# [amsat-bb] Re: Path to HEO

James Duffey jamesduffey at comcast.net
Sun Apr 28 20:34:47 PDT 2013

```Well I did a rough back of the envelope calculation for the time required to accumulate the energy necessary to get from LEO to HEO, but there are a lot of details that still need to be calculated. And the devil is in the details. But this will get things started

The difference in orbital energy between a LEO and GEO is about 25 MJ/kg. So, for a 10 kg nano sat, we would need to supply at least 250 MJ. Now I suspect that when all is said and done, it cannot be done for that, but I haven't done any detailed orbital transfer calculations.

OK, suppose we have Nick's 50 Watt solar panel, and lets also say that initially half of that power can be put into propulsion, the other half being needed for navigation, housekeeping, comm, and telemetry. You could probably get away with more for propulsion.

So say we need to generate at least 250,000,000 (it is probably more) Joules of energy to get from LEO to HEO. The solar panel can supply 25 Watts or 25 Joules per second. so it will take 10,000,000 seconds to generate the 250MJ required.

Now the satellite is only illuminated for roughly half an orbit, so we need to double the time to 20,000,000 seconds on orbit. Now there 31,536,000 seconds in a year, so it would take 231 days to accumulate the minimum amount of energy to get to GEO.

Well, I neglected inefficiencies in the system, such as the ability of the ion-thruster to convert electricity into thrust and how efficiently the batteries or capacitors can be charged and store energy. I also ignored the drag at lower latitudes, which may be considerable. I suppose that one could only operate the thrusters while the spacecraft is illuminated and that would eliminate the storage problem. Say the whole system is 50% efficient, and I am guessing here, that would make it 462 days, or 15 months.

I suppose that whether or not that is a long time, depends on your point of view. I'll bet if the transfer burn strategy is calculated it gets even worse. Things seldom get better. You can't do a simple Hohmann transfer, but would need to do multiple burns, or a continuous burn over the illuminated part of the orbit. I suppose that would produce an orbit that is not really circular at any given time but it might all average out over all the burns. A constant burn may be more efficient in terms of energy use that a Hohmann; I don't remember. I do remember that one wants to burn at apogee to get the biggest bang for the buck, and I suspect that the illuminated portion of the orbit is not always at apogee, so the energy will not be used efficiently.

Now a GEO orbit, while a desirable goal, is not necessarily what is needed for amateur radio communication. Something short of GEO, and even elliptical would still be useful and only require repointing of the antenna from day to day, and perhaps hour to hour at Apogee. Orbits significantly higher than LEO, but lower than GEO are also very useful. Compare for example the available time per pass between ISS and AO-7, and for that matter the RS10, 11, 12 and 13 birds.

One would need to plan how to go through the Van Allen belts, as with such a slow burn one would spend a lot of time where the radiation is high.

All of this is not meant to be a rigorous calculation, but rather just an indication of whether it is reasonable, and if it is worth pursuing further. It does to seem to be within the realm of possibly, and probably should be pursued further, at least until a real show stopper shows up. - Duffey KK6MC

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KK6MC
James Duffey
Cedar Crest NM

On Apr 28, 2013, at 3:34 PM, Franklin Antonio <antonio at qti.qualcomm.com> wrote:

> At 11:14 AM 4/28/2013, Nick Pugh wrote:
>> I have just returned from a satellite conference and I think new technology
>> will now give us a path to HEO.
>
> I've thought for a long time that ion engines (small thrust pushing for a long time, powered by electricity) could be of great value to us.
>
> Has anyone done the calculation to see how long it would take to go from LEO to HEO with an achievable ion engine?  This seems like the first thing to calculate.  If it takes less than 1 year, it seems worth serious investigation.
>
> There are many other hurdles, of course, such as attitude control (keeping solar panels pointed at the sun while at the same time keeping engine pointed in the direction we want thrust, over a long period of time).  The schemes and compromises for these issues can be worked if the basic thrust math works out.
>
> N6NKF
>
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