(* Next Solar Maxima - 26th one *)
data={{1,1761.5},{2,1769.75},{3,1778.41},{4,1788.16},{5,1805.16},{6,1816.41},{7,1829.92},{8,1837.25},{9,1848.16},{10,1860.16},{11,1870.67},{12,1884.0},{13,1894.08},{14,1906.16},{15,1917.66},{16,1928.41},{17,1937.41},{18,1947.41},{19,1957.0},{20,1968.91},{21,1980},{22,1989.11},{23,2000.5},{24,2014.33},{25,2024.83}};
Table[{i, data[[i+1,2]]-data[[i,2]]},{i,1,Length[data]-1}];
g1=ListPlot[data,PlotStyle-> {Blue, Pointsize[0.02]}];
mm=10 ;(* no of polynomials *)
mod=Table[Table[t^n,{n,0,m}],{m,1,mm}];
ff=Table[Fit[data,mod[[i]],t],{i,1,Length[mod]}];
ss=Table[ff[[i]]/.t->{26,27,28},{i,1,mm}];
Do[Print["Next Three Maximas (26th, 27th & 28th) are from ",i," order polynomial ",ss[[i]]],{i,1,mm}];
g2=Table[Plot[ff[[i]],{t,First[data][[1]],Last[data][[1]]},PlotStyle-> Hue[1/i]],{i,1,Length[mod]}];
Show[{g1,g2}]