  Explicitly covariant analytical expressions are derived that describe the
boundaries of shadows cast by massive particles scattered by a gravitating
object. This covers scenarios with particles having effectively variable mass,
such as photons in plasma, geodesics in higher dimensions, and particles
interacting with a scalar field. The derived formula takes advantage of recent
advances in understanding the relationship between slice-reducible Killing
tensors and massive particle surfaces that generalize photon surfaces. The
formula allows us to obtain simple approximations of scaling as the particle
energy changes. We illustrate this structure using Kerr-NUT and EMD black holes
for both massive particles and photons in plasma. The versatility of this
framework extends beyond astrophysics and has potential applications in analog
models of gravity and condensed matter physics.
