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 MMA 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:

![Mathematica graphics](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}]