Plastic polish and elbow grease does it every time. I used some plastic polish (very light abrasive is what makes it work) on the plastic covering the steering wheel MB star emblem in the middle of the steering wheel... it was both lightly scuffed and had accumulated dirt and grit from the prior owner having ground the dirt and grit into the plastic by improperly cleaning it once in a great while. It polished back to the original clear as a bell plastic. But I'll warn you.... use a soft, soft cloth, and rub and rub and rub.... since you're actually removing both the dirt accumulated, AND then you get to the oxidized / UV damaged plastic before you get back to the original plastic material. If you use a larger grit 1st to speed the process, you're going to scratch into the original plastic (under the oxidized/UV damaged material) and then you'll spend even more time with the fine grit polish getting rid of the fine scatches you created with the larger grit.
Another option is to use 1200 or higher grit wet or dry polishing paper (but use it wet) - 3M polishing products but with a piece of hardish rubber as the backing ... like a school kid's pink eraser (so your finger pressure doesn't start making hills and valley's on the surface you're using it on). Then finish with the plastic polish....but go lightly with the 1200 or higher grit wet/dry polishing paper, and use a lot of water (or even use WD 40 or equivalent oil... since what you want to do is create a film lubricant between the protruding grit on the paper and the surface you're polishing... that limits the depth of protrusion of the grit material into the soft plastic.... so you can't scratch the surface readily). Also flush frequently and copiously with clean water so that the loose grit and whatever dirt that comes loose after being embedded in the plastic doesn't start scratching the surface. One of the major constituants of the dirt, by the way, on your plastic is made of a lot of Silicon Oxide particles.... up to several microns in size. Silicon oxide is also used as a polishing compound for rough polishing... a lot of material removal.
Just for your reference... polishing is actually nothing more than making lots of little tiny scratches in the object being polished... the size of the polishing grit determines the depth and widths of these little tiny scratches. The surface appears polished to a sheen and perfect mirror finish to the naked eye or even under low magnification when the depth and width of the scratches is on the order of 1/2 micron or less. Normal paint polishing compounds for "buffing" automobiles is on the order of 2 - 5 microns, but the buffing pad doesn't let the full size of the particles scratch into the paint (or clear-coat), so the depth and width of the scratches are less than 2 microns --- depending on the buffing compound supplier's quality ---- the more you pay the more uniform the size distribution of the polishing particles in a narrower range.
The other action in a buffing compound is the 'wax'... which fills the scratches partially... taking some of the "valley" out of them... making them appear 'smoother'. I say 'wax', but the material used to partially fill the scratch valley's can be any reasonably clear polymer that hardens somewhat on exposure to air --- usually after the carrier (Solvent) evaporates.
The same thing applies to plastic polishes... but what you're after in that case is the smallest scratches you can make with the polishing grit material.... so the smaller the grit, the better the sheen and original surface characteristics... without the polymer or wax that partially fills the valley's.
If this dissertation doesn't help, just remember that almost no surface is actually 'smooth'.... 'smooth as glass' is actually a pretty rough surface finish viewed by scanning electron microscopic methods.... you'ed be surprised how non-discerning the human eye is.... which is precisely why we 'see' a polished surface as being smooth and reflective when in fact it's actually pretty rough. It's called "resolving power".
Longtooth
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