In astronomy, right ascension is usually plotted with positive values that increase from right to left. I have seen discussions of successful and unsuccessful attempts to reverse the order of an axis in *Mathematica*, but I haven't seen anything that applies specifically to the `ParametricPlot[]` function, and perhaps I am not good enough at *Mathematica* to see how the other solutions using `ScalingFunctions` or `Transpose` might be applied here. I tried a few to no avail. 

Plot 2 uses the default frame ticks, showing reversal of plotting order by reversing the signs of the $x$-coordinates of the plot objects. In the `Ticks` option, their specs seem to be ordered `{{left, right}, {bottom, top}}` with respect to the frame sides. I believe that replacing one of these terms, say left, with something like `{-1, 1}` would replace `-1` with `1` on the left side. But when I attempted to change the names of the ticks on the $x$-axis in plot 2 to positive numbers, the ticks and their names both disappeared, as in plot 3. I could replace the missing ticks with a cumbersome `Epilog` list, but I would prefer something more elegant. It strikes me as odd that the mathematicians who created *Mathematica* would arbitrarily limit their orientation, so there must be a native way of reversing order, no? The following three scripts produce these three plots in a row:

![attempts to plot with reversed axes](https://i.sstatic.net/wl0M9.png)

    Clear["Global`*"]
    
    spiral[a_, t_, x_, y_] := {a*t*Cos[t] + x, a*t*Sin[t] + y} // N;
    
    fs = 8; (* font size *)
    objects = 5;
    fl = {X, Rotate[Y, -Pi/2]}; (* frame label *)

    unreversed = 
     ParametricPlot[
      spiral[.002*#^(5/3), t, #, #] & /@ Range[objects], {t, 0, 10*Pi},
       PlotRange -> {{0, objects + 1}, {0, objects + 1}}, 
       PlotLabel -> Style["1. x axis not reversed", FontSize -> fs], 
       Frame -> True, FrameLabel -> fl, GridLines -> Automatic];
    
    reversed1 = 
      ParametricPlot[
       spiral[.002*#^(5/3), t, -#, #] & /@ Range[objects], {t, 0, 
        10*Pi}, PlotRange -> {{-objects - 1, 0}, {0, objects + 1}}, 
       PlotLabel -> Style["2. x axis reversed", FontSize -> fs], 
       Frame -> True, FrameLabel -> fl, GridLines -> Automatic];
    
    ticks = {{Automatic, None}, {{-#, #}, None}} & /@ 
       Reverse[Range[objects]];
    
    reversed2 = 
      ParametricPlot[
       spiral[.002*#^(5/3), t, -#, #] & /@ Range[objects], {t, 0, 
        10*Pi}, PlotRange -> {{-objects - 1, 0}, {0, objects + 1}}, 
       PlotLabel -> 
        Style["3. x axis reversed\nticks lost", FontSize -> fs], 
       Frame -> True, FrameLabel -> fl, GridLines -> Automatic, 
       FrameTicks -> ticks (* causes ticks to disappear *)];
    
    GraphicsRow[{unreversed, reversed1, reversed2}]