Optimum Location to Intercept Interstellar Objects with Build-and-wait Missions

Until now, only two Interstellar Objects (ISOs) have been discovered: 1I/'Oumuamua and 2I/Borisov. Despite a limited amount of observations, they present high scientific interest for the research community. In order to further analyze these objects, in-situ data is required. However, beginning the mission design and spacecraft manufacture after ISO detection would significantly lower mission success probability. Consequently,"build-and-wait" is an appealing mission concept. To prepare the upcoming missions to ISOs it is required to have a deeper knowledge on the probability analysis to locate these objects within the Solar System. Therefore, the optimum location to intercept these objects has been studied by performing a computational analysis using the Runge-Kutta RKF4(5) numerical method. This method has been used to determine the likelihood of ISOs trajectories intercepting the ecliptic. The results show a peak at a distance of ~1 AU from the Sun. Therefore, the vicinity of the Earth's orbit is the best position to send or place a spacecraft for ISO interception. In addition, these results add validity to the theory of panspermia via ISO impact. The author has estimated an annual probability of ISO-Earth impact of 10$^{-7}$.