The sheath structure around a rocket payload charged up to 460 V negative relative to the ambient ionospheric plasma is investigated experimentally and by computer simulations. Our experimental results come from the CHARGE 2 sounding rocket experiment in which the payload was split into two separate sections (mother and daughter) connected with a conducting, insulated tether. In one of the experimental modes, the voltage between the payloads was increased linearly from 0 to 460 V in 2.5 s. In this case the tethered mother/daughter functioned as a double probe, the negative probe (mother) reaching large negative potentials, while the positive probe (daughter) stayed close to the ambient plasma potential. A floating probe array was mounted on the mother with probes located 25, 50, 75, and 100 cm from the rocket surface. The internal impedance of the array was smaller than the probe/plasma impedance, which influenced the potential measurements. However, the measurements contain signatures, which we interpret as resulting from the outward expansion of the ion sheath with increasing negative mother potential. This conclusion is substantiated by NASCAP/LEO computer simulations of space charge limited flow. At high potentials, the observed ion current flowing to the mother increased more strongly with bias potential than found from the simulations. It is suggested that the enhancement of the current is generated by secondary electrons emitted by the ions bombarding the payload skin. The effects of the motion of the mother (540-580 m/s) and of the ambient magnetic field have been assessed by the code. It was estimated that the ion current to the mother was increased by 20% relative to a stationary payload, while the incorporation of a magnetic field had no practical influence on the simulation results.