How do we currently compensate for the gravitational effects of the moon on GSO satellites?
The more persistent problems for a geostationary orbit is the non-sphericity of the earth:
Geosynchronous Orbit
A geosynchronous orbit is an orbit that has the same period (single revolution) that is equal to the time it takes the Earth to complete one revolution about its axis (one sidereal day). A sidereal day is measured with respect to the stars as apposed to the sun (one solar day). This is approximately 23 hours and 56 minutes. The semi-major axis for a circular orbit that has this period is approximately 42,164 kilometers and a mean altitude of approximately 35,790 kilometers above mean sea level. One of the unique features of this orbit is that as the inclination approaches zero (stays on the equator) and the orbit is circular, the object orbiting will stay over the same location on the Earth due to the fact it is moving at the save speed as the Earth is turning under it. This special type of geosynchronous orbit is called aGeostationary Orbit (stationary with respect to the surface of the Earth). As the inclination increases for a geosynchronous orbit, the ground trace of the orbit on the Earth plots a figure eight (8) pattern.
A more in depth discussion of geostationary orbits
First, from the above paragraph, you may have deduced that a geosynchronous orbit is not necessarily a geostationary orbit. However a geostationary orbit must be a geosynchronous orbit. These terms are often used interchangeably since most geosynchronous orbits are also geostationary. However, that is not always the case. It is the zero (0) degree inclination that makes it that special orbit called the geostationary orbit.
I used the term sidereal day for describing geosynchronous orbits. How do we measure a day? Usually we measure it in reference to the sun being in the same position from one day to the next (i.e. noon to noon). However, that is not the same time it takes the Earth to rotate once on its axis. Remember the Earth is also in orbit around the sun requiring it to travel just a tiny bit further in its rotation for the same spot on the Earth to be pointing towards the sun each day. This is the difference between the Mean Solar Day (our normal 24 hour day) and the Sidereal Day. The difference is approximately 4 minutes per day.
For a geosynchronous orbit, this orbit must be synched to the actual rotation period of the Earth (sidereal day). Even though a satellite is place in a near geostationary orbit upon launch there are forces that act upon the satellite that increase the orbital inclination. Remember an inclination of zero (0) for a geosynchronous orbit is also a geostationary orbit. The primary cause of this is that the equatorial plane is coincident with the ecliptic. So both the sun and the moon slowly over time increase the satellites orbital inclination. Also since the Earth is not a true sphere, the geosynchronous satellites drift (in-track) towards two stable equilibrium points over the Earths equator. This is why station keeping is required for geostationary satellites. Satellites are typically maintained within a band that is approximately 0.10 degrees. When station keeping is no longer possible (all the fuel is used) or there is a satellite malfunction, most geostationary satellites are boosted into a higher orbit (end of life orbit boost) so they will not drift into an area where another geostationary satellite is operating.
Here is another non-intuitive repositioning delta-v. For a geostationary satellite, you fire the thrusters in the same direction you want the vehicle to move. What is happening is you are changing the velocity of your vehicle that directly correlates to Kepler's third law. So if you fire the thrusters away from (behind) the direction of flight, causing the satellite to increase its altitude just a tiny bit, its velocity in respect to the velocity of the surface if the Earth will actually be slower. This allows the Earth to turn underneath it faster and the satellites subpoint (the point directly below the satellite) will move westward (or backwards in the same the direction you fired the thrusters).
If you fire the thrusters in the direction of flight (eastward), the satellite will drop to a lower orbit causing it to speed up relative to its subpoint and it will move relative to the surface of the Earth in the direction you fired the thrusters once again.
With only two firings (this is a Hohmann transfer orbit BTW) you can reposition a geostationary satellite.
Now that we are this far along, how about a little chat on satellites and spacecraft since they have been in the news recently:
Since the Earth is not a perfect sphere (it is an Oblate Spheroid), satellites drift from their predicted position due to the Earths non-spherical shape. Also at low Earth orbits, the atmosphere creates a drag on the satellite also causing a drift (perturbation) in its orbit. At higher altitudes, such as a geosynchronous orbit, the solar wind and effects from the moon are more pronounced. This requires us to update the ephemeris periodically.
Satellites (and spacecraft) are incredibly precise machines with exquisite craftsmanship. The life of a satellite is often computed by the onboard fuel requirements. For geostationary satellites, periodic maneuvers (delta-Vs) must be accomplished to keep them on station. This is also required for many lower orbiting satellites as well. For an orbit plane change (move it into a different orbit), mass must be ejected to move the satellite.
Note: Super geek alert #1:
The Hohmann transfer orbit is the most energy efficient (minimum energy solution) way of getting from one circular orbit to a higher or lower circular orbit. This type of transfer orbit is used by interplanetary spacecraft to travel to the other planets in our solar system.
Now that we have a better understanding of its orbital position, we need to concentrate on its pointing (Attitude Control).
Why do we need to worry about pointing? If the satellite has solar panels (arrays), they need to point towards the sun to provide power. Sensors need to point at their respective targets, such as a star sensor, sun sensor etc. Thermal and possible contamination consideration must be taken into effect when pointing also.
Remember for every action there is an equal and opposite reaction. So if I spew mass (jet of gas out of a thruster nozzle), the satellite will move in the opposite direction. Also if I spin a wheel onboard the satellite, the result will be the satellite spins in the opposite direction.
Since fuel is precious and usually cannot be replenished (called consumables), other methods of pointing were devised that did not require mass ejecta from the satellite. Spinning reaction wheels were one. If you have orthogonal reaction wheels, just by spinning them you can provide precise pointing. Unfortunately, external forced (perturbations) adds unwanted momentum to the wheels. To compensate (unload momentum from the wheels) for this, I have seen both low-level monopropellant jets or torque rods used for this purpose.
Note: Super geek alert #2:
A monopropellant is one that does not require an oxidizer to function. Usually monopropellants are composed of a liquid compound called Hydrazine (N2H4). When this liquid comes in contact with a platinum catalyst, it is decomposed into gaseous ammonia (Nh3), nitrogen and hydrogen. This gas is then ejected (fired thru a nozzle) out a jet to providing motion for the satellite or spacecraft.
An ingenious method of unloading momentum without the use of fuel was devised using simple electromagnets. Remember the Earth is surrounded by a magnetic field (why your compass works). If you attach orthogonal electromagnets on your satellite and turn them on, the resultant field interacts with the Earths field causing a torque on the satellite. These are what are known as Torque Rods.
Since the reaction wheels, gyros, and torque rods all work using electricity and the solar arrays provide that electricity, theoretically the life of the satellite is indefinite. Unfortunately, there are degradations of the thermal coatings, blankets, sensors, and failures of both the gyros and reaction wheels that ultimately limit the life of any satellite.
Over a period of time, these degrade to the point that the satellites can no longer function within design spec. At some point, you either have to replace the satellite, repair it, or say farewell.
Or are there lunar hurdles other than this that would be showstoppers?
The bigs are the Moon will tend to pull the loop in a crosstrack direction and the Earth in an intrack direction. I don't see how this can remain stable.
Thanks for the reply. It is a very good in-depth read that I found quite informative. One question, though...
It seems that the biggest problem in maintaining a stable geostationary orbit in light of the pull of the moon is fuel limitations. Considering that a space elevator would by its very nature be able to refuel its positioning thrusters cheaply and in quantities that would allow even brute force orbital adjustments to be feasible, would this still be an insurmountable obstacle?