This paper proposes a new routing problem that can handle the synergy of exploring multiple sites for planetary surface exploration planning. The new problem aims to maximize the sum of profits (e.g., scientific information) obtainable by visiting a subset of candidate sites with given resource constraints (e.g., time and fuel) while considering the synergy (both positive and negative) from visiting two or more related sites. A mathematical formulation for this new problem referred to as the vehicle routing problem with profits considering synergy is developed. A special formulation for the problem considering the synergy only within a single route, referred to as the vehicle routing problem with profits considering single-route synergy, is also investigated. Column-generation-based procedures to find near-optimal solutions and corresponding optimality gaps for these problems are presented. The effectiveness of the proposed problem formulations and solution procedures are demonstrated through numerical experiments.