Compute remaining horizontal space in align environment

takes a couple of runs:

\documentclass{article}
\usepackage{showframe}
\usepackage[fleqn]{amsmath}

\newcommand*{\RubbishText}{This was obvious once it was determind that the earlier versions $E = mc$ and $E = mc^3$ were not quite accurate.}%

\makeatletter
\newcount\zzz
\def\foo{%
\global\advance\zzz\@ne
\ifmeasuring@
\else
\expandafter\ifx\csname zz\romannumeral\zzz\endcsname\relax
\else
\edef\RemainingSpace{\the\dimexpr 30000000sp - 
         \csname zz\romannumeral\zzz\endcsname sp\relax}%
\typeout{\the\zzz: \RemainingSpace}%
\fi
\pdfsavepos
\edef\tmp{\write\@auxout{%
  \gdef\noexpand\noexpand\expandafter\noexpand
    \csname zz\romannumeral\zzz\endcsname{\noexpand\the\pdflastxpos}}}
\tmp
\fi
}
\makeatother

\newcommand*{\RemainingSpace}{9.0cm}%

\begin{document}\noindent


First using \verb|align*| with a \verb|\quad| for spacing:
\begin{align*}
    E &= mc^2 \quad\foo\parbox[t]{\RemainingSpace}{\RubbishText}\\
    F &= ma + \sin^2 x + cos^2 x - 1.
\end{align*}
Or could use \verb|&&| for spacing (but less important than the above version):
\begin{align*}
    E &= mc^2 &&\foo\parbox[t]{\RemainingSpace}{\RubbishText}\\
    F &= ma + \sin^2 x + cos^2 x - 1
\end{align*}
Or, using \verb|alignat*|
\begin{alignat*}{2}
    E &= mc^2 \quad\foo\parbox[t]{\RemainingSpace}{\RubbishText}\\
    F &= ma + \sin^2 x + cos^2 x - 1
\end{alignat*}
\end{document}

The package linegoal and its \linegoal macro produce —after two compilations—the correct output. But they throws errors and warnings, probably due to how amsmath’s environments process their contents.

egreg saved me from going through answers and code and provided the \ifmeasuring@ conditional from amsmath.

I have defined a \Note macro that hides the text from the measuring. Sadly, this does not work for the && version of align* as amsmath needs to know the width to align the columns correctly.

I have therefore provided a starred version of \Note that does the same as before, still producing warnings and errors.

Note that I have included the \quad in the un-starred version of \Note.

Code

\documentclass{article}
\usepackage{showframe}
\usepackage{linegoal}
\usepackage[fleqn]{amsmath}

\newcommand*{\RubbishText}{This was obvious once it was determind that the earlier versions $E = mc$ and $E = mc^3$ were not quite accurate.}%

\makeatletter
\newcommand*{\Note}{\@ifstar\s@Note\@Note}
  \newcommand*{\@Note}[1]{\ifmeasuring@\else\quad\parbox[t]{\linegoal}{#1}\fi}
  \newcommand*{\s@Note}[1]{\parbox[t]{\linegoal}{#1}}
\makeatother

\begin{document}\noindent
First using \verb|align*| with a \verb|\quad| for spacing:
\begin{align*}
    E &= mc^2 \Note{\RubbishText} \\
    F &= ma + \sin^2 x + cos^2 x - 1.
\end{align*}
Or could use \verb|&&| for spacing (but less important than the above version):
\begin{align*}
    E &= mc^2 & \Note*{\RubbishText}\\
    F &= ma + \sin^2 x + cos^2 x - 1
\end{align*}
Or, using \verb|alignat*|
\begin{alignat*}{2}
    E &= mc^2 \Note{\RubbishText}  \\
    F &= ma + \sin^2 x + cos^2 x - 1
\end{alignat*}
\end{document}

Output