Clear[n, deltat, Bfield, acceleration]

Bfield[r_] = (1/(r^n))

acceleration[{x_, y_, vx_, vy_}] = {
        x + vx deltat - (1/2) vy Bfield[(Sqrt[(x^2) + (y^2)])] (deltat^2), 
        y + vy deltat + (1/2) vx Bfield[(Sqrt[(x^2) + (y^2)])] (deltat^2), 
        vx - vy Bfield[(Sqrt[(x^2) + (y^2)])] deltat, 
        vy + vx Bfield[(Sqrt[(x^2) + (y^2)])] deltat}

n = 1.25

deltat =  .005

vector0 = {0. , -1. , 1. , 0. }

vector = {vector0}

Do[vector = 
        Append[vector, 
          acceleration[
            vector[[Dimensions[vector]
                  [[1
                ]]]]]]; , {1300}]

xy = 
      Table[{vector[[n, 1]], 
          vector[[n, 2]]}, {n, 1, 
          Dimensions[vector][[1]]}];

plot1 = ListPlot[xy, PlotJoined -> True]

vector1 = {0. , - .9, 1. , 0. }

vector = {vector1}

Do[vector = 
        Append[vector, 
          acceleration[
            vector[[Dimensions[vector]
                  [[1
                ]]]]]]; , {1300}]

xy = 
      Table[{vector[[n, 1]], 
          vector[[n, 2]]}, {n, 1, 
          Dimensions[vector][[1]]}];

plot2 = ListPlot[xy, PlotJoined -> True]

Show[plot1, plot2]

vector2 = {0. , -1. ,  .9, 0. }

vector = {vector2}

Do[vector = 
        Append[vector, 
          acceleration[
            vector[[Dimensions[vector]
                  [[1
                ]]]]]]; , {1300}]

xy = 
      Table[{vector[[n, 1]], 
          vector[[n, 2]]}, {n, 1, 
          Dimensions[vector][[1]]}];

plot3 = ListPlot[xy, PlotJoined -> True]

Show[plot1, plot3]