  We report on the design and the construction of a sounding rocket payload
capable of performing atom interferometry with Bose-Einstein condensates of
$^{41}$K and $^{87}$Rb. The apparatus is designed to be launched in two
consecutive missions with a VSB-30 sounding rocket and is qualified to
withstand the expected vibrational loads of 1.8 g root-mean-square in a
frequency range between 20 - 2000 Hz and the expected static loads during
ascent and re-entry of 25 g. We present a modular design of the scientific
payload comprising a physics package, a laser system, an electronics system and
a battery module. A dedicated on-board software provides a largely automated
process of predefined experiments. To operate the payload safely in laboratory
and flight mode, a thermal control system and ground support equipment has been
implemented and will be presented. The payload presented here represents a
cornerstone for future applications of matter wave interferometry with
ultracold atoms on satellites.
