Philip,

Probably.

All craft on the geostationary ring experience perturbations. Firstly, solar radiation pressure - and depending on the a/m (and albedo) of your proposed craft, these perturbations could easily drive you far from the desired station.

Other perturbations (gravitaional harmonics, luni-solar effects, etc.) are present - but for 0° inclination orbits at least your nodes won't regress (see a doctor if they do). BUt a brief Google - to supplant my 20+ year knowledge says, 

"http://onlinelibrary.wiley.com/doi/10.1029/92JE00032/abstract"

May I ask what sort of craft you are proposing? The a/m will be the kicker for this project I suspect.

A 1 to 3 meter inert, rotating sphere with high albedo is needed simply as a scatterer.  The goal would be to monitor the solar irradiance of the earth by measuring light scattered from the sphere in direct comparison with photometric stellar standards- standard stars of about 8-10 magnitude.   About 0.1 milli-magnitude precision is needed (1 part in 10^4 of the flux). This is done already for stars from the ground.   Such a "fake sun" at the antisun point could be used in principle for decades to monitor the solar irradiance, earth's albedo (when observed near the horizon) and it could be used for other purposes too.  I call this the most boring satellite ever launched.  The orbital stability is of first importance, and we would not want any contaminants such as from station keeping motors.  A very simple idea, too simple?

Philip

Am I right that the primary mission is to scatter sunlight reflected from the Earth, i.e. the measured light takes the path A: Sun - Earth - Satellite - Earth? This sounds like it might be difficult to arrange given the difficulty in distinguishing light from path A from that of "pollution" from path B: Sun - Satellite - Earth.

You hint at a secondary mission to monitor solar irradiance,  presumably taking path B. This might be easier because the polluting contribution from path A will be rather smaller than the other way around, though you could just measure it directly without the scattering satellite in the way.

Back to the orbits, neither of these scenarios seems particularly demanding, unless I have missed something.

1.  As James mentioned A/M will have an effect, for which the heavier the satellite the better, but it will mainly increase eccentricity without changing the orbital period.

2. There are two zones for which longitude is relatively stable, at 75E and 105W, but the precise motion around the stable point is more complex.

3. Inclination and RAAN will both precess  starting off at about a degree a year though as the abstract that James cited points out, if you can tolerate an inclination of  ~7.5degrees, then the long term perturbation is much less.

Thanks to both James and Duncan for their answers! The idea is primarily to look merely at the scattered sunlight for many decades and calibrate against standard stars: sun-satellite-earth telescope.  The secondary process of Sun-Earth-spacecraft-earth telescope scattering is a higher order effect that nevertheless should be measurable with care using observations when the Sun is, for example, at pre-dawn and post-dusk, on a daily basis. Both processes inform us of the effects of solar radiation on climate using standard stars, removing some extreme difficulties in the usual low earth orbit measurements made since 1978 with radiometers, at a significant expense. One correction to my earlier response - this is a geostationary orbit not an antisun orbit (lagrange point).

Hi Philip, 

Speaking from a dynamicist's point of view, this is certainly possible. As already mentioned by James and Duncan, and, in particular, speaking about the results of the paper by Friesen, an inactive (initially) geostationary (equatorial, circular- synchronous) satellite (low A/m) will precess about a 'frozen' equilibrium point; the so-called Laplace plane in the planetary science's literature. This is a stable orbit (in fact, the natural regular satellites of the giant planets form in this plane), but it's only defined in terms of the gravitational torques acting on the orbit (lunar, solar, and oblateness perturbations). It's also, as discussed by Friesen et al., an idealization for Earth-orbiting applications, since the Moon's orbit itself is precessing about the pole of the Ecliptic plane. What this means is that a geostationary satellite will approximately precess about the pole of the Laplace plane with a period of about 53 years, and it's inclination will reach 15 degrees after 26.5 years before coming back down to equatorial. If such a satellite was placed initially in this plane, however, it would be fixed on average (the 'true' orbit, due to the regression of the lunar nodes, which is not taken into account in the analytical theories, will actually have a bounded inclination between 6 and 8.5 degrees, and an ascending node between +/- 10 degrees). 

This, as I mentioned previously, is only defined for satellites that are not appreciably perturbed by solar radiation pressure. In your case, however, you may want to consider the modified Laplace plane, which is the generalization that accounts for the SRP. This is described in the following papers:

http://www.sciencedirect.com/science/article/pii/S027311771400088X

http://iopscience.iop.org/0004-637X/786/1/45

Also, as described by Duncan, there is another mode acting in the system, which involves the perturbations caused by the ellipticity of the Earth. This effects the semi-major axis and stroboscopic mean node (primary variables of interest for ground track control). What this means is that your satellite will not remain fixed (w.r.t. the rotation of the Earth) over a single point on the equator throughout the day. The two main modes (motion in eccentricity/inclination and motion in semi-major axis) operate independently and on different timescales.

To conclude, 'stable' inclined geosynchronous orbits exist, but there are a few questions that need to be considered:

(1) Is the spacecraft required to be in the Earth's equatorial plane, or is an inclined geosynchronous orbit feasible for the proposed mission (The former is not possible without station-keeping? An inclined geosynchronous orbit will produce a distorted figure-8 ground track.) 

(2) Is the spacecraft required to be fixed over a particular point on the Earth? (Not possible, in general, without East-West station-keeping; but without control, it'll tend to move towards one of the stable longitudes as described by Duncan)

(3) Is the eccentricity required to be fixed? (Solar radiation pressure will cause the orbit eccentricity to undergo an approximately yearly oscillation with amplitude increasing with increasing A/m.) 

I hope this helps, and please let me know if you need any particular references on this, or have any specific questions.

Thanks 

My short response above is all that survived a much longer answer owing to something I did wrong

Our publication is now available on the arxiv:

http://arxiv.org/abs/1501.01253

Thanks to all for the useful discussion!