Due to the failure of the second reaction wheel, a new mission was conceived for the otherwise healthy Kepler space telescope. In the course of the K2 Mission, the telescope is staring at the plane of the Ecliptic, hence thousands of Solar System bodies cross the K2 fields, usually causing extra noise in the highly accurate photometric data. In this paper we follow the someone's noise is another one's signal principle and investigate the possibility of deriving continuous asteroid light curves, that has been unprecedented to date. In general, we are interested in the photometric precision that the K2 Mission can deliver on moving Solar System bodies. In particular, we investigate space photometric optical light curves of main-belt asteroids. We study the K2 superstamps covering the M35 and Neptune/Nereid fields observed in the long cadence (29.4-min sampling) mode. Asteroid light curves are generated by applying elongated apertures. We use the Lomb-Scargle method to find periodicities due to rotation. We derived K2 light curves of 924 main-belt asteroids in the M35 field, and 96 in the path of Neptune and Nereid. The light curves are quasi-continuous and several days long. K2 observations are sensitive to longer rotational periods than usual ground-based surveys. Rotational periods are derived for 26 main-belt asteroids for the first time. The asteroid sample is dominated by faint (>20 mag) objects. Due to the faintness of the asteroids and the high density of stars in the M35 field, only 4.0% of the asteroids with at least 12 data points show clear periodicities or trend signalling a long rotational period, as opposed to 15.9% in the less crowded Neptune field. We found that the duty cycle of the observations had to reach ~60% in order to successfully recover rotational periods.
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