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| Deletions are marked like this. | Additions are marked like this. |
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| == Partial night sky coverage, no night light pollution == | == Semi-complete night sky coverage, some night light pollution == |
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| MORE LATER | This maneuver will put some scattered light into the night sky, but not much compared to perpendicular solar illumination all the way into shadow. In the worst case, assume that the surface has an albedo of 0.5 (typical solar cells with an antireflective coating are less than 0.3) and that the reflected light is entirely Lambertian (isotropic) without specular reflections (which will all be away from the earth). At a 60° angle, just before shadow, the light emitted by the front surface will be 1366W/m^2^ × 0.5 (albedo) × 0.5 ( cos 60° ), and it will be scattered over 2π steradians, so the illumination per steradian will be 54W/m^2^-steradian . Just before entering eclipse, the thinsat will "see" around π^2^/27 steridians of the night sky (WAG), so entire the night sky will receive about 20W of reflected light per m^2^ of thinsats at that 60° angle. |
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| == Complete night sky coverage, some night light pollution == | Estimate that the light pollution varies from 0W to 20W between 90° and 150° and that the average light pollution is 10W for 120\° of the orbit. Since 1/3 of the thinsats are in that band, the light pollution for the entire constellation of thinsats is 3.3W/m^2^ of thinsat. |
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| This maneuver will put some scattered light into the night sky, but not much compared to perpendicular solar illumination all the way into shadow. | The sun is 500,000 times brighter than the full moon, which means the full moon illuminates the night side of the earth with 2.7mW/m^2^ near the equator. A square meter of thinsat at 6400km distance produces 54W/(6×6400000^2^ or 0.22 picowatts per m^4^ times the area of all thinsats. If this is restricted to 5% of the full moon brightness, then we can have 600 km^2^ of thinsat up there, or about 50GW of thinsat at m288. |
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| || time min || orbit degrees || rotation rate || sun angle || || 0 to 60 || 0° to 90° ||$0 ~ \Large\omega$|| 0° || || 60 to 100 || 90° to 150° ||$1 ~ \Large\omega$|| 0° to 60° || || 100 to 140 || 150° to 210° ||$4 ~ \Large\omega$|| 60° to 300° || || 140 to 180 || 210° to 270° ||$1 ~ \Large\omega$|| 300° to 0° || || 180 to 240 || 270° to 0° ||$0 ~ \Large\omega$|| 0° || |
|| time min || orbit degrees || rotation rate || sun angle || Illumination || Night Light || || 0 to 60 || 0° to 90° ||$0 ~ \Large\omega$|| 0° || 100% || 0W || || 60 to 100 || 90° to 150° ||$1 ~ \Large\omega$|| 0° to 60° || 100% to 50% || 0W to 54W || || 100 to 140 || 150° to 210° ||$4 ~ \Large\omega$|| 60° to 300° || Eclipse || 0W || || 140 to 180 || 210° to 270° ||$1 ~ \Large\omega$|| 300° to 0° || 50% to 100% || 54W to 0W || || 180 to 240 || 270° to 0° ||$0 ~ \Large\omega$|| 0° || 100% || 0W || |
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| MORE LATER | == Partial night sky coverage, no night light pollution == In this case, in the night half of the sky the edge of the thinsat is always turned towards the terminator. As long as the thinsats stay in control, they will never produce any nighttime light pollution, because the illuminated side of the thinsat is always pointed away from the night side of the earth. |
Night Side Maneuvers
We can minimize night light pollution, and advance perigee against light pressure orbit distortion, by turning the thinsat as we approach eclipse. The overall goal is to perform 1 complete rotation of the thinsat per orbit, with it perpendicular to the sun on the day-side of the earth, but turning it by varying amounts on the night side.
Another advantage of the turn is that if thinsat maneuverability is destroyed by radiation or a collision on the night side, it will come out of night side with a slow tumble that won't be corrected. The passive radar signature of the tumble will help identify the destroyed thinsat to other thinsats in the array, allowing another sacrificial thinsat to perform a "rendezvous and de-orbit". If the destroyed thinsat is in shards, the shards will tumble. The tumbling shards ( or a continuously tumbling thinsat ) will eventually fall out of the normal orbit, no longer get J_2 correction, and the thinsat orbit will "eccentrify", decay, and reenter. This is the fail-safe way the arrays will reenter, if all active control ceases.
Maneuvering thrust and satellite power
Neglecting tides, the synodic angular velocity of the m288 orbit is \Large\omega = 4.3633e-4 rad/sec = 0.025°/s. The angular acceleration of a thinsat is 13.056e-6 rad/sec2 = 7.481e-4°/s2 with a sun angle of 0°, and 3.740e-4°/s2 at a sun angle of 60°. Because of tidal forces, a thinsat entering eclipse will start to turn towards sideways alignment with the center of the earth; it will come out of eclipse at a different velocity and angle than it went in with.
If the thinsat is rotating at \omega and either tangential or perpendicular to the gravity vector, it will not turn while it passes into eclipse. Otherwise, the tidal acceleration is \ddot\theta = (3/2) \omega^2 \sin 2 \delta where \delta is the angle to the tangent of the orbit. If we enter eclipse with the thinsat not turning, and oriented directly to the sun, then \delta = 30° .
MORE LATER
Full power night sky coverage, maximum night light pollution
MORE LATER
Semi-complete night sky coverage, some night light pollution
This maneuver will put some scattered light into the night sky, but not much compared to perpendicular solar illumination all the way into shadow. In the worst case, assume that the surface has an albedo of 0.5 (typical solar cells with an antireflective coating are less than 0.3) and that the reflected light is entirely Lambertian (isotropic) without specular reflections (which will all be away from the earth). At a 60° angle, just before shadow, the light emitted by the front surface will be 1366W/m2 × 0.5 (albedo) × 0.5 ( cos 60° ), and it will be scattered over 2π steradians, so the illumination per steradian will be 54W/m2-steradian . Just before entering eclipse, the thinsat will "see" around π2/27 steridians of the night sky (WAG), so entire the night sky will receive about 20W of reflected light per m2 of thinsats at that 60° angle.
Estimate that the light pollution varies from 0W to 20W between 90° and 150° and that the average light pollution is 10W for 120\° of the orbit. Since 1/3 of the thinsats are in that band, the light pollution for the entire constellation of thinsats is 3.3W/m2 of thinsat.
The sun is 500,000 times brighter than the full moon, which means the full moon illuminates the night side of the earth with 2.7mW/m2 near the equator. A square meter of thinsat at 6400km distance produces 54W/(6×64000002 or 0.22 picowatts per m4 times the area of all thinsats. If this is restricted to 5% of the full moon brightness, then we can have 600 km2 of thinsat up there, or about 50GW of thinsat at m288.
The orientation of the thinsat over a 240 minute synodic m288 orbit at the equinox is as follows, relative to the sun:
time min |
orbit degrees |
rotation rate |
sun angle |
Illumination |
Night Light |
0 to 60 |
0° to 90° |
0 ~ \Large\omega |
0° |
100% |
0W |
60 to 100 |
90° to 150° |
1 ~ \Large\omega |
0° to 60° |
100% to 50% |
0W to 54W |
100 to 140 |
150° to 210° |
4 ~ \Large\omega |
60° to 300° |
Eclipse |
0W |
140 to 180 |
210° to 270° |
1 ~ \Large\omega |
300° to 0° |
50% to 100% |
54W to 0W |
180 to 240 |
270° to 0° |
0 ~ \Large\omega |
0° |
100% |
0W |
The angular velocity change at 0° takes 250/7.481 = 33.4 seconds, and during that time the thinsat turns 0.42° with negligible effect on thrust or power. The angular velocity change at 60° takes 750/3.74 = 200.5 seconds, and during that time the thinsat turns 12.5°, perhaps from 53.7° to 66.3°, reducing power and thrust from 59% to 40%, a significant change. The actual thrust change versus time will be more complicated (especially with tidal forces), but however it is done, the acceleration must be accomplished before the thinsat enters eclipse.
Partial night sky coverage, no night light pollution
In this case, in the night half of the sky the edge of the thinsat is always turned towards the terminator. As long as the thinsats stay in control, they will never produce any nighttime light pollution, because the illuminated side of the thinsat is always pointed away from the night side of the earth.