Orbit considerations


#1

I understand the reason for choosing a low earth orbit, but the problem with such an orbit is that the sat will only be “visable” in the target region for about 20 minutes, only about 6 of which will be at a useful broadcast angle because of the increased density of atmosphere from a low angle of reception (relative to the listening node) In order to improve the broadcast time over the target area, perhaps a moderately eliptical orbit should be considered. Something like a molniya orbit, but with a shorter period. If the apogee dwell time can be extended to 30 minutes or an hour, this would both reduce the problems with doplar shifting and potentially reduce the demands on the target zone tracking requirements of the cubesat.


#2

The 6 minute broadcast time is probably about right, depending on orbit, but it is also a function of distance rather than atmospheric density or antenna angle (Horizon is always there!). A higher orbit would just make the range problem worse. Twice the range requires four times the power. Legal power is an issue.


#3

I understand that, but an eliptical orbit would significantly improve the sight time without too much of a free space loss hit.


#4

An actual Molniya Satellite’s orbit has a maximum altitude of near 40,000 km.That is a considerably larger distance than a slant range of 1000 km. The path loss is therefore about 32 dB greater. (ie 1600 times the power required).

One thing that is not intuitively obviius is that the altitude of a cubesat is only about 500 km, while the orbital radius (nearly circular) is 6870 km, so to get much eccentricity in the orbit, you really add a considerable amount of altitude over the surface.


#5

Well, I’m not talking about an actual Molniya orbit. I’m talking about considering a slightly elliptical orbit to improve line of sight times over the target areas.


#6

Molniya orbits work because they are synchronous - they dwell over the same part of the earth - high latitude Russia, not visible from geostationary orbit… A LEO satellite with a higher, slower apogee will mostly do so uselessly over the ocean, many times per day, and will zip through the sky faster when it is near perigee.

There are three tradeoffs with LEO and MEO satellite altitudes which must be addressed:

  1. The tradeoff between visibility and power divided by bitrate . The higher the satellite, the more ground it can see at one time. For > 20 degree elevation above the horizon, and 300km (ISS altitude) there must be 350 satellites to have an average of one in the sky. Assuming no maneuvering to stay in a tight constellation, the number actually visible will follow a Poisson distribution, so with an average of one, there will be none 37% of the time. For 98% availability, there might need to be an average of 5 in the sky, 1700 total satellites. The maximum distance to a satellite 20 degrees off the horizon is 764 kilometers. The maximum distance I can see an omnidirectional wifi access point is about 100 meters - given inverse square law, this would need 7640^2 or 60 million times the power. If the power is divided by factor X, so is the bit rate.

  2. The tradeoff between orbit drag and radiation dose. The atmosphere tapers off exponentially, but even at ISS altitudes the station must be reboosted many times per year or it will drop and re-enter. At higher orbits, there is less atmosphere and drag, but the radiation from the lower van Allen belt increases rapidly.

  3. The tradeoff between payload fraction and orbit crowding. Higher orbits require more delta V and a lot more rocket to get to. So most satellites orbit as low as possible. Which means it is crowded there, mostly with dead satellites that are hard to locate, because they are not visible for very long from earth radar.

  4. There’s also a tradeoff between inclination and collision rate and closing velocity. Higher inclinations can be seen further north, but that means more north/south velocity. The maximum is for satellites orbiting over the poles - two satellites approaching the pole from opposite directions will smash at nearly twice orbital velocity, creating a huge cloud of shrapnel. This is not theoretical - the 2009 collision between Iridium 33 and the derelict Cosmos 2251 was nearly head-on. Predicted miss distance? Almost a kilometer. Accuracy of prediction? Plus or minus a kilometer. Such near-misses happen many times per week, and even with better tracking, active satellites have limited maneuvering fuel.

That’s some of many reasons why most comsats are in higher orbits, with active thruster control and high gain antennas. The antennas and multikilowatt transmitters are needed to talk to lots of customers.

There are other ways to do satellite constellations - see server sky, where I explain many of these things in detail. I provide all the technical details that I can, and have presented them at 20 conferences and in half-a-dozen papers.

There’s no point to hiding anything - if you don’t share the details, the international telecommunications union won’t let you launch it. They set the rules which the member states (almost all countries) enforce (with military force if necessary). Those member states have carved up ownership of geosynchronous orbit - don’t even think you can put anything there without buying an orbital slot that has a big comsat in it now.

I will be on the east coast at the end of June - anyone want a presentation?

Keith Lofstrom, server sky


#7

BTW, all orbits precess because of the equatorial bulge, creating a non-symmetric gravity field. That means an orbit’s ascending node (where it crosses the equatorial plane towards the north) and argument of perigee (the perigee angle) rotates in relation to the fixed stars. Sun-synchronous orbits are arranged so that the precession matches the earth’s yearly orbit around the sun - useful for earth observation at the same time every day. The precession is a function of orbit inclination and eccentricity. Even the moon’s orbit precesses.

Of course, orbits are in relation to the fixed stars, not the turning earth, which does not affect satellites, except for dragging the magnetic field that traps the van Allen belt through the orbit, and a very, very tiny relativistic effect called frame drag, shifting earth orbits by centimeters per century.

So a non-synchronous orbit’s apogee will have no relation to the ground underneath, except that both are functions of time.

Even a circular orbit, such as geostationary orbit for comsats, is not really stationary. Neither the sun nor the moon are in the same plane as the rotation of the earth, bobbing above and below over the year and the month. This puts a small amount of tidal drag on comsats, adding inclination to their orbits and pulling them out of line of sight of all the millions of high gain antennas pointing at them from the ground. Comsat operators fix this by continuously firing high ISP, low fuel consumption xenon ion thrusters to counter the tidal force, almost a hundred meters per second of delta V per year, consuming significant power. The limited fuel on board a comsat determines its maximum lifetime, though radiation degradation of the solar panels and technological obsolescence are more important limits. Those orbit slots (typically one degree wide) are worth billions of dollars per year to operators, they put their most profitable assets in them.

For a good explanation of these orbital effects and many other things, I strongly recommend “The Space Environment and Its Effects on Space Systems” by Vincent Pisacane. You will need to know far more to build, launch, and operate satellites, but Pisacane is a great start.