<p>We compute the rational homotopy groups in degrees up to approximately <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mfrac> <mrow> <mn>3</mn> </mrow> <mn>2</mn> </mfrac> <mi>d</mi> </math></EquationSource> <EquationSource Format="TEX">$\tfrac{3}{2}d$</EquationSource> </InlineEquation> of the group of diffeomorphisms of a closed <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>d</mi> </math></EquationSource> <EquationSource Format="TEX">$d$</EquationSource> </InlineEquation>-dimensional disc fixing the boundary. Based on this we determine the optimal rational concordance stable range for high-dimensional discs, describe the rational homotopy type of <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>B</mi> <mi mathvariant="normal">Top</mi> <mo stretchy="false">(</mo> <mi>d</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$B\mathrm {Top}(d)$</EquationSource> </InlineEquation> in a range, and calculate the second rational derivative of the functor <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <mi>B</mi> <mi mathvariant="normal">Top</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$B\mathrm {Top}(-)$</EquationSource> </InlineEquation> in the sense of Weiss’ orthogonal calculus.</p>