Light pressure effects on sun-synchronous orbits
Roger Arnold
k.a.c...@sympatico.ca
Roger;
You wrote:
Quick question for anyone on the list with chops on sun-synchronous orbits and perturbations from light pressure: would a very high area to mass ratio for a satellite in sun-synchronous orbit seriously disrupt the orbital precession that keeps it sun-synchronous?
Intuitively, I wouldn't expect it to. Light pressure would push the orbital plane of the satellite slightly anti-sunward with respect to Earth's center of gravity, but the asymmetry of the gravitational field that causes the near-polar orbit to precess by 360 degrees per year should still cause the slightly displaced orbit to precess at the same rate. I think.
Beyond the need for occasional boosts to counter residual atmospheric drag in any low earth orbit, I'd expect the orbit to be stable.
The quick answer is: it depends on the manner in which the sunlight falling on that satellite is reflected. More specifically, it depends on the direction in which the satellite reflects the sunlight, which depends on the satellite’s shape, the reflectivity of its various surfaces, and its orientation as a function of time (and hence with respect to its location along its orbital path).
That’s a pretty general statement; I’ll get more specific below. To answer this question completely, you have to consider the principles of solar sailing (something I’ve spent much time on over the years).
One special case is where the satellite is designed, and kept oriented, such that the sunlight impinging on the satellite is reflected back directly towards the Sun. In that case, the situation you described above will result --- a small shift anti-Sunwards of the orbit plane, and no other significant effects. (There would be a *tiny* change in the precession rate, too small to be discernible, due to the centre-point of the orbit no longer coinciding with the Earth’s mas centre, which would alter slightly the coefficients of the spherical harmonic expansion of the Earth’s gravity failed about the orbit’s centre-point.)
This case could be achieved regardless of the satellite’s orientation, if the satellite were spherical, and had a uniform surface optical coating. This is in fact the assumption that is made in some quite-serious orbit propagation models (I discovered this assumption lurking in the solar radiation pressure module of the Goddard Trajectory Determination System (GTDS) orbit propagator, which NASA and others have used as the basis for orbit-identification operations for countless satellite). This is the simplest model of solar radiation pressure induced perturbations of a satellite’s orbit, and is also usually quite wrong (reminding one of the joke whose punchline is “first, assume a spherical cow…” 😊). Although there have been *some* satellites for which this is not a bad approximation --- the early Echo satellites (big spherical balloons made of reflective mylar) came about as close to this as you can possibly get.
More generally, we solar sailing afficianados model the actual geometry of a satellite’s external surfaces, and the optical properties (reflectivity, absorptivity, emissivity) of each surface, and orientation of each surface, and then calculate the force induced by sunlight on each of those surface (some photons being absorbed, some being reflected specularly, some being reflected diffusely), and then adding up all those forces to get a net force. Which will generally change with the satellite’s orientation with respect to the Sun, and hence with time, unless the satellite is controlled to keep that orientation constant.
In designing a proper solar sail, we do the opposite of “assuming a spherical cow,” as it were --- generally we design the spacecraft to be mostly a big, planar reflector, whose reflectivity is as specular and as large as possible, in order to provide the ability to generate the largest possible force from the incoming solar radiation, plus the ability to direct that force away from the anti-Sun direction as desired (by altering the sail’s orientation).
Real spacecraft are generally somewhere between those two extremes. The answer to your question thus depends on the specifics of your particular spacecraft.
In the late 1990s I came across on very specific case, involving the Canadians Space Agency’s satellite Radarsat. This was launched into an ~ 850 km altitude dawn/dusk (ascending/descending nodes at 6 AM and 6 PM local time) sun-synchronous orbit, and was controlled by its operators to stay in that orbit very accurately (part of the mission was to have a repeating ground track with quite high accuracy, to enable its synthetic aperture radar data to be used to do interferometric measurements from repeat fly-overs, which needed very high accuracy in the ground track repeatability). One of Radarsat’s operators at CSA, whose job was to track its orbit in order to decide when to do the next orbit-maintenance manoeuvre, noticed a variation between the actual orbit behaviour and that predicted by their simulator (GTDS). After much head-scratching, he inferred that the extra perturbation must be due to solar radiation pressure, with a force component along the satellite’s orbit velocity vector; this was actually opposing the atmospheric-drag perturbation (also in the orbit-velocity-vector direction) to a significant extent --- Radarsat was actually solar sailing, with the solar sailing force reducing the amount of drag-makeup propellant that had to be expended.
(His colleagues at CSA didn’t give him any credence, and so he reached out to me, as I was the main solar-sailing proponent in Canada at the time. He sent me a copy of his analysis, and it made total sense to me. If you want to see that, let me know off-list, and I’ll send it to you.) The reason this was able to happen is because Radarsat has a huge, flat radar array, which is covered with a highly reflective coating, and which is oriented to point *nearly* towards the Sun, but yawed a bit, in such a way as to create an along-track force as a result of solar radiation pressure. The satellite designers (several of whom are friends of mine) totally did not think of this when designing it; the attitude of the satellite is driven entirely by radar-related considerations. So it’s an accidental solar sail!
So, Radarsat is a worked example of the question you asked --- a real-world satellite in a sun-synch orbit that so happens to have its orbit significantly altered by solar radiation pressure (in such a way that its semi-major axis gets larger with time).
But I don't fully understand how the torque responsible for the precession arises in the first place. So I can't say with any certainty how an anti-sunward shift in the orbital plane might affect the precession.
I find a useful way to think about the situation is from the orbit angular momentum perspective. A satellite orbiting the Earth has an angular momentum with respect to the Earth’s centre of mass; barring perturbations, that angular momentum is constant. Consider a satellite orbiting in a circular orbit, at some altitude, and some inclination with respect to the equator. The Earth’s mass distribution is not perfectly spherical; for the purposes of sun synchronous orbits, the main deviation from sphericity is that the Earth has an equatorial bulge --- like an extra doughnut-ring of mass around the equator (in spherical-harmonic-math terms, this creates a non-zero J2 harmonic term in the Earth’s spherical-harmonic gravity field expansion). The spherical part of the Earth does not cause any precession of the orbit’s node line (i.e., the line between the orbit’s two equator-crossing points), but the equatorial-bulge part (i.e., the J2 term) does. When the satellite is near the northern and southern extremes of its orbit, the equatorial-bulge doughnut of mass exerts an equator-wards pull on the satellite, which creates a torque on the satellite’s orbit angular momentum vector, that torque vector being aligned with the satellite’s node-line. (I find it easier to visualize this if I think of the satellite as if its mass were smeared out along its entire orbital path, forming a spinning wheel --- in which case the gravitational effect of the equatorial bulge is to pull the northern part of the rim of the wheel southwards, and the southward part northwards.) Finally, as is always the case when you apply a torque to a spinning wheel, the wheel’s spin axis precesses in a direction that is sort-of at right angles to the applied torque (to be accurate, in the direction of the vector that is the cross-product between the wheel’s spin axis vector and the torque vector).
(This is all explained with more rigor in https://en.wikipedia.org/wiki/Sun-synchronous_orbit, as well an many textbooks on orbit dynamics.)
Hope that helps a bit!
- Kieran