I study six novel observational tests of general relativity. First, I show
that a gravitational wave pulse from a major merger of massive black holes at
the Galactic center induces a permanent increase in the Earth-Moon separation.
For black holes of a few million solar masses, the shift in the local
gravitational potential is comparable to the Earth-Moon potential, leading to
the Moon being perturbed relative to the Earth during the passage of the pulse.
The permanent increase in the Earth-Moon separation is a fraction of a
millimeter, measurable by lunar ranging for future merger events. Second, I
show that General Relativity sets an absolute upper limit on the energy flux
observed from a cosmological source as a function of its redshift. Third, I
consider the implications of modified inertia at low accelerations for rockets.
An attractive interpretation of MOdified Newtonian Dynamics (MOND) as an
alternative to dark matter, changes the inertia of matter at accelerations
a<a_0=1.2×10^{-8} cm/s^2. I show that if inertia is modified rockets operating
at a<<a_0 might allow intergalactic travel with a modest fuel-to-payload mass
ratio. Fourth, I show that in MOND the amplitude of the observed dipole of the
Cosmic Microwave Background (CMB) can originate from the primordial fluctuation
amplitude on the scale of the cosmic horizon. Fifth, I show that the tidal
gravitational potential of the Milky-Way galaxy removes fuzzy dark matter from
its satellite dwarf galaxies through quantum-mechanical tunneling. Sixth, I
show that a charged particle can be accelerated to arbitrarily high energies by
maintaining a permanent resonance with the phase of a planar gravitational wave
propagating along a uniform magnetic field. The Doppler-shifted cyclotron
autoresonance could potentially result in electromagnetic afterglows near
gravitational-wave sources.
