In this paper we propose a mathematical model for the fuel consumption analysis during aircraft cruise. A closed-form formula that expresses the aircraft's weight variation over time, and hence, the fuel flow rate, is obtained as a result. Furthermore, a closed-form expression of the aircraft's main performance parameters is also obtained. We compare the values of such parameters computed by using the Piano-X software and computed by using our mathematical model. Simulation results confirm that our mathematical model provides results very close to reality. Finally, the closed-form formula of the fuel flow rate provided by our model is used to improve the calculation of the carbon dioxide emissions for four example routes, which, unlike here, are usually obtained under the assumption of a constant value of the fuel flow rate.