Tesseract Inc.
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Omnimapper Architecture.
Orbital Mechanics and Earth Coverage
Imaging the entire earth’s surface from space requires launching satellites into high-inclination, low earth orbit. The company Eurockot Launch Services provides such a service and has a mission planned for 2016 which could insert our constellation of CubeSats into an orbit of 98.750 inclination and altitude of 824km. Evenly spaced along this orbit, 25 CubeSats will effectively cover the globe every day and provided high resolution imagery of the earth’s surface.
Each satellite will have an orbital period of 101 min and complete roughly 14.2 revolutions in one day. Figure 1 shows the satellite track for a single satellite.
The payload onboard each of the 25 satellites is the 80 Megapixel iXU Aeriel Camera system with a 110mm zoom lens. At an altitude of 824km, this camera system will provide 22 m resolution imagery of roughly 32,000 km^2.
Including 25 evenly-spaced satellites on this orbit will allow these frames to be stitched together and provide complete coverage of the earth as shown in Figure 4.
Downloading Satellite Imagery
Mapping all 197 million sq. miles of the earth with less than 22 meters of resolution on a daily basis generates an immense amount of data that needs to be transmitted to earth-based receivers. Engineers at Tesseract Inc. have found a cost effective solution for this problem.
The 25 CubeSats are able to map the entire earth’s surface daily with a grand total of 16800 high-resolution pictures. These pictures are then compressed and transmitted back to earth.
Each CubeSat completes 14 revolutions each day and takes 48 pictures per revolution. To allow for the quick transmission of images, each CubeSat talks to one of the seven earth stations along its path each revolution. Thus this requires a total of 84 Earth Stations. These Earth Stations are strategically positioned around the globe and transmits data to a central hub that does additional processing.
The number of Earth Stations was calculated as follows:
Altitude of Cube satellite = 824km
Time taken for 1 Revolution = (Arc Length @ 120 Degrees*)/Orbital Velocity = 2029 seconds/Revolution
HPBW of the Earth Station = 16 degrees
Time window for transmission = (Arc Length @ HPBW)/Orbital Velocity = 271 seconds
Number of Pictures taken per second = 13/second
Size per Picture = 80 MB (uncompressed)
Size per Picture = 4 MB (compressed)
Total Pictures per Revolution = Time taken for 1 Revolution/Pictures per second = 48 Pictures/Revolution
Total Data Size per Revolution = Size per Picture * Total Pictures per Revolution = 196608 kB /Revolution
Down Link Data Rate for the Earth Station = 1 Mbps = 125 kBps
Total Time Taken to transmit 48 pictures/Revolution = 1572 seconds
Number of Earth Stations required per Satellite per Revolution = ceiling (1572/271) = 6 Earth Stations/Revolution
Number of Revolutions: 14
Total Number of Earth Stations required per satellite = 6 * 14 = 84 Earth Station/Satellite
Total Number of Satellites = 25
Allowing each of the 84 earth-based receivers to actuate side to side will allow them to cover all 25 satellites as they pass overhead one-by-one.
*: During the course of a single day, the CubeSat does not capture images for more than 12 hours, as half the Earth is in the dark. Also additionally 1/12 of the Earth is at Dusk and another 1/12 of the Earth is at Dawn - both of which are sub-optimal light conditions. As a result, only 1/3 of the Earth is photographed every day i.e. 120 degrees.