  We obtain a strong bound on the second moment of the $GL_3$ standard
$L$-function on the critical line. The method builds on the recent work of
Aggarwal, Leung, and Munshi which treated shorter intervals. We deduce some
corollaries including an improvement on the error term in the Rankin-Selberg
problem, and on certain subconvexity bounds for $GL_3 \times GL_2$ and $GL_3$
$L$-functions. As a byproduct of the method of proof, we also obtain an
estimate for an average of shifted convolution sums of $GL_3$ Fourier
coefficients.
