Server-sat propulsion, navigation, and orientation

A server-sat is light enough to be significantly accelerated by light pressure. At the earth's distance from the sun, the illumination is 1300 Watts per square meter, on average. The light pressure for absorbed light is the power divided by the speed of light, or about 4E-6 N/m² or 4 microPascal. If the light is reflected, the pressure doubles to 8 microPascal. This is a tiny pressure (sea level atmospheric pressure is 100 kiloPascals) but it is continuous. When pushing on something as thin and light as a server-sat, it can add significant velocity over hours, weeks, and years. The areal density of a 100 micron thick server-sat is 0.233kg/m² , and the albedo of a solar cell is around 0.15, so the acceleration is 1.15x4e-6/0.233 or approximately 20 micrometers/second², or 7 centimeters/minute², or 256 meters/hour², or 20 million kilometers per year² .

Not quite, though. Server-sats are in orbit, and if they are pointed directly at the sun, and they are accelerated directly away from it. That adds to orbital velocity as their orbit takes them away from the sun, but subtracts from orbital velocity as they approach it. If they are tilted in relation to the sun, less area is exposed to light pressure, and the "albedo vector" of reflected light is tilted also, which can add a small sideways thrust.

• The earth rotates towards the east, counterclockwise when viewed from the north pole. It makes 366.24 turns relative to the fixed stars per year, and makes 365.24 turns relative to the sun. Orbits launched from earth also travel east, only faster. On the surface of the rotating earth at midnight, east is in the direction of the earth's orbit around the sun, and on the surface of the rotating earth at noon, the earth appears to be moving west. For the sake of argument, we will assume that the earth is moving east in its orbit. Thus, an object in orbit around the earth is moving towards the sun on the east side of the earth, and away from the sun on the west side of the earth. I may have this backwards compared to some convention, so please add a note and a reference if I goofed this up!

Server-sats need full sunlight for normal operation. If they are tilted 45 degrees sideways, they get 30% less light and must reduce computing and radio functions, but they will still operate. With a 60 degree tilt, they get half power. So if they are turned 60 degrees on the east side of the orbit (moving towards the sun), and 0 degrees on the west (as they move away from it), the average acceleration adding to the orbital velocity is about 1/6th of the possible peak acceleration. For the m288 orbit ( approximately 4 hours sidereal ), the velocity change is 48 millimeters per second per orbit. This seems small compared to the 5590 meters per second of orbital velocity, but after a year of such small increments, the velocity change is more than 100 meters per second.

 *** PROBLEM *** The total velocity change is correct, but it isn't that simple.  Velocity added to the west side of the orbit adds _altitude_ on the east side, not velocity.  Velocity subtracted from the east side reduces altitude on the west side.  While this will average out over a year, it actually screws up stationkeeping and makes the orbit elliptical (perigee on the east, apogee on the west).  This requires more thought!

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Light pressure from LCD thrusters

The version 1 design has three round liquid crystal light pressure thrusters at 120 degree angles around the periphery. These are either black or transparent. They are 10cm in diameter (about 4 inches), and have areas of 8e-3 m^2. When black, an ideal thruster produces perhaps 32 nanoNewtons, and when transparent it produces zero. Assume that the glass makes it somewhat reflective, and the transparency is a bit more reflective, so the thrust may vary between 40nN and 10nN (WAG). If one thruster on one side is fully black, while the other two are clear, the thrusters together produce a moment of 30nN times 20 cm or 6 nanoNewton-meters. If the entire server-sat has a mass of 0.03 kg and an average moment arm of 10 cm, the angular acceleration is 300 microradians per second squared. Accelerating for 24 seconds, then decelerating (applying opposite acceleration) for 24 seconds, will turn the array 10 degrees. Accelerating for 60 seconds, then decelerating for 60 seconds, turns the array approximately 60 degrees (not quite, as the thrusters are moving out of plane and become less effective when turned).

Imagine some perturbation like a collision starts the server-sat spinning on its axis at 1 revolution per second.

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Correcting for tidal forces

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