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| That is 95 degrees from vertical. The GPS satellites are in a 12 hour orbit, which is GEO radius (42164 km) times (12/24)^^2/3^^ or 26562 km. If $/alpha$ is the angle off nadir (the line between the satellite and the center of the Earth) then by the law of sines $ \sin( \alpha ) / 26562 ~ = ~ \sin( 95\degrees ) / 6371 $ so $ /alpha = 15.4 \degrees $. | That is 95 degrees from vertical. The GPS satellites are in a 12 hour orbit, which is GEO radius (42164 km) times (12/24)^2/3^ or 26562 km. If α is the angle off nadir (the line between the satellite and the center of the Earth) then by the law of sines sin(α)/26562 = sin(95°)/6371, so α = 15.4°. |
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| This [[attachment: | Lockheed document ]] specifies the SSV (space service volume) out to $23\degrees$ for the L1 channel and $26\degrees for the L2 and L5 channels. More to learn, but by phase-comparing the signals from antennas on the sides of a cubesat sized satellite, it should be possible to estimate angular orientation to the strongest GPS satellites; crude orientation from the direction to the strongest average signal (for detumbling), and precision orientation to the strongest available satellite with more sophisticated CDMA signal selection for specific satellites. As a backup, some phototransistors can also help with detumbling. | This [[attachment: | Lockheed document ]] specifies the SSV (space service volume) out to 23° for the L1 channel and 26° for the L2 and L5 channels. More to learn, but by phase-comparing the signals from antennas on the sides of a cubesat sized satellite, it should be possible to estimate angular orientation to the strongest GPS satellites; crude orientation from the direction to the strongest average signal (for detumbling), and precision orientation to the strongest available satellite with more sophisticated CDMA signal selection for specific satellites. As a backup, some phototransistors can also help with detumbling. |
Orienting small satellites with GPS
GPS Block IIf and GPS III satellites are specified to light up the Earth out to 5 degrees from edge of earth (EoE). That is 95 degrees from vertical. The GPS satellites are in a 12 hour orbit, which is GEO radius (42164 km) times (12/24)2/3 or 26562 km. If α is the angle off nadir (the line between the satellite and the center of the Earth) then by the law of sines sin(α)/26562 = sin(95°)/6371, so α = 15.4°.
This Lockheed document specifies the SSV (space service volume) out to 23° for the L1 channel and 26° for the L2 and L5 channels. More to learn, but by phase-comparing the signals from antennas on the sides of a cubesat sized satellite, it should be possible to estimate angular orientation to the strongest GPS satellites; crude orientation from the direction to the strongest average signal (for detumbling), and precision orientation to the strongest available satellite with more sophisticated CDMA signal selection for specific satellites. As a backup, some phototransistors can also help with detumbling.
see papers at http://www.lockheedmartin.com/us/products/gps/gps-publications.html