Low Earth Orbit (LEO) Earth Observation (EO) satellites have changed the way we monitor Earth. Acting like moving cameras, EO satellites are formed in constellations with different missions and priorities, and capture vast data that needs to be transmitted to the ground for processing. However, EO satellites have very limited downlink communication capability, limited by transmission bandwidth, number and location of ground stations, and small transmission windows due to high velocity satellite movement. To optimize resource utilization, EO constellations are expected to share communication spectrum and ground stations for maximum communication efficiency. In this paper, we investigate a new attack surface exposed by resource competition in EO constellations, targeting the delay or drop of Earth monitoring data using legitimate EO services. Specifically, an attacker can inject high-priority requests to temporarily preempt low-priority data transmission windows. Furthermore, we show that by utilizing predictable satellite dynamics, an attacker can intelligently target critical data from low-priority satellites, either delaying its delivery or irreversibly dropping the data. We formulate two attacks, the data delay attack and the data overflow attack, design algorithms to assist attackers in devising attack strategies, and analyze their feasibility or optimality in typical scenarios. We then conduct trace-driven simulations using real-world satellite images and orbit data to evaluate the success probability of launching these attacks under realistic satellite communication settings. We also discuss possible defenses against these attacks.