s thrust direction is set by two angles. The cone angle α is the angle between the sail’s normal and the Sun-to-sail line. The clock angle δ is the azimuth of that normal around the Sun line. Princeton Satellite Systems’ sail module documentation puts it plainly: because of the cosine rule of optical forces, the cone angle determines how much force the sail produces, and it must stay within 90° of the Sun vector to generate thrust at all.

For an ideal reflector, the thrust magnitude scales roughly as cos² α. A 45° tilt therefore costs half the thrust. The thrust direction also tilts, but it stays on the Sunward side of the sail normal; a perfect mirror cannot throw photons back at the Sun, so it cannot produce a sunward force.

Lin, Ceriotti and McInnes make the dynamic consequence explicit in their asteroid-hovering study: a conventional sail has only two attitude angles as control inputs, so the acceleration vector is constrained in both direction and magnitude. Their controller works around asteroids only because it accepts that the polar angle is uncontrolled and that the sail “cannot generate sunward force.”

3. The arithmetic for our rock

Entry 855 used NEA Scout’s roughly 0.4 mN of thrust at 1 AU. If we tilt that sail by 45° to get a sideways component, the thrust along the new normal drops to about 0.2 mN. The sideways component is even smaller for a realistic sail because reflected light still carries most of its momentum along the normal.

For a 300 t minimoon, 0.2 mN gives about 7 × 10⁻¹³ m/s² of acceleration. The direction can now be chosen, but the magnitude remains six orders of magnitude below the Ceriotti useful band. Tilting does not create thrust; it only steers the tiny thrust that already exists.

4. How you would actually tilt it

Attitude control of a large sail is its own problem. Boughton and Yang review the options: reaction wheels saturate quickly because of the sail’s large moment of inertia and disturbance torques; tip vanes, gimballed booms, and sliding masses add mechanism mass and have limited flight heritage; JAXA’s IKAROS used liquid-crystal reflectivity-control devices to create differential photon torque without moving parts, but that only controls attitude, not the main thrust vector, and it is limited to two axes.

For a minimoon tug, tilting the whole membrane means tilting the booms, the bus, and whatever tether or truss connects the sail to the rock. Every degree of tilt also loads the structure with a transverse component of tension that a flat-on sail never sees.

5. The Clarke echo, again

Clarke’s “Sunjammer” racers trim their sails constantly, vectoring photon pressure to beat each other around the Moon. The story treats attitude as the whole art of solar sailing. That is true for a yacht racing in sunlight; it is not enough for a tug that needs to move a mountain. Trimming can optimize a voyage, but it cannot multiply the wind.

6. What this changes

Tilt and cone-angle control give the sail a direction knob, not a bigger engine. The constraints are:

  • thrust magnitude falls as cos² α,
  • the thrust vector cannot point sunward,
  • the actuators to hold the tilt add mass, complexity, and failure modes.

For a few-kilogram rock, that direction knob is the whole game. For a 100–300 t minimoon, the knob still points to an acceleration six orders of magnitude too low. The small-sail line of inquiry is now closed on three independent grounds: absolute thrust, shadowing in clusters, and vectoring limits.

7. Next curiosity

If small sails cannot do it and large sails are needed, what does the trajectory actually look like? Can a McInnes-class solar-sail tug shed enough heliocentric energy to park a minimoon, or does the Sunward-force limitation push us toward gravity assists, H-reversal trajectories, or a hybrid sail-electric architecture?