Systematic errors in high precision gravity measurements by light-pulse atom interferometry on ground and in space.

We focus on the fact that light-pulse atom interferometers measure the atoms' acceleration with only 3 data points per drop. As a result the measured effect of gravity gradient is systematically larger than the real one, an error almost unnoticed so far. We show how it affects the absolute measurement of the gravitational acceleration $g$ as well as ground and space experiments based on gradiometers such as those designed for space geodesy, the measurement of the universal constant of gravity and the detection of gravitational waves. Tests of the weak equivalence principle need two different atom species. If both species can be operated with the same laser the error reported here cancels out. If not, the fractional differences in pulse timing and momentum transfer set the precision of the test at unacceptable levels and severely limit the atoms' choice, whereby most tests use isotopes of the same $\rm Rb$ atom which differ by two neutrons only.