ROCKETS I: Investigating the Impact of the Rocket Effect on Two Nearby Young Open Clusters Encased in Infrared Bubbles

We introduce ROCKETS (Rocket-driven Cluster Kinematics & Triggered Star-formation), a Gaia based programme investigating kinematic fingerprints of stellar feedback or rocket effect in young star forming regions. We analyse two young clusters with O-type stars enclosed by mid-infrared bubbles, Collinder 69 and IC 1396 as a methodological demonstration on two nearby benchmark regions. Co-moving candidates are selected within an astrometric ellipse defined by the median and median absolute deviation of Class I/II YSOs with Gaia data. For each star, we compute a relative proper-motion angle (RPMA) relative to the ionising source. In both regions the RPMA distribution shows a strong excess at RPMA $<15^{\circ}$, corresponding to sources moving away from the respective ionising sources. We quantify this using the Rocket Effect Index (REI), finding $\mathrm{REI}\simeq 1.1$ for Collinder 69 and $\mathrm{REI}\simeq 1.7$ for IC 1396. When considering only Class I/II YSOs, the REI of both regions increases to $\mathrm{REI}\gtrsim 10$. Velocity-structure analysis of the sample shows that the RPMA $<15^\circ$ subset has stronger positive pairwise expansion than the full co-moving population, providing additional support for the rocket effect. The outward-moving stars are not uniformly distributed; instead, their position angles are strongly anisotropic and preferentially aligned towards the bright-rimmed clouds. Gaia colour-magnitude diagrams show no strong age offset between sources moving outward and literature cluster members. The observed kinematic signatures support feedback-driven acceleration of gas and triggered star formation preferentially towards higher density regions of expanding bubbles due to the rocket effect.