Superscript hours, minutes, seconds over decimal for angles

Define your own \dotdeg and \dotem, possibly in the following way:

\documentclass{article}

\newcommand{\dotdeg}{\rlap{.}^\circ}
\newcommand{\dotem}{\rlap{.}^m}

\begin{document}

\begin{enumerate}
  \item
  $\theta = 8 \dotdeg 855 + 0 \dotdeg 98561 t + 1 \dotdeg 916 \sin (0 \dotdeg 9856 t - 3 \dotdeg 819)
    + 0 \dotdeg 020 \sin( 1 \dotdeg 9712 t - 7 \dotdeg 638 )$

  \item
  $T = 35 \dotem 421 + 3 \dotem 94244 t - 4 \dotem 0 \arctan [ ( \tan \theta ) / 0.91747 ]$
\end{enumerate}

\end{document}

---

A bit cleaner interface that takes a decimal number as argument for \dotdeg and \dotem (requires a period . within the decimal):

\documentclass{article}

\def\addtodot#1.#2\relax{#1\rlap{.}^{\dotadd}#2}
\newcommand{\dotdeg}[1]{\def\dotadd{\circ}\addtodot#1\relax}
\newcommand{\dotem}[1]{\def\dotadd{m}\addtodot#1\relax}

\begin{document}

\begin{enumerate}
  \item
  $\theta = \dotdeg{8.855} + \dotdeg{0.98561}t + \dotdeg{1.916} \sin ( \dotdeg{0.9856} t - \dotdeg{3.819} )
    + \dotdeg{0.020} \sin( \dotdeg{1.9712} t - \dotdeg{7.638} )$

  \item
  $T = \dotem{35.421} + \dotem{3.94244} t - \dotem{4.0} \arctan [ ( \tan \theta ) / 0.91747 ]$
\end{enumerate}

\end{document}

A stackengine approach. I create \angdot that takes an optional argument (default \circ) to set above the dot. The alignment is to the left.

\documentclass{article}
\usepackage{stackengine}
\newcommand\angdot[1][\circ]{%
  \stackengine{0pt}{.}{${}^{\mathrm{#1}}$}{O}{l}{F}{F}{L}}
\begin{document}
$\theta = 8\angdot855 + 3\angdot[m]94244 t$
\end{document}