  We study the light-cone Siegel transform, transforming functions on the light
cone of a rational indefinite quadratic form $Q$ to a function on the
homogenous space $\text{SO}^+_Q(\mathbb{Z})\backslash
\text{SO}^+_Q(\mathbb{R})$. In particular, we prove a second moment formula for
this transform for forms of signature $(n+1,1)$, and show how it can be used
for various applications for counting integer points on the light cone. In
particular, we prove some new results on intrinsic Diophantine approximations
on ellipsoids as well as on the distribution of values of random linear and
quadratic forms on the light cone.
