First, there IS such a thing as a "precessing polar orbit". To explain it, let's start with an imaginary non-rotating world somewhere in Space.
We immediately have a problem in that if it is not rotating, it doesn't have a North Pole or a South Pole, since those are defined by the axis of rotation.
So let's thus pretend the imaginary world is rotating extremely slowly, say once every thousand years. We can treat it as nonrotating if we examine it for a short period of time, say one day. But we can also talk about its poles, and thus a polar orbit.
In a simple polar orbit, the orbiting object passes over both poles at regular intervals, let's say once every three hours. If the world is not rotating, the orbiting object will also pass directly over the same places all around the world, every time. You could draw a north-south circle on the world, around the world, and orbiting object would always be directly above some point on that circle. We can call that circle "the ground route".
In precessing polar orbit, the orbiting object DOESN'T follow the same ground route every time. Instead the initial ground route might be followed by a new ground route that is displaced east or west by one degree. It would take 360 orbits, precessing all the way around the world, before the orbiting object retraced the first ground route.
The rate of precession does not have to be one degree of displacement east-or-west per orbit. It could be two degrees or five or ten...
Now let's pick a particular polar orbit around the Earth. I'll call it "the noon/midnight orbit" here. I don't care WHERE on Earth it might be noon or midnight, because the Earth is rotating lots faster than that imaginary world discussed above. I only care about the disc of the Earth as it faces the Sun, and the fact that if an object is in a polar orbit traversing the middle of the disk, it will either be noon or midnight directly below the orbiting object.
Now we add precession, just enough to keep the object in the noon/midnight orbit as the Earth goes around the Sun. That means it would take about 365 1/4 days to do a full precession, pretty slow.
Now let's pick an altitude for our orbiting object, say 500 miles (800 Km). This is high enough to be out of the way of most things that are in Low Earth Orbit.
Now to describe the orbiting object. This is a simple ribbon of some reasonably common mirror-like metal like aluminum, that we can obtain from the Moon. We want a LONG LONG ribbon; we want it to go all the way around the Earth, in that orbit. We might consider a lattice-like construction that is covered with aluminum foil. It will have too much mass to be blown about by the Solar Wind, and if some part of it gets damaged by a meteoroid, it can be repaired easily.
Remember, the mirror-ribbon is an ORBITING object. There's nothing fancy except for its size. It's high enough above the atmosphere that it should stay in orbit for a long long time.
So, we have length (all the way around the world), thickness (lattice structure, probably no more than a few centimeters or inches), and the only remaining thing to talk about is its width.
They say that the Earth's average temperature is expected to rise by some percentage, due to Global Warming. Let's pretend 2%, just to show the flexibility of this Idea.
First, compute the area of the disc of the Earth, as seen from the Sun. I'll use a radius of 4000 miles, so we square that and multiply by pi to get a bit more than 50 million square miles (about 128 million sq km).
Next, since here we are using a diameter for the Earth of 8000 (double the radius) miles (12,800 Km), suppose we viewed it from the Sun and equated it a rectangle having an 8000-mile "height". How wide would it be? Just divide 8000 into 50 million to get 6250 miles (10000 Km).
With all that preparatory computation done, we can now ask, "What is 2% of 6250 miles?" The answer is 125 miles (200 Km). THAT'S how wide our orbiting mirror-ribbon should be! That is, if we reflect 2% of sunlight impinging upon the Earth with a mirror, then the Earth's temperature should go down by 2%. We simply make the orbiting mirror-ribbon as wide or as narrow as we need, to effectively and permanently balance Global Warming.
ON the Earth, as noon approaches as the world rotates, a short eclipse of the Sun may occur. Every day for a few minutes at most. This will not be enough to interfere with the normal growth of plants and other things that require sunlight.