The Launch Opportunity

Given the mentioned constraints, the planets must be properly aligned so that when the spacecraft leaves terrestrial orbit with the right impulse given by the rocket burn to enter an orbit such that its perihelion coincides with the radius of the Earth orbit (what we will call dEarth) and that aphelion will constitute the radius of the Martian orbit (what we will call dMars) Mars will be in the correct position so that when the spacecraft arrives in its orbit Mars is there.

In order to calculate the relative angle between the planets, that is, the difference aEarth-aMars in the figure, we first need to calculate the difference in velocity required to transfer from one orbit to another and based on that change in velocity then estimate the time necessary for the transfer. Once the time is known we can calculate the position of the planes so that Mars "passes" through the same point as the spacecraft.