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| Failed brain fart. | Testing the first server sky thinsat arrays may be challenging - they don't belong in a common orbit, they won't last long below 1000 km altitude due to ram drag. It would be nice to deploy the first tests at M288, but that will require a custom launch. |
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| Testing the first server sky thinsat arrays may be challenging - they don't belong in a common orbit, they won't last long below 2000 km altitude due to ram drag. It would be nice to deploy the first tests at M288, but that will require a custom launch. | If we dispensed thinsats from a GTO transfer orbit with a 622 km perigee ( 7000 km radius ), the atmospheric density could be as high as 4E-13 kg/m^3^ at perigee. Lets assume that we orient the thinsats edge-on to the stream as it passes through perigee, with a ram area of perhaps 20 cm^2^. The perigee velocity is 9.88 km/s, so the drag is 2e-3 * 4e-13 * 9880^3^ or 7.7 e-4 N, 0.15 m/s^2^ decelleration of a 5 gram thinsat. If that level drag occurs within 50 kilometers above perigee ($ r_1 $ =7050 km), then the orbital angle is computed from: $ \large r_1 = a \Large { {1-e^2} \over { 1 + e \cos(\theta) } } $ |
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| But there's a trick. | $ \large \cos(\theta) = { { \Large { { a ~ (1-e^2) } \over { r_1 } } - 1 } \over e } $ |
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| Thinsats can be tested in a highly elliptical orbit above LEO and below GEO. Deploying them as hitchhikers from a GTO bound upper stage would work - except that the perigee of the GTO orbit would be too low. | $ \large \cos(\theta) = { { \Large { { 24582 ~ (1-0.7152^2) } \over 7050 } - 1 } \over 0.7152 } = $ 0.183 radians |
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| What if we used a tether? Ivan Bekey proposed sending shuttle back from the space station by lowering it on a tether, first. The combined two-mass-and-a-string system would orbit around the center of gravity, with shuttle pulled down and ISS pulled up by tides. ISS moves up, going faster than natural orbital velocity, and shuttle is slower. When the tether is released (twang!) the ISS orbit rises, and shuttle reenters with somewhat less velocity than it would otherwise. Spool the tether back into ISS, and do the same thing for the next visit. This could significantly reduce the amount of propellant needed to raise orbit. |
The seconds per radian is $ r_p / v_p $ = 7000 / 9.88 = 708.3 s / radian, so the time spent in the high drag region is 2 * 0.183 * 708.3 = 260 seconds, and the velocity lost for the first pass is about 40 m/s, 9880 to 9840 m/s. For the second pass, the velocity and drag will be smaller, but apogee will drop significantly and more time will be spent in the drag zone. After about 50 orbits, the orbit decays sufficiently that a thinsat will start a fast spiral to burnup, lasting less than a day. If the thinsat loses control, it will decay in perhaps 10 orbits. The experiment will stay in orbit for perhaps 2 weeks. |
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| Well, it might not ''really'' work because that would jerk ISS around, and subject it to "milligravity" that it isn't designed for. And the released tether will get frisky, might break something or even puncture a hole. | This would be a good first test for the first maneuverable thinsat, if we can hitch a 5 gram ride on a GTO transfer vehicle. However, this is far too much drag and buffeting to keep an array assembled by light pressure intact. |
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| But a tether between the GTO stage and a server sky experiment package? We want to reenter the GTO stage, and raise experimental perigee. Doesn't have to be much. | === 24 GHz instead of 70 GHz === |
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| Let's assume the experiment weighs 50 kg and is at the top of the tether, and the empty stage weighs 450 kg and is at the bottom. They are connected by a tether length L, and turning at rate $ \omega $, highest at perigee, lowest at apogee where they will separate. The tidal force in orbit is $ 3 {\omega}^2 \Delta r $, and balances around the center of mass. The experiment is going 0.9 \times L \times \omega $ faster than the center of the GTO orbit. | The 1.25 cm amateur radio band extends from 24.0 GHz to 24.05 GHz, and is barely used. This is near the [[PathAttenuation | 23 GHz water peak]], perhaps .18 dB/km at 7.5g/m^3^ water saturation. At 10 degrees elevation and 7 km lapse rate, that is 7.3 dB attenuation; a factor of 5.3, which might be lousy for ordinary high bandwidth satellite communication, but perfectly adequate for low bandwidth telemetry. |
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| || apogee || perigee || || 42164 || 6700 || km radius GTO || |
=== The $20 Toy Rocket Motor Trick === |
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| Let's raise perigee just enough to make 92 each 5 gram thinsats (V = 3 array) last a couple of months - lets assume that is 922 km altitude perigee (7300 km radius). Assume a carrier that brings the total mass up to a kilogram. Start with a GTO transfer orbit with a perigee of 622 km altitude (7000 km radius), with an apogee velocity of 1640.7 m/s. The test orbit has an apogee velocity of 1692.4 m/s, for a delta V of 29.5 meters per second for one kilogram, the impulse of 30 Newton-seconds. | |
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| Oops. DOESNT WORK, because the apogee omega is so small. We have nothing to spin the pair with, either | That is similar to one Estes E9-4 model rocket engine (30 N-s, 57 grams, 2.8 seconds). Perigee velocity is 5.53 km/s. Let's assume that we are edge on as before. The average air density at 922 km altitude is about 4e-15 kg/m^3^ and that drag occurs within 100 km of perigee; a 30 degree arc, 0.52 radians, 390 seconds of drag time. The normal air density is 4e-15 kg/m^3^. The edge-on drag through perigee is $ A \rho V^3 $, or $ 0.002 * 4e-15 * 9650^3^ or 2.7e-5 N, decellerating the 5 gram thinsat by 5.4e-3 m/s^2^, or 2 m/s per orbit. Circular orbit velocity at that altitude is 7390 m/s, 2260 m/s less than our starting orbit perige, so we would get about 1000 experimental orbits before the altitude starts decaying fast. We will use three more toy rocket motors on the 500 gram carrier at apogee, after thinsat release, to bring the perigee down to 0 km altitude, for reentry. That requires 90 m/s delta V, 45 N-s impulse. Three is overkill, but means we can deorbit the whole predeployment assembly if something goes wrong. |
Hitchhiker Server Sky Test
Testing the first server sky thinsat arrays may be challenging - they don't belong in a common orbit, they won't last long below 1000 km altitude due to ram drag. It would be nice to deploy the first tests at M288, but that will require a custom launch.
If we dispensed thinsats from a GTO transfer orbit with a 622 km perigee ( 7000 km radius ), the atmospheric density could be as high as 4E-13 kg/m3 at perigee. Lets assume that we orient the thinsats edge-on to the stream as it passes through perigee, with a ram area of perhaps 20 cm2. The perigee velocity is 9.88 km/s, so the drag is 2e-3 * 4e-13 * 98803 or 7.7 e-4 N, 0.15 m/s2 decelleration of a 5 gram thinsat. If that level drag occurs within 50 kilometers above perigee ( r_1 =7050 km), then the orbital angle is computed from:
\large r_1 = a \Large { {1-e^2} \over { 1 + e \cos(\theta) } }
\large \cos(\theta) = { { \Large { { a ~ (1-e^2) } \over { r_1 } } - 1 } \over e }
\large \cos(\theta) = { { \Large { { 24582 ~ (1-0.7152^2) } \over 7050 } - 1 } \over 0.7152 } = 0.183 radians
The seconds per radian is r_p / v_p = 7000 / 9.88 = 708.3 s / radian, so the time spent in the high drag region is 2 * 0.183 * 708.3 = 260 seconds, and the velocity lost for the first pass is about 40 m/s, 9880 to 9840 m/s. For the second pass, the velocity and drag will be smaller, but apogee will drop significantly and more time will be spent in the drag zone. After about 50 orbits, the orbit decays sufficiently that a thinsat will start a fast spiral to burnup, lasting less than a day. If the thinsat loses control, it will decay in perhaps 10 orbits. The experiment will stay in orbit for perhaps 2 weeks.
This would be a good first test for the first maneuverable thinsat, if we can hitch a 5 gram ride on a GTO transfer vehicle. However, this is far too much drag and buffeting to keep an array assembled by light pressure intact.
24 GHz instead of 70 GHz
The 1.25 cm amateur radio band extends from 24.0 GHz to 24.05 GHz, and is barely used. This is near the 23 GHz water peak, perhaps .18 dB/km at 7.5g/m3 water saturation. At 10 degrees elevation and 7 km lapse rate, that is 7.3 dB attenuation; a factor of 5.3, which might be lousy for ordinary high bandwidth satellite communication, but perfectly adequate for low bandwidth telemetry.
The $20 Toy Rocket Motor Trick
Let's raise perigee just enough to make 92 each 5 gram thinsats (V = 3 array) last a couple of months - lets assume that is 922 km altitude perigee (7300 km radius). Assume a carrier that brings the total mass up to a kilogram. Start with a GTO transfer orbit with a perigee of 622 km altitude (7000 km radius), with an apogee velocity of 1640.7 m/s. The test orbit has an apogee velocity of 1692.4 m/s, for a delta V of 29.5 meters per second for one kilogram, the impulse of 30 Newton-seconds.
That is similar to one Estes E9-4 model rocket engine (30 N-s, 57 grams, 2.8 seconds).
Perigee velocity is 5.53 km/s. Let's assume that we are edge on as before. The average air density at 922 km altitude is about 4e-15 kg/m3 and that drag occurs within 100 km of perigee; a 30 degree arc, 0.52 radians, 390 seconds of drag time.
The normal air density is 4e-15 kg/m3. The edge-on drag through perigee is A \rho V^3 , or $ 0.002 * 4e-15 * 96503 or 2.7e-5 N, decellerating the 5 gram thinsat by 5.4e-3 m/s2, or 2 m/s per orbit.
Circular orbit velocity at that altitude is 7390 m/s, 2260 m/s less than our starting orbit perige, so we would get about 1000 experimental orbits before the altitude starts decaying fast.
We will use three more toy rocket motors on the 500 gram carrier at apogee, after thinsat release, to bring the perigee down to 0 km altitude, for reentry. That requires 90 m/s delta V, 45 N-s impulse. Three is overkill, but means we can deorbit the whole predeployment assembly if something goes wrong.