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| If we dispensed thinsats from a GTO transfer orbit with a 622 km perigee ( 7000 km radius ), MORE LATER | 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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| $ \large \cos(\theta) = { { \Large { { a ~ (1-e^2) } \over { r_1 } } - 1 } \over e } $ | |
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| $ \large \cos(\theta) = { { \Large { { 24582 ~ (1-0.7152^2) } \over 7050 } - 1 } \over 0.7152 } = $ 0.183 radians | |
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| 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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| === But there's a trick. === | 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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| 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 is too low. Raise it, just enough to make 92 5 gram thinsats (V = 3 array) last a month or two - lets assume that is 1322 km altitude perigee (7700 km radius). 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 1708.7 m/s, for a delta V of 68 meters per second, an impulse of 31 Newton-seconds. | === The $20 Toy Rocket Motor Trick === |
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| That is similar to one Estes E9-4 model rocket engine (30 N-s, 57 grams, 2.8 seconds). Of course, we would want a custom engine with a much slower burn, lighter casing, etc. | 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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| Perigee velocity is 5.53 km/s. Let's assume that we are in full area ram drag for 80% of the orbit perigees, and edge-on for 20% of the orbit perigees, and that drag occurs within 200 km of perigee; a 42 degree arc, 0.73 radians, 5600 kilometers at an apogee velocity of 9357 m/s, 600 seconds. | That is similar to one Estes E9-4 model rocket engine (30 N-s, 57 grams, 2.8 seconds). |
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| Air drag - Larson and Wertz tells us that mean density at 1250 km is 1.11e-15 kg/m^3^, and 5.21e-16 kg/m^3^ at 1500 km. Let's assume 1e-15 kg/m^3 at 1322 km altitude, edge on for 20% of the orbits, and ram drag for 80% of the orbits. The average drag through perigee is $ 0.8 A \rho V^3 $, or $ 0.8 * 0.025 * 1e-15 * 9357^3^ or 1.64e-5 N, decellerating the 5 gram thinsat by 3.3e-3 m/s^2^, or 2 m/s per orbit. | 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. |
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| Circular orbit velocity at that altitude is 7195 m/s, 2162 m/s less than GTO, so we would get about 1000 experimental orbits before the altitude starts decaying fast. | 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.
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.