What is the minimum altitude required for a Cubesat*-like object to orbit around the Earth? Could you initiate an orbit inside the Earth's atmosphere?
*A CubeSat is a 10 cm (1 liter) cube with a mass of no more than 1.33 kilograms.
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$\begingroup$ Arguably, the ISS orbits "inside the atmosphere" since it has to be boosted every once in a while. Most people consider it outside the atmosphere, but it is not a definite line $\endgroup$ – gillonba Nov 3 '14 at 22:39
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The answer varies with atmospheric density (due to varying solar activity), with satellite geometry and mass, and with attitude. But for a typical 3U cubesat, the minimum altitude for a circular orbit to complete at least one revolution is approximately 150 km.
My colleagues and I collected the following orbital data from a cubesat we were operating:
The vertical jumps on the graph are where the orbit model was updated with new ranging measurements. We last made contact with it at 145 km altitude, about 40 minutes prior to its final destruction.
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7$\begingroup$ The 150 km is about right. Assuming a spherical cubesat (sorry, couldn't resist), and a mean atmosphere, I get an initial altitude over the equator of 142 km to get an orbital lifetime of one orbit. As noted, this can vary quite a bit due to solar activity, as well as diurnal effects and a semiannual variation. $\endgroup$ – Mark Adler Nov 4 '14 at 4:34
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$\begingroup$ I would add that the maximum altitude would also vary (slightly) with the density of the satellite - a "satellite" of solid lead would last longer than a hollow aluminum one, since the kinetic energy of the satellite varies linearly with the mass, while the force exerted by drag is going to be the same for same-size/shape satellites. Of course, the lead one will take a bigger rocket (or more fuel) to get into orbit... $\endgroup$ – Kirkaiya Nov 4 '14 at 22:12
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$\begingroup$ Indeed, ballistic coefficient is very important. This is what I was getting at by saying that the answer depends on mass and geometry. $\endgroup$ – pericynthion Nov 4 '14 at 22:21
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$\begingroup$ Nice answer. However, isn't a 3U Cubesat specifically not your typical Cubesat. Those launched by universities are usually 1U, aren't they? $\endgroup$ – ChrisR Nov 4 '14 at 23:57
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$\begingroup$ More 3Us have been launched than 1Us by this point... the difference in ballistic coefficient (which also depends on deployables) is likely to be lost in the noise of atmospheric density variations anyway. $\endgroup$ – pericynthion Nov 5 '14 at 1:35
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Here's a quick database exercise based on TLE data for the FLOCK 3U Cubesat constellation. I took the last published elset for each of the 28 objects and calculated the apogee & perigee:
Perigee: 162.6 +- 13.2 km
Apogee: 175.1 +- 14.8 km
Lots of caveats here. Tracking can get sketchy near decay, and sensor coverage can vary alot from rev to rev. So it's not clear how many revs were left for these objects. I'd look at this as a rough upper bound. pericynthion's data is based on last operator contact, so will be more accurate.
An aside, but something that threw me for a bit when looking at this was the launch date. Event though the FLOCK satellites went up on an Antares in Feb of 2014, they were deployed from ISS. So they were assigned the international designator (1998-067*) and launch date (1998-11-20) for ISS. Something to keep in mind when working with this data. The catalog numbers are sequential, the rest of the stuff can surprise you.
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$\begingroup$ One important point is that the definition of "altitude" can vary - is it apogee/perigee radius minus earth radius (of which you can choose equatorial, polar or mean radius)? Is it the minimum and maximum geometric height above the geoid surface? Above ground level? Further, interpreting Space Track TLE data can be quite a black art. Their identifications are not always correct, and nor are there TLEs. I'm working on a paper on the topic :) $\endgroup$ – pericynthion Nov 3 '14 at 23:07
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$\begingroup$ Agree on all counts. I'm using a and e derived from the mean elements (which isn't really correct either) minus the WGS72 equatorial radius (6378.135 km). Given the magnitude of the major sins, I omitted some of the smaller ones. And trust me, I've seen some ugly stuff in TLE data. $\endgroup$ – CoAstroGeek Nov 3 '14 at 23:15
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2$\begingroup$ In case you'd like somewhat higher quality data on the Flock satellites, check out ephemerides.planet-labs.com (but we don't optimize our orbit fit for the last couple of days of life, nor do we always try hard to make contact over the last hours) $\endgroup$ – pericynthion Nov 4 '14 at 21:57
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Theoretically - You could orbit at any height, as long as the lowest point of your orbit doesn't hit the Earth...
Your problem is that an orbit within the atmosphere has quite a bit of drag (minor understatement) so it will decay really quickly, and with a lot of spectacular light and sound.
For a Cubesat, and in fact any satellite you want to complete at least one orbit, you are really going to have to be outside the atmosphere.
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3$\begingroup$ Depends how you define "outside the atmosphere" I guess. Lot's of LEO stuff operates in a regime of significant atmospheric drag. $\endgroup$ – CoAstroGeek Nov 3 '14 at 20:03
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$\begingroup$ Very true. I like peri's answer for that useful data# $\endgroup$ – Rory Alsop Nov 3 '14 at 20:32
